Attila's math desk, now open for business!

[AttilaTheGeek]

Not sure what's the best choice? I can help you out.

I'm a math nerd who's done statistics and calculus (though I imagine one will be more helpful than the other), and looking for some interesting D&D math problems. Here, people can come to me with a choice of abilities, and I will math out which is better. I've answered questions like "Is Keen better than Flaming" (not without crit feats) and "Which 2nd-level Evocation in Pathfinder does the most damage" (Flaming Sphere), but not "Is Silent Image better than Charm Person", because that's impossible.

I have just a couple caveats. First, I need to be able to find the spells/feats/abilities you're talking about, so please include SRD links or books and page numbers. Second, I play Pathfinder instead of 3.5, so unless you specify otherwise I'll assume you're talking about Pathfinder. Third, I don't want to trawl all over the web, so I will do things like "Which of these things in this finite list is the best", but not "what feat is the best", because with my luck I'm going to miss that one amazing feat that didn't get playtested. Can't wait to see what the playground comes up with!

[limejuicepowder]

Well this isn't exactly the kind of question you said you're open to answer, but I've always wanted to know how to calculate the likelihood of winning opposed rolls; i.e., what's the actually chance of success to trip someone with your +11 trip attack, and your opponent has 20 str.

[Story]

That's a fairly easy calculation, though it depends on how ties are broken.

Here's the table assuming attacker wins ties. So for example, if you have +11 and your opponent has +5, you have a 77.25% chance of winning assuming you win ties, and a 73.75% chance if you lose ties.

-19 : 0.25%
-18 : 0.75%
-17 : 1.50%
-16 : 2.50%
-15 : 3.75%
-14 : 5.25%
-13 : 7.00%
-12 : 9.00%
-11 : 11.25%
-10 : 13.75%
-9 : 16.50%
-8 : 19.50%
-7 : 22.75%
-6 : 26.25%
-5 : 30.00%
-4 : 34.00%
-3 : 38.25%
-2 : 42.75%
-1 : 47.50%
+0 : 52.50%
+1 : 57.25%
+2 : 61.75%
+3 : 66.00%
+4 : 70.00%
+5 : 73.75%
+6 : 77.25%
+7 : 80.50%
+8 : 83.50%
+9 : 86.25%
+10 : 88.75%
+11 : 91.00%
+12 : 93.00%
+13 : 94.75%
+14 : 96.25%
+15 : 97.50%
+16 : 98.50%
+17 : 99.25%
+18 : 99.75%
+19 : 100.00%

[AttilaTheGeek]

I had this whole long thing typed up, too, but then you beat me to it.

[Harugami]

I'm working on a homebrew ruling for prosthetic in game (non-magical, alchemical/hydraulic with a bit of clockwork to fit the setting) and I'm going to need help on the pricing later so would you mind if when I'm at the part where I calculate price based on weight by used material and parts plus extra based on time to make it and surgery to attach it, would you mind totaling stuff like that for me? Also based on the called shot rules what is the chance of losing a limb if I were to say 2 debilitating blows on the same part is a chance of limb loss via percentile?

so for the second one I'm counting full damage hits as debilitating blows with the half hp ruling(if full damage dice on callshot hit= debilitating,if half or more hp on hit=debilitating, If confirmed crit=debilitating) after 2 debilitating before healing the part the person rolled a percentile to keep the limb and had to get an 80% or better what is the chance of danger of limb loss? what I'm asking is whats the chance of limb loss if I had a player who takes a lot of hits to the arm (slash weapons of course) what is the chance of an enemy cutting off his arm using the above rule? and this question for the sake of ease we are saying the enemy has +8 to hit and the defender has 16 ac?

[RFLS]

Would allowing Improved Critical and Keen to stack (a feat and a +1 enchant) result in a numerically superior choice compared to other, similar choices, such as any of the following:

Power Attack and a +1 enhancement
Power Attack and Flaming
Improved Critical and a +1 enhancement
Point Blank Shot and the Splitting enchant (not sure if splitting is +1, though)

[Loki_42]

I've got an attack bonus of two, and I rolled a two on the die, could you tell me what my actual attack roll is?:smalltongue:

In all seriousness though, this could be a neat resource. I don't have any math questions right now, but no one in my group is actually all that good at math, so we get stumped pretty easily. Now we can just check this thread.

[AttilaTheGeek]

I'm working on a homebrew ruling for prosthetic in game (non-magical, alchemical/hydraulic with a bit of clockwork to fit the setting) and I'm going to need help on the pricing later so would you mind if when I'm at the part where I calculate price based on weight by used material and parts plus extra based on time to make it and surgery to attach it, would you mind totaling stuff like that for me?

That's just addition :smalltongue:


Also based on the called shot rules what is the chance of losing a limb if I were to say 2 debilitating blows on the same part is a chance of limb loss via percentile?

so for the second one I'm counting full damage hits as debilitating blows with the half hp ruling(if full damage dice on callshot hit= debilitating,if half or more hp on hit=debilitating, If confirmed crit=debilitating) after 2 debilitating before healing the part the person rolled a percentile to keep the limb and had to get an 80% or better what is the chance of danger of limb loss? what I'm asking is whats the chance of limb loss if I had a player who takes a lot of hits to the arm (slash weapons of course) what is the chance of an enemy cutting off his arm using the above rule? and this question for the sake of ease we are saying the enemy has +8 to hit and the defender has 16 ac?

By full damage hits, you mean hits where the maximum possible number is rolled on the weapon damage dice, correct? For the person to lose a limb, several things have to happen.
They need to be hit.
The hit needs to be debilitating.
They need to be hit again.
The second hit also has to be debilitating.
They have to roll 20% on a percentile die.


The chance of all these things happening is the chance to hit squared (11/20, rolling a 10 or above, because called shots to the arm take a -2 penalty) times the chance for it to be debilitating (1/X, where X depends on the damage die of the weapon, plus the chance for it to hit over half the target's health, which depends on the scenario. Let's assume it's 0, because it's very small.) squared. All of that times one fifth.

If the weapon is a Longsword, the person has a chance of 0.005% of severing a limb after two attacks. If it's a Greataxe, the chance is 0.042%. If it's a Bastard Sword or other d10 weapon, the chance is 0.061%. If the weapon hits for 1d6, the chance is 0.168%, and if the weapon hits for 1d4, the chance is 0.378%. The reason why severing blows get more likely as the damage dice gets smaller is because the attacker is more likely to roll full damage on a d4 than on 2d6.

[TuggyNE]

Would allowing Improved Critical and Keen to stack (a feat and a +1 enchant) result in a numerically superior choice compared to other, similar choices, such as any of the following:

Power Attack and a +1 enhancement
Power Attack and Flaming
Improved Critical and a +1 enhancement
Point Blank Shot and the Splitting enchant (not sure if splitting is +1, though)

Splitting is actually +3.

I was going to suggest Collision and Improved Critical, but Collision is +2. :smallannoyed:

[Harugami]

wow that's so cool, could you tell me on average how many hits before its a 50% chance of limb lose?

[Story]

For small probabilities, you can approximate it by mutiplying the probability by .693

So for example, if you have a 1 in 1000 chance each time, you need 693 hits to have a 50% chance. Of course it has a long tail, so the mean would be 1000 hits.

Of course that assumes that they are independent. It looks like you're actually talking about something that occurs over multiple hits with a persistent effect. Unfortunately, I don't understand the called shot rules, so I can't really help you there.

[AttilaTheGeek]

Would allowing Improved Critical and Keen to stack (a feat and a +1 enchant) result in a numerically superior choice compared to other, similar choices, such as any of the following:

Power Attack and a +1 enhancement
Power Attack and Flaming
Improved Critical and a +1 enhancement
Point Blank Shot and the Splitting enchant (not sure if splitting is +1, though)

Good question. It depends on the weapon, so I'll say you're using Pathfinder's Elven Curveblade (1d10, crits on 18-20/x2) because it hits almost as hard as a greatsword while still having a great crit range. I'm also assuming that the fighter has a +5 STR modifier, which is reasonable at 8th level, and that the fighter needs a d20 roll of 8 to hit a target.

The damage added by Improved Critical and Keen on any given attack is equal to the chance to hit (12/20), times the chance of rolling a critical threat that would not have been a critical threat without Keen (9/20), times the chance to confirm the crit (which is the same as the chance to hit, (12/20) again), times the damage added. The 1d10 averages to 5.5, or 10.5 damage on the average non-critical hit. Note that this number improves if you stack on critical feats, but it's not really possible to model their effects because the damage of other melee characters in the party also increases when the target is debuffed.


Improved Critical and Keen: (12/20)*(9/20)*(12/20)*(10.5) = 1.701 damage added per attack.

To compare Power Attack and +1, we need to first look at how much the weapon hits for on every attack without any additions. That's just the hit chance (12/20) times damage (10.5), plus crit chance ((3/20) times hit chance (12/20)) times damage.


No enhancements: (12/20)*(10.5) + (3/20)(12/20)(10.5) = 7.245 damage per attack.

Power Attack takes a -3 penalty to attack for +6 damage, which, combined with the +1 enchantment, gives -2 to attack and +7 damage. Like before, we have (hit chance times damage) plus crit threat chance times crit chance times damage.


Power Attack and +1: (10/20)*(17.5) + (3/20)(10/20)(17.5) = 10.063 damage per attack, or 2.818 damage added per attack.

Flaming is like +1, except it adds 3.5 damage instead of +1 to hit and damage. Also it looks cool.


Power Attack and Flaming: (9/20)*(20) + (3/20)(9/20)(20) = 10.350 damage per attack, or 3.105 damage added per attack.

The Splitting enchantment is vastly undercosted at +3, and it basically says you do twice as much damage.


Any arrow or bolt fired from a splitting weapon magically splits into two missiles in mid-flight. Both missiles are identical, sharing the nonsplitting properties of the original missile; for example, a +1 splitting arrow splits into two +1 arrows in mid-flight. Both missiles strike the same target. Make a separate attack roll for each missile using the same attack bonus.

It's not even in the same league as any of the others; it's going to be way above the rest. I won't even bother mathing it out.

Final answer: Improved Critical and Keen is still weak. Power Attack and Flaming adds nearly twice as much damage, but critical feats could change this.

[Story]

By the way, is there any easy way to search through your own posts? I once calculated the exact probabilities for different highest starting stats under the standard rolling rules, but I can't find it anymore.

[Harugami]

Thank you for that story, and the rule I was going on is generally a called shot to the arm will cripple it. I was adding to this rule by saying any called shot to that arm after it's crippled that hits hard enough would have a decent chance of just lopping it off. that being said you answered my question nonconsecutive debilitating blows in the same battle should have dire consequences that aren't really accounted for in the book, the frequency of these consequences was what I was asking for and you answered it accordingly. Thank you I just needed a general number and 693 is good enough, that being said do you mind if I print your post so I can explain this to my group?

[Story]

Feel free. This is a public forum after all.

[TuggyNE]

By the way, is there any easy way to search through your own posts? I once calculated the exact probabilities for different highest starting stats under the standard rolling rules, but I can't find it anymore.

Not really, with site search down; if you have a relatively unique username (like mine *cough*) you can pull off "site:giantitp.com <username> <search terms>" but otherwise you're basically stuck. Well, unless you have a special signature, that might help.

[Story]

I've probably got one of the worst usernames for searching.

[AttilaTheGeek]

Anyone else have math requests?

[RFLS]

Sure, I'll throw another your way. With only the enchantments found in PHB+DMG, which weapon enchant gives the most return on damage per +1 of enchantment value? Assume a hypothetical weapon that does 1d8 + Str on hit, and has a 19-20/x2 crit range. If a core weapon would be much more ideal, that can be subbed in as the weapon.

[AttilaTheGeek]

Sure, I'll throw another your way. With only the enchantments found in PHB+DMG, which weapon enchant gives the most return on damage per +1 of enchantment value? Assume a hypothetical weapon that does 1d8 + Str on hit, and has a 19-20/x2 crit range. If a core weapon would be much more ideal, that can be subbed in as the weapon.

Hmm. Assumptions I'm going to make are that the fighter has 20 STR, is holding a one-handed weapon, has three iterative attacks on a full attack, needs an 9 on a d20 attack roll to hit, and fights Evil creatures half the time. Those assumptions need to be made because some enhancements (keen, for example) are better when the weapon hits harder, and the attack roll is given a reasonable value so I can output hard numbers as opposed to "The damage added is 1/2 times the strength squared times the chance to hit plus 1/4 hit chance cubed", which, while versatile, leaves a lot of work to the reader and is more difficult to interpret. The three iterative attacks matters for Speed, which doubles your damage if you have a single attack but only increases it by 25% if you have four attacks already, and the earliest it's feasibly available is around when a full BAB class would get its third attack anyway. I also chose to assume you were referring to a one-handed weapon because two-handers tend to hit harder than 1d8. The evil clause is so that Holy doesn't show up as incredibly powerful, because fighting evil enemies all the time isn't reasonable.

The ones that won't be tested are
Frost, Shocking, Icy Burst, Shocking Burst, Merciful, Unholy, Anarchic, and Axiomatic, because they function identically to ones I am testing,
Bane and Disruption, because they're unpredictable,
Defending and Ghost Touch because they don't add any damage,
Ki Focus, because the damage it adds depends on unarmed strike damage, which is different for different characters,
Mighty Cleaving, because it also costs a feat, and feats and gold are apples and oranges,
Spell Storing because it depends on how many melee attacks are made during a fight (it unloads all its power all at once and then is useless),
and Brilliant Energy, Vorpal, and Wounding, because they depend on the creature being attacked.


In the table below, the important number is "Value"- how much damage it adds on every attack swing divided by the price of its bonus.

{table=head]Ability|Damage|Price|Value|Other notes
None|6.27|0|0|
Flaming|8.37|+1|2.10|Identical to Frost, Shocking, Merciful, and Corrosive.
Keen|7.125|+1|0.885
Thundering|6.54|+1|0.27
Vicious|10.47|+1|4.20|Deals 1d6 damage to the wielder every hit.
Holy|8.37|+2|1.05|
Flaming Burst|8.70|+2|1.215|Identical to Icy Burst, Shocking Burst, and Corrosive Burst.
Keen + Thundering|7.38|+2|0.555
Speed|8.36|+3|0.697
Dancing|12.54|+3|2.09
[/table]

Conclusion: Vicious is extraordinary, but 1d6 damage to the wielder every hit can add up. Aside from that, 1d6 energy enhancements give the best value, followed closely by Dancing. All the math is in this spoiler.
The damage by default, with no enhancements, is the chance to hit (12/20) times damage (1d8+5 averages to 9.5) plus crit chance (1/10) times the chance to confirm the crit (12/20) times extra damage on the crit (9.5).


No enhancements: (12/20)*(9.5)+(2/20)*(12/20)*(9.5)= 6.27 damage per attack.

Flaming adds 1d6 damage, which averages to 3.5.


Flaming: (12/20)*(13)+(2/20)*(12/20)*(9.5)= 8.37 damage per attack.

Keen increases the chance to threaten a critical from 19-20 (1/10) to 17-20 (1/5).


Keen: (12/20)*(9.5)+(4/20)*(12/20)*(9.5)= 7.125 damage per attack.

Thundering adds 1d8 (averages to 4.5) on a critical hit.


Thundering: (12/20)*(9.5)+(2/20)*(12/20)*(9.5+4.5)= 6.54 damage per attack.

Vicious deals an extra 2d6 (7) on every hit. Its downside is that it also deals 1d6 damage to the wielder every time it hits.


Vicious: (12/20)*(16.5)+(2/20)*(12/20)*(9.5)= 10.47 damage per attack.

Holy adds 2d6 damage, just like Vicious does, but only to evil creatures. Since I'm assuming the wielder fights evil creaturees half the time, it essentially adds half the damage. It also bypasses DR/good and doesn't deal damage to the wielder.


Holy: (12/20)*(9.5 + 0.5*(7))+(2/20)*(12/20)*(9.5)= 8.37 damage per attack.


Flaming Burst adds 1d6 (3.5) on every hit plus an additional 1d10 (5.5) on crits.


Flaming Burst: (12/20)*(13)+(2/20)*(12/20)*(15)= 8.70 damage per attack.

Keen and Thundering is a synergistic combination, increasing the likelihood of extra damage from crits.


Keen and Thundering: (12/20)*(9.5)+(4/20)*(12/20)*(9.5+4.5)= 7.38 damage per attack.

Speed grants an extra attack, but only on a full attack action. A weapon attack is added for each full attack, so to get its damage in terms of "damage per strike" like the others, the added damage has to be "distributed" among the other attacks by adding 1/3 of the extra damage to each of the three attacks.


Speed: (12/20)*(9.5)+(1/10)*(12/20)*(9.5)=6.27 damage added per full attack, (6.27/3)+6.27 = 8.36 damage per attack.

Dancing lets a weapon fight on its own, making as many attacks as you can make. As long as the wielder also makes full attacks for the four rounds it dances, it essentially doubles damage.


Dancing: 2*[(12/20)*(9.5)+(2/20)*(12/20)*(9.5)] = 2*[6.27] = 12.54 damage per attack.

[Krazzman]

Nice, I hope this is going to be mathematically solveable.

In PF, pretty low Wealth, 8th level.
Half Elf Barbarian with 18 Str. Already in possession: +1 Keen Greatsword.
With a Crafter on hand with Magic Arms and Armor what is the best (cheapest) way to use 3000 gp to raise the damage she can deal? (If this is importan she has Elemental Rage and Elemental Rage, lesser).

For a 8th level sorcerer with Craft WOndrous and Craft Magic Arms and Armor 5000 gp. Gear in possession: Cloak of Resistance +1, Bracers of Armor +1, Pearl of Power 1st level. And the spell selection shown in the thread you already gave advice for (+ for 8th level Shout/Enervation, Stone Call and Tiny Hut) what is the better solution:
Building a Headband of Intellect +2? + something other?
Building a Pearl of Power 3rd Level? + keeping some spare change?
Or an other Wondrous Item/enchantment I should look at?

And if this is possible how good is Enervation compared to Shout in terms of "killing enemies" in a damage aspect (loss of HP) and debuff?

[AttilaTheGeek]

Disclaimer: I can't think of everything. If you come across something that's slipped my mind that you think might be better than anything I recommend here, let me know and I'll crunch the numbers.


In PF, pretty low Wealth, 8th level.
Half Elf Barbarian with 18 Str. Already in possession: +1 Keen Greatsword.
With a Crafter on hand with Magic Arms and Armor what is the best (cheapest) way to use 3000 gp to raise the damage she can deal? (If this is importan she has Elemental Rage and Elemental Rage, lesser).

Well, I'd start by selling the sword you have. You should be able to "trade it in" for an equivalent sword by selling it for half its worth and then using that gold to craft a new one. *points two posts up* Keen is such an ineffective enhancement that if you can exchange it for a +1 Flaming Greatsword instead, your damage will go up by about 1.7 points every time you swing your weapon, misses included, or 2.6 damage every hit. Of course, if you're fighting fire-resistant enemies, Icy, Shocking, and Corrosive work just as well.

Math:The damage added by Keen on every hit is the chance to threaten a crit (2/20) times the chance to confirm it (again, 12/20 as an assumption, plus 1/20 because it's a +1 weapon) times the damage added (2d6+7 averages to 14), which multiplies out to 0.91 damage per hit. Flaming just adds 3.5 damage per hit, which comes out to a difference of 2.59 damage per hit in favor of Flaming. Multiplied by the chance to hit (13/20) gives 1.684 additional damage with Flaming instead of Keen on every weapon swing.

However, if Ultimate Equipment is allowed in your game, you might want to look at the Furious (http://www.d20pfsrd.com/magic-items/magic-weapons/magic-weapon-special-abilities/furious) enchant. It reads:


A furious weapon serves as a focus for its wielder's anger. When the wielder is raging or under the effect of a rage spell, the weapon's enhancement bonus is +2 better than normal.

Taking Furious, which is effectively a +2 bonus for the price of +1 because you're always raging, over Flaming increases your damage by about 0.665 points each swing.

Math:Flaming adds 3.5 damage per hit, but Furious adds +2 damage on hit and +2 attack. Over your base +1 weapon, Flaming adds (13/20)*3.5 = 2.275 damage per swing, but Furious adds the chance to hit when you wouldn't otherwise have (2/20) times the damage you would gain there (16) plus the chance to hit normally (12/20) times damage gained there (2) plus crit chance (2/20)*(14/20) times the damage gained there (2), for a grand total of 2.940 damage per swing.

If you can't do either of those, you can't do much. 3000gp can't upgrade your +2 weapon to a +3 weapon, but it's 3/4 of the way to buying a Belt of +2 STR. That's the third thing I'd recommend.


For a 8th level sorcerer with Craft WOndrous and Craft Magic Arms and Armor 5000 gp. Gear in possession: Cloak of Resistance +1, Bracers of Armor +1, Pearl of Power 1st level. And the spell selection shown in the thread you already gave advice for (+ for 8th level Shout/Enervation, Stone Call and Tiny Hut) what is the better solution:
Building a Headband of Intellect +2? + something other?
Building a Pearl of Power 3rd Level? + keeping some spare change?
Or an other Wondrous Item/enchantment I should look at?

And if this is possible how good is Enervation compared to Shout in terms of "killing enemies" in a damage aspect (loss of HP) and debuff?

(emphasis mine)
Huh? I don't ever remember recommending Tiny Hut, especially not for a sorcerer.

I'd suggest a Headband of +2 CHA, if you don't have one already, because it gives you bonus spells and higher DCs for all your spells, but you'd only need another 3000 to craft a headband of CHA +4 if you feel like saving. If you don't have a Handy Haversack, it certainly is handy. It's not really possible to math out what the best thing for you is because it depends on the rest of your party and what they need. For example, if there's only one melee character, a Ring of Protection or Amulet of Natural Armor will serve you well. But if the party is the Sorcerer, a Barbarian, two Fighters, a Paladin, and a Rogue, it would be better to focus on spell support.

Enervation is a tricky one. It's incredibly complicated to find out how much damage is prevented by giving the BBEG -1d4 to hit because it depends on how likely it is to attack and then to hit each of your party members. In terms of just doing damage, it doesn't do any. Crushing Despair is just about as good and affects multiple targets, but they get a save, so depending on your DCs, that might be a better debuff for you. Slow is great too. However, like I said, without knowing the entire party makeup and encounter, you can't predict how effective debuffing will be.

However, from a damage perspective, I can tell you that shout is awful. It's Burning Hands with a 15' longer cone, a different damage type, and a chance to deafen...for three levels higher. There aren't a lot of good 4th-level Evocations. And by a lot, I mean any. Shout is worse than Fireball. (5d6, save half, as opposed to 8d6, save half).

[Krazzman]

The advice you gave was about Lightning Bolt or another 3rd level blast spell. But due to the nature of our surroundings we came to the conclusion I take Tiny Hut and the Wizard takes Secure Shelter (the 4th level one).

Party composition is:
Buff/Heal Cleric, Elven Abjuration Wizard, Dwarven [archetype] Paladin (Axe'n'Shield), Dwarven Dual Wield Ranger, Half-Elf Barbarian and me as a Human Sage Sorcerer (Casting and class features via Int with 18 in Int).

"common" or pretty likely monsters: Demons/Devils and such nasty stuff.

For the Barbarian: Keen was so she doesn't need to take the feat and can take a critical feat next level. Belt of +2 Str was enhancement (so I don't have to buff her Bull's strength anymore because it doesn't stack, right?)... going to propose this offer.

For enchantments I was thinking about giving everyone in the group Holy Weapons (the +2d6 against evil stuff) and something along the lines of Furious for her too as I don't think she will trade in her weapon... (do you know if Corrosive stacks with extra corrosive damage from the elemental rage? and would Icy and flaming cancel each other out?)

[AttilaTheGeek]

For enchantments I was thinking about giving everyone in the group Holy Weapons (the +2d6 against evil stuff) and something along the lines of Furious for her too as I don't think she will trade in her weapon... (do you know if Corrosive stacks with extra corrosive damage from the elemental rage? and would Icy and flaming cancel each other out?)

Why wouldn't all the damage types stack?

[TuggyNE]

Defending, Ghost Touch, Holy, Unholy, Axiomatic, Anarchic, because they don't add any damage,

Correction: Holy, Unholy, Axiomatic, and Anarchic do add 2d6 damage, but only to certain alignments. So you could add those in with the provisional note that they're only of any value while you're fighting those alignments, which does complicate things.

[AttilaTheGeek]

Correction: Holy, Unholy, Axiomatic, and Anarchic do add 2d6 damage, but only to certain alignments. So you could add those in with the provisional note that they're only of any value while you're fighting those alignments, which does complicate things.

Good catch. I added those in with the assumption that creatures of the opposed alignment would be fought half the time, and calculated overall value from there.

[Zahhak]

Just saying, but probability would be more relevant then statistics in this case. And even then, it really isn't all that difficult, since each die has an easy to figure average:

1d2: 1.5
1d3: 2
1d4: 2.5
1d6: 3.5
1d8: 4.5
2d4: 5
1d10: 5.5
1d12: 6.5
1d20: 10.5, 5% chance per side
"1d100": 60.5

After that (with damage, for example) its just a matter of figuring likely outcome on 100 rolls.
For example, assuming a 1d8 weapon:
Normal on 100 average rolls: 45 points of damage, plus an average of 22.5 from criticals
Crit chance 19-20: +22.5 extra crit damage
+d6 Damage: +35 points of damage

So, the +d6 damage weapon is the better choice.

I'm feeling bored, so, formula!
(bD*100)+(aD*100)+(.05*TR*100)
Where bD is base weapon damage average roll (so, a d8 base weapon damage would be the above 4.5), aD is the same but for the bonus, and TR is the threat range. And you can basically adapt this to just about anything.

[TypoNinja]

I'm usually pretty decent at math myself, but a couple of things.

How do you multiply odds together? Like for example if you are looking for multiple unlikely events, the probability of the whole string coming up as needed (for example two events with 50/50, what are the odds of both being in your favor).

I've completely forgotten how to go about actually solving that. I'm sure there's a formula to describe it but my google-fu has failed me, and hell if I can remember half of what I learned in school anymore :P

3.5 Question

I've got a Swift hunter who I've planned out fairly carefully, my final choice on a weapon is Mighty Composite L.Bow +3 Splitting, Holy, bane x2 (evil outsider, and chaotic outsider).

Our campaign is such that I expect to see plenty of both demons and devils, so evil outsiders will definitely be a great choice, as will holy, and splitting seems like a no brainier. +3 is to allow for Weapon Augment Crystals (demolition, true death, and revelation as needed)

Chaotic outsiders is my next choice as sort of a default, Demons my slight preference since an encounter with a Devil is slightly less likely to result in combat. Is there a better option for damage? Or something that would limit my need to rely on exotic material arrows to deal with all the outsiders I'll be fighting? Only having a +1 available is kind of limiting

[elonin]

Not really, with site search down; if you have a relatively unique username (like mine *cough*) you can pull off "site:giantitp.com <username> <search terms>" but otherwise you're basically stuck. Well, unless you have a special signature, that might help.

Instead of searching using your name click private messages and one of the menu choices allows you to pull up a list of subscriptions.

[AttilaTheGeek]

I'm usually pretty decent at math myself, but a couple of things.

How do you multiply odds together? Like for example if you are looking for multiple unlikely events, the probability of the whole string coming up as needed (for example two events with 50/50, what are the odds of both being in your favor).

You had it right- you just multiply. For example, the odds of flipping heads, then tails, then rolling a natural 20 are (1/2)*(1/2)*(1/20), or 1/80.


I've got a Swift hunter who I've planned out fairly carefully, my final choice on a weapon is Mighty Composite L.Bow +3 Splitting, Holy, bane x2 (evil outsider, and chaotic outsider).

Our campaign is such that I expect to see plenty of both demons and devils, so evil outsiders will definitely be a great choice, as will holy, and splitting seems like a no brainier. +3 is to allow for Weapon Augment Crystals (demolition, true death, and revelation as needed)

Chaotic outsiders is my next choice as sort of a default, Demons my slight preference since an encounter with a Devil is slightly less likely to result in combat. Is there a better option for damage? Or something that would limit my need to rely on exotic material arrows to deal with all the outsiders I'll be fighting? Only having a +1 available is kind of limiting

I'm not sure of the question. Are you asking if there's a better way to spend gold than on Chaotic Outsider Bane?

[Animastryfe]

I've got an attack bonus of two, and I rolled a two on the die, could you tell me what my actual attack roll is?:smalltongue:

In all seriousness though, this could be a neat resource. I don't have any math questions right now, but no one in my group is actually all that good at math, so we get stumped pretty easily. Now we can just check this thread.

If you are able to form your question well, then try also using wolframalpha.com.

[AttilaTheGeek]

If you are able to form your question well, then try also using wolframalpha.com.

Wolfram is fantastic. It even does calculus for you.

[TuggyNE]

Instead of searching using your name click private messages and one of the menu choices allows you to pull up a list of subscriptions.

True, but that only works if you have it set to auto-subscribe to all threads you post in or start, which isn't the default. (And it's not the way I have it anymore either; I post in way too many threads for my inbox to survive that. :smalltongue:) It's also quite useless for searching on someone else's name.

[Story]

Sadly I didn't have it subscribed.

[Chilingsworth]

Ok, this might be an annoying request, but:

I just did some (very) basic analysis of the characters offered for a PbP I've applied to (just maximum, minimum, and average values for a variety of scores.) Others among the group would like a more through analysis of the data. Might you be able to provide a proper statistical analysis?

The table of links to the relevant character sheets (http://www.giantitp.com/forums/showpost.php?p=14648740&postcount=219)

The first table I posted (concerning ability modifiers) (http://www.giantitp.com/forums/showpost.php?p=14652118&postcount=252)

The second table I posted (concerning AC's, Save, and Attack bonuses) (http://www.giantitp.com/forums/showpost.php?p=14652676&postcount=261)

[TypoNinja]

You had it right- you just multiply. For example, the odds of flipping heads, then tails, then rolling a natural 20 are (1/2)*(1/2)*(1/20), or 1/80.



I'm not sure of the question. Are you asking if there's a better way to spend gold than on Chaotic Outsider Bane?

Not necessarily the gold, but yes. That's my long term plan on a weapon, I'm quite happy with everything except the chaotic outsider bane, but it seems to be the best option left.

My DM has a MIC but I don't so my ability to just skim the book looking for goodies is limited, though I can happily use any material from it if I'm merely pointed at it.

So two 25%'s back to back would be .25x.25 for .0625 or 6.2%? I guess I expected another step.

Given that that is multiplication, it should work for any base % and any number of iterations yes?

[zimmerwald1915]

I apologize for this off-topic non sequitur, but I had to share that I first read the title as "Attila's Death Mask".

[TuggyNE]

I apologize for this off-topic non sequitur, but I had to share that I first read the title as "Attila's Death Mask".

Someone should homebrew one of those.

[Story]

I tried adding a signature, but it doesn't seem to apply retroactively.

[strider24seven]

Wolfram is fantastic. It even does calculus for you.

Amen to Mathematica products.

Now I pose some simple, straightforward questions:

1) I wish to accumulate a large amount of damage on a creature- let us say G-64 (http://en.wikipedia.org/wiki/Graham%27s_number), using darts. I may non-magical, standard PHB darts of any size, up to Colossal.

Assume the target's AC is 0 and has Regeneration 40 and DR 1/-.
Assume I have no bonus to damage (except strength bonus, obviously), a to-hit of +20, and I have 2 attacks per round.

Special: I can take 2 more attacks than the previous round if I take a cumulative -2 penalty on all of my attacks in the current round (so 2 attacks = -0 penalty, 4 attacks = -2 penalty, 6 attacks = -4 penalty, etc). I may never decrease my number of attacks in this manner, but may choose to instead reset the tempo to 2 attacks per round.

Note: Keep in mind that I must be able to lift the darts in order to throw them.

What is the shortest amount of time in which the given creature accumulates an average of G-64 damage? What is the smallest number of darts that I would have to use in that time? What is the smallest strength score I would require?

2) How much wood could a woodchuck chuck in a given round, given that a woodchuck could chuck wood?

[Story]

No matter what you do, it's going to take far more than the age of the universe. Grahm's Number is infinite for all practical purposes. Even an exponential growth rate won't help you.

Anyway, the best bet is to increase your attacks as fast as possible and eat the 95% miss rate. This will at least get you quadratic growth. Dart size, strength bonus, regeneration, and damage reduction are all irrelevant, since they only affect the time up to a constant multiple.

[TypoNinja]

2) How much wood could a woodchuck chuck in a given round, given that a woodchuck could chuck wood?

A woodchuck would chuck as much wood as a woodchuck could chuck, if a woodchuck could chuck wood.

[warmachine]

A character who has Second Chance (http://www.d20pfsrd.com/feats/combat-feats/second-chance-combat) and a second attack due to +6 BAB should re-roll a missed first attack, rather than try a second attack, as the second attack is at relative -5. However, having a third attack due to +11 or better BAB may allow more hits instead. Assuming no other feats, under what conditions should a character try a second and third attack, rather than re-roll the first?

[Greenish]

Assuming you don't have to confirm your critical hits, how much damage do you have to do with each attack for Keen to be better than Flaming (etc.)?

[yougi]

Imagine an ability that allows you to reroll your attack roll, but force you to keep the second result: how much of a bonus is that equivalent to? (wow, I suck at this syntax thing...) What about if you could roll twice and keep the best roll?

Also, is there a formula to calculate how to optimize your Power Attack in 3.5? I mean, I know there's a way to calculate it, but I mean a way that would be simple enough to do the math at the table?

[AttilaTheGeek]

A character who has Second Chance (http://www.d20pfsrd.com/feats/combat-feats/second-chance-combat) and a second attack due to +6 BAB should re-roll a missed first attack, rather than try a second attack, as the second attack is at relative -5. However, having a third attack due to +11 or better BAB may allow more hits instead. Assuming no other feats, under what conditions should a character try a second and third attack, rather than re-roll the first?

Second Chance with three iterative attacks is useful if rolling a 6 (on the d20) on your first attack would hit. It makes sense because two attacks at a lower bonus are better only if you're likely to hit with both of them. I did the math out on paper, and I'm kind of rushed at the moment, so I'll post it later.


Assuming you don't have to confirm your critical hits, how much damage do you have to do with each attack for Keen to be better than Flaming (etc.)?

If you don't have to confirm crits, Keen becomes much better and competitive. I'll see if I can get you an answer tonight.


Imagine an ability that allows you to reroll your attack roll, but force you to keep the second result: how much of a bonus is that equivalent to? (wow, I suck at this syntax thing...) What about if you could roll twice and keep the best roll?

Also, is there a formula to calculate how to optimize your Power Attack in 3.5? I mean, I know there's a way to calculate it, but I mean a way that would be simple enough to do the math at the table?

For the second question, I remember writing a formula about a year ago; I'll see if I can dig it up. I'll work on the first question tonight or tomorrow morning.

[AttilaTheGeek]

Assuming you don't have to confirm your critical hits, how much damage do you have to do with each attack for Keen to be better than Flaming (etc.)?

I think I'll just put all the maths in a spoiler from now on so that if you're looking for an answer, you can just find it quickly.
It (of course) depends on the crit range of the weapon. But we start with an inequality:

1/20 * (Crit multipliers added) * (Weapon damage) > 3.5

By "crit multipliers", I mean the number of possible extra weapon damage terms added. For example, an 18-20/x2 crit range adds three extra weapon damage components (on an 18, 19, or 20), as does a 20-20/x4 range (on 20, times three). In other words, the crit multipliers of the range is equal to (21 minus the minimum needed to crit) times (the crit multiplier (x2, x3, or x4) -1), because a crit of x1 isn't a crit at all.

From there, we just divide 3.5 by the number of crit multipliers and multiply by 20 to solve for weapon damage.

{table=head]Crit range|Crit multipliers|Damage
20-20/x2|1|70
19-20/x2|2|35
18-20/x2|3|23.3
20-20/x3|2|35
19-20/x3|4|17.5
20-20/x4|3|23.3[/table]

Keen is better than Flaming (or another +1d6 energy enhancement) if your weapon damage is greater than the number in the table and you don't have to confirm crits.

[AttilaTheGeek]

Also, is there a formula to calculate how to optimize your Power Attack in 3.5? I mean, I know there's a way to calculate it, but I mean a way that would be simple enough to do the math at the table?

I can't find any flaws in the logic or the math, and the formula seems right, but I think I remember coming up with something different before. Math spoiler is here. Warning: calculus involved.I began with three variables: how much you power attack for, P, how much weapon damage you do on a hit, W, and the natural d20 roll you'd need to hit the target, A. (If A is small, then you're likely to hit, because you need to roll above that small number).

For a two-handed weapon, I defined a function f of W, A, and P and rearranged for P.

f (W, A, P) = (1/20)*(21-A-P)*(W+2P)
= (1/20)* [21W-AW-WP+42P-2AP-2P^2]
= (1/20)* [(-2)P^2 + (42-W-2A)P + (21W-AW)]

Now, since we're trying to solve the value of P that maximizes f, we take the partial derivative of f with respect to P and set it to 0. It's a maximum because the function doesn't have a minimum, and we don't have to worry about saddle points because we're holding W and A constant.

∂f/∂p = (1/20)* [ -4P + 42 - W - 2A] = 0

And from here, we solve for P in terms of W and A. The 1/20 multiplies out because the other side is 0.

42-W-2A = 4P
P = (42-W-2A)/4

For a 2H weapon, power attack = (42 - weapon damage - two times d20 roll needed to hit) divided by 4. For example, if you need to roll at least an 8 on your d20 to hit, and you hit for 20 damage, then (42-20-8)/4 = 3.5, which rounds down to 3. It makes intuitive sense to an optimizer, because if you hit for a million, you don't want to risk a 1/20 chance of missing for only 2 extra damage, and it would actually be better to reduce damage for an increased chance to hit, so the formula outputs a negative number. But if you know you're going to hit anyway, but not for much, then power attack adds a lot.

For a 1H weapon, the math is similar.
f (W, A, P) = (1/20)*(21-A-P)*(W+P)
= (1/20)* [21W-AW-PW+21P-AP-P^2]
= (1/20)* [(-1)P^2 + (21-W-A)P + (21W-AW)]
∂f/∂p = (1/20)*[-2P+21-W-A]=0
2P=21-W-A
P=(21-W-A)2

For a 1H weapon, power attack = (21 - weapon damage - d20 roll needed to hit) divided by 2.

Edit: I found my error in the 2H calculations. the formula is now " - two times d20 roll needed to hit", as opposed to " - d20 roll needed to hit".

[yougi]

I can't find any flaws in the logic or the math, and the formula seems right, but I think I remember coming up with something different before. Math spoiler is here. Warning: calculus involved.I began with three variables: how much you power attack for, P, how much weapon damage you do on a hit, W, and the natural d20 roll you'd need to hit the target, A. (If A is small, then you're likely to hit, because you need to roll above that small number).

For a two-handed weapon, I defined a function f of W, A, and P and rearranged for P.

f (W, A, P) = (1/20)*(21-A-P)*(W+2P)
= (1/20)* [21W-AW-WP+42P-AP-2P^2]
= (1/20)* [(-2)P^2 + (42-W-A)P + (21W-AW)]

Now, since we're trying to solve the value of P that maximizes f, we take the partial derivative of f with respect to P and set it to 0. It's a maximum because the function doesn't have a minimum, and we don't have to worry about saddle points because we're holding W and A constant.

∂f/∂p = (1/20)* [ -4P + 42 - W - A] = 0

And from here, we solve for P in terms of W and A. The 1/20 multiplies out because the other side is 0.

42-W-A = 4P
P = (42-W-A)/4

For a 2H weapon, power attack = (42 - weapon damage - d20 roll needed to hit) divided by 4. For example, if you need to roll at least an 8 on your d20 to hit, and you hit for 20 damage, then (42-20-8)/4 = 3.5, which rounds down to 3. It makes intuitive sense to an optimizer, because if you hit for a million, you don't want to risk a 1/20 chance of missing for only 2 extra damage, and it would actually be better to reduce damage for an increased chance to hit, so the formula outputs a negative number. But if you know you're going to hit anyway, but not for much, then power attack adds a lot.

While I did not understand the math behind it at all, I believe this did not account for critical hits. Could that be calculated?

[Greenish]

{table=head]Crit range|Crit multipliers|Damage
20-20/x2|1|70
19-20/x2|2|35
18-20/x2|3|23.3
20-20/x3|2|35
19-20/x3|4|17.5
20-20/x4|3|23.3[/table]

Keen is better than Flaming (or another +1d6 energy enhancement) if your weapon damage is greater than the number in the table and you don't have to confirm crits.Cheers!


While I did not understand the math behind it at all, I believe this did not account for critical hits. Could that be calculated?In addition, what would "reverse PA" (sacrifice damage for accuracy) formula look like? Say, with +1 to hit for each -3 to damage? (Why yes, that just happens to coincide with Legend's Precise Strike. :smallwink:)

[AttilaTheGeek]

While I did not understand the math behind it at all, I believe this did not account for critical hits. Could that be calculated?


Exception: Extra damage over and above a weapon’s normal damage, such as that dealt by a sneak attack or the special ability of a flaming sword, is not multiplied when you score a critical hit.

Would this not apply to Power Attack as well?


In addition, what would "reverse PA" (sacrifice damage for accuracy) formula look like? Say, with +1 to hit for each -3 to damage?

It's exactly the same. If the formula is negative, then using reverse PA is better; if it's positive, then it's more optimal to power attack. However, I do think you have a typo there- according to power attack's description (http://dndtools.eu/feats/players-handbook-v35--6/power-attack--2208/), each -1 to hit only gives +2 to damage with a two-handed weapon.

[Greenish]

Would this not apply to Power Attack as well?It's generally interpreted to refer to effect that add extra dice of damage, not to fixed damage.


It's exactly the same. If the formula is negative, then using reverse PA is better; if it's positive, then it's more optimal to power attack. However, I do think you have a typo there- according to power attack's description (http://dndtools.eu/feats/players-handbook-v35--6/power-attack--2208/), each -1 to hit only gives +2 to damage with a two-handed weapon.Not a typo. I was hoping for something relevant to Legend's Precise Strike (since it's not like such an ability even exists in 3.5 or PF).

[thethird]

For a 2H weapon, power attack = (42 - weapon damage - two times d20 roll needed to hit) divided by 4.

So 42 isn't just the meaning of life. :smalltongue:

[AttilaTheGeek]

So 42 isn't just the meaning of life. :smalltongue:

Actually, I found a small error in that formula. It's "minus two times d20 roll needed to hit", if you could add that into the quote? I don't want people to get confused.

[yougi]

It's generally interpreted to refer to effect that add extra dice of damage, not to fixed damage.

Pretty much that.

And aside from crits, I don't think your calculations included iterative attacks, right? (wow, is that getting complicated or what?)

And with a 1H, would it be the same formula, but divided by 8?

[AttilaTheGeek]

It's generally interpreted to refer to effect that add extra dice of damage, not to fixed damage.

Ahh. Well, then.

*sound of crunching numbers*

*crunch crunch crunch*

Edit to add:


Pretty much that.

And aside from crits, I don't think your calculations included iterative attacks, right? (wow, is that getting complicated or what?)

And with a 1H, would it be the same formula, but divided by 8?

That's what I initially expected for 1H weapons, but actually the numbers are slightly different. I edited that formula in.

I think I'll now need five or six different variables: P for how much you power attack for, W for weapon damage, A for d20 roll needed to hit (the A comes from AC), I for number of iterative attacks, and C for damage added by crits. Instead of editing into that old post, I'll just make a new one. And possibly K for how much power attack is added in- K=1 for 1H weapons, K=2 for 2H weapons, and K=3 for Greenish's Precise Strike.

[thethird]

And then you can make a revenant blade frenzied berserker and check that for the lulz.

[AttilaTheGeek]

And then you can make a revenant blade frenzied berserker and check that for the lulz.

*is a pathfinder player*
*is confused*

[Greenish]

And then you can make a revenant blade frenzied berserker and check that for the lulz.At that point, you'd have Shock Trooper, and the math becomes very simple: always PA for full. Always.

[Edit]: Revenant Blade isn't really relevant to the math, but Frenzied Berserker is a PrC that improves your PA ratio. Among other things.

[thethird]

A revenant blade can power attack with a double scimitar (a double weapon used for TWF) as if it was a THW. A frenzied berserker gains +4 damage for every -1 penalty to attack when power attacking.

Revenant blade is from Player's guide to Eberron pg 142. Frenzied Berserker is from Complete Warrior pg. 34

[Sudain]

3.5 -
For contact other plane(http://www.d20srd.org/srd/spells/contactOtherPlane.htm) how high must my INT be to get a greater than 50% chance of a correct answer, while still maintaining a less than 30% chance of having the int&charisma reduction. I'm hoping for my fatepsinner abilities will allow me to re-roll a bad roll and keep my total chance of getting lobotomized below 10%.

Assume 0 WBL because I'm getting hosed on cash in this campaign.

Thank you in advance,


P.S. - As a side note if anyone knows of a way avoid the int/charisma reduction from two bad rolls - I'm all ears. I will have contingency available to me.

Edited to adjust failure rate to account for fate-spinner re-roll abilities.

[Amphetryon]

In 3.5, is the Collision (http://www.d20srd.org/srd/psionic/items/weapons.htm#collision) Weapon Ability overpriced, underpriced, or in line with other +2 equivalent enhancements?

[AttilaTheGeek]

Looking back through this thread, I just realized I've missed a bunch of questions. Sorry about that.


Ok, this might be an annoying request, but:

I just did some (very) basic analysis of the characters offered for a PbP I've applied to (just maximum, minimum, and average values for a variety of scores.) Others among the group would like a more through analysis of the data. Might you be able to provide a proper statistical analysis?

The table of links to the relevant character sheets (http://www.giantitp.com/forums/showpost.php?p=14648740&postcount=219)

The first table I posted (concerning ability modifiers) (http://www.giantitp.com/forums/showpost.php?p=14652118&postcount=252)

The second table I posted (concerning AC's, Save, and Attack bonuses) (http://www.giantitp.com/forums/showpost.php?p=14652676&postcount=261)

I'm not sure what you mean by "proper statistical analysis". What exactly am I supposed to be comparing?


So two 25%'s back to back would be .25x.25 for .0625 or 6.2%? I guess I expected another step.

Given that that is multiplication, it should work for any base % and any number of iterations yes?

Yep. If you have two events, A and B, with probabilities A and B, that's how you do the probability of event A AND event B occurring. To do "NOT A", the probability is 1-A, and for "A OR B" it's 1-((1-A)(1-B)), which says NOT ((NOT A) AND (NOT B)), or "not neither of them". A XOR B is just A(1-B). And that's how you do logic gates with probability!

TL,DR: Yes.


3.5 -
For contact other plane(http://www.d20srd.org/srd/spells/contactOtherPlane.htm) how high must my INT be to get a greater than 50% chance of a correct answer, while still maintaining a less than 30% chance of having the int&charisma reduction. I'm hoping for my fatepsinner abilities will allow me to re-roll a bad roll and keep my total chance of getting lobotomized below 10%.

Your INT doesn't affect the chance of a correct answer at all, only whether you get an answer. Are you talking about a specific plane?

(Of course, the short answer is "don't ever cast Contact Other Plane because it will lobotomize you")


In 3.5, is the Collision (http://www.d20srd.org/srd/psionic/items/weapons.htm#collision) Weapon Ability overpriced, underpriced, or in line with other +2 equivalent enhancements?

{table=head]Ability|Damage|Price|Value|Other notes
None|6.27|0|0|
Flaming|8.37|+1|2.10|Identical to Frost, Shocking, Merciful, and Corrosive.
Keen|7.125|+1|0.885
Thundering|6.54|+1|0.27
Vicious|10.47|+1|4.20|Deals 1d6 damage to the wielder every hit.
Holy|8.37|+2|1.05|
Flaming Burst|8.70|+2|1.215|Identical to Icy Burst, Shocking Burst, and Corrosive Burst.
Keen + Thundering|7.38|+2|0.555
Collision (http://www.d20srd.org/srd/psionic/items/weapons.htm#collision)|9.57|+2|1.65
Speed|8.36|+3|0.697
Dancing|12.54|+3|2.09
[/table]

Collision is powerful, but not underpriced. It's better than most, but not the clear best option.

See the other post (http://www.giantitp.com/forums/showpost.php?p=14648708&postcount=20) for how I did this. Here, I'm just showing my work (out of habit).

Collision: (12/20)*(9.5+5)+(2/20)*(12/20)*(9.5+5)= 9.57 damage per attack.

[Sudain]

I guess I was consdering a 'true' answer to be a correct answer versus 'don't know, lie, or random(which in some cases is as good as a lie)'. I think the outer Plane, Demideity would work, putting a DC 10

+5 int, would give me a 25% chance of failing. Re-roll would give me a 6% chance of being lobotomized, correct?

Wha'ts the fun in being a fate spinner if you don't dance with Thantos occasionally? After all, I don't want it to get board and come seeking me out. :)

[Chilingsworth]

I'm sorry. I meant, I wanted to know the distribution of the varrious scores (ability scores, saves, melee and ranged attack bonuses, hp, and the three types of AC) among the characters found linked in the first table I presented.

If this still makes no sense, or is utterly useless, or is a waste of time, I appologize for making you expend even a thought on it.

Actually, if you could point me to a decent (and free and easy to use) statistics engine (is that the term I want? I mean a program or website I can plug data points into and get a statistical breakdown of the set as output.) I'd be grateful. I searched, but I only found links to data analysis suites for sale.

[AttilaTheGeek]

I guess I was consdering a 'true' answer to be a correct answer versus 'don't know, lie, or random(which in some cases is as good as a lie)'. I think the outer Plane, Demideity would work, putting a DC 10

+5 int, would give me a 25% chance of failing. Re-roll would give me a 6% chance of being lobotomized, correct?

That's correct.


Wha'ts the fun in being a fate spinner if you don't dance with Thantos occasionally? After all, I don't want it to get board and come seeking me out. :)

Dude, don't taunt the god-killing abomination. (http://www.giantitp.com/comics/oots0275.html)

[AttilaTheGeek]

I'm sorry. I meant, I wanted to know the distribution of the varrious scores (ability scores, saves, melee and ranged attack bonuses, hp, and the three types of AC) among the characters found linked in the first table I presented.

If this still makes no sense, or is utterly useless, or is a waste of time, I appologize for making you expend even a thought on it.

Actually, if you could point me to a decent (and free and easy to use) statistics engine (is that the term I want? I mean a program or website I can plug data points into and get a statistical breakdown of the set as output.) I'd be grateful. I searched, but I only found links to data analysis suites for sale.

Statistical analysis like that is only really useful on large groups of characters, to comment on them as a whole. For example, the standard deviation of HPs in a 6-person party is still a measure of how spread-out the HPs are, but since there's only 6 people you can just look at their HP as a whole. I think it would be more time-efficient (and effective) to just ask each player "How high-op is your character", and use the responses you get from that to plan encounters accordingly.

I use my TI-84 calculator (http://en.wikipedia.org/wiki/TI-84_Plus_series). It does lots of things and is easy, but rather expensive, and the manual is badly written. If you're looking for specific equations, WolframAlpha (http://www.wolframalpha.com/) does everything. Other than that, I can't really help you, sorry.

[Chilingsworth]

Statistical analysis like that is only really useful on large groups of characters, to comment on them as a whole. For example, the standard deviation of HPs in a 6-person party is still a measure of how spread-out the HPs are, but since there's only 6 people you can just look at their HP as a whole. I think it would be more time-efficient (and effective) to just ask each player "How high-op is your character", and use the responses you get from that to plan encounters accordingly.

I use my TI-84 calculator (http://en.wikipedia.org/wiki/TI-84_Plus_series). It does lots of things and is easy, but rather expensive, and the manual is badly written. If you're looking for specific equations, WolframAlpha (http://www.wolframalpha.com/) does everything. Other than that, I can't really help you, sorry.

I figured as much. Thanks. :smallbiggrin:

[Story]

P.S. - As a side note if anyone knows of a way avoid the int/charisma reduction from two bad rolls - I'm all ears. I will have contingency available to me.


An often overlooked rule is that you can take 10 on ability checks as well, meaning that any Wizard smart enough to cast Contact Other Plane will autopass all but the hardest checks. I'm guessing the check is only there for Sorcerors.

[Chilingsworth]

An often overlooked rule is that you can take 10 on ability checks as well, meaning that any Wizard smart enough to cast Contact Other Plane will autopass all but the hardest checks. I'm guessing the check is only there for Sorcerors.

No, you can't usually take ten when under stress. Now, wrestling with an entity greater than yourself, who will lobotimize you if you lose the struggle? Yeah, I think that would put one under stress.

[Story]

I interpreted it as the int check coming at the beginning of the spell, and it's not a spell you usually cast in combat, so there isn't any stress.

But if your DM does rule that you can't take 10, things get a lot harder. However, you can still stack enough int bonuses and reroll chances to pass the Greater Deity reliably. On the other hand, a DM like that will probably start RPing the deity rather than following the description anyway.

[TuggyNE]

No, you can't usually take ten when under stress. Now, wrestling with an entity greater than yourself, who will lobotimize you if you lose the struggle? Yeah, I think that would put one under stress.

Similarly, climbing a tall cliff, where any slip is likely to kill you?

But Climb is explicitly mentioned as allowing taking 10.

[Sudain]

Eh, I guess there's some wiggle room to 'try' to take 10. Considering what I'm doing with the spell I expect to loose that and I should just plan on that not being an option though. Thank you very much Attila & other people! :)

Now back to your regularly scheduled math questions!

[warmachine]

This may require too much data collection. For the typical encounters for each PC level from 1 to 20, what proportion of creatures will have Spell Resistance and of those that do, what are the chances of a basic spellcaster of that level overcoming Spell Resistance? It is appreciated that enumerating the typical encounters for each level makes a lot of assumptions and displaying such details would need too much space. The final calculations for each level will suffice.

[sabelo2000]

By what method would you go about contrasting the damage of a longsword (1d8) and a falchion (2d4) over the course of an encounter? It would seem that on a single swing, the Longsword (average damage 4.5) is outclassed by the Falchion (statistical probability of rolling 5) but I know my logic is faulty in that instance. But over the course of an encounter in which each hits, say, 20 times, the longsword has an increased chance of rolling either 1 or 8 damage. So which is optimal, if we ignore criticals?

And is the same formula directly applicable to a Greataxe (1d12) and a Greatsword (2d6)?

Apologies in advance for the garbled question.

[AttilaTheGeek]

This may require too much data collection. For the typical encounters for each PC level from 1 to 20, what proportion of creatures will have Spell Resistance and of those that do, what are the chances of a basic spellcaster of that level overcoming Spell Resistance? It is appreciated that enumerating the typical encounters for each level makes a lot of assumptions and displaying such details would need too much space. The final calculations for each level will suffice.

Yeah, sorry. I'm not going to answer that because it's too much work. :smalltongue:


By what method would you go about contrasting the damage of a longsword (1d8) and a falchion (2d4) over the course of an encounter? It would seem that on a single swing, the Longsword (average damage 4.5) is outclassed by the Falchion (statistical probability of rolling 5) but I know my logic is faulty in that instance. But over the course of an encounter in which each hits, say, 20 times, the longsword has an increased chance of rolling either 1 or 8 damage. So which is optimal, if we ignore criticals?

And is the same formula directly applicable to a Greataxe (1d12) and a Greatsword (2d6)?

Apologies in advance for the garbled question.

You had it right. The Falchion does an average of 0.5 damage more on a single hit, so on a single encounter of 20 hits it'll do 10 damage more. Not only is it applicable to weapons, but to every die roll in the game. The average of a dx for any x is 0.5+(X/2), (3.5 for a d6, 4.5 for a d8, etc.), and the average of ndx is x*[0.5+(x/2)] because you are just taking n "dx"s and integrating from 0 to n adding them together. (har har calculus joke). For that example, a Greataxe (1d12) averages 6.5, and the Greatsword (2d6) averages 2*3.5=7, so a greatsword will, in general, hit harder than a greataxe.

[Twilightwyrm]

I actually have a Pathfinder question, and one that has been eating at me ever since I made a Gunslinger. I've been thinking of cross-classing, so I was wondering, if we assume 5-7 levels of Gunslinger (Musket Master), and 5-7 levels of Fighter or 5-7 levels of Rogue, which multiclass combination (Gunslinger/Fighter or Gunslinger/Rogue) produces the optimal damage output per round?
Assumptions:
Dex 20 (+5 to hit and damage), Half-Elf (if it makes a difference), will be carrying a +1 Holy, Flaming, Shocking, Distance Musket.
Assume he possesses the Deadly Aim, Rapid Reload, Point Blank Shot and Rapid Shot feats.
Assume he will constantly be within the first range increment for the musket.
Assume he will be using all Alchemical Cartridges, which when combined with Rapid Reload and Fast Musket, let him reload as a free action, meaning he can fire at his BAB.
Assume that he will be able to either catch the opponent flat-footed, or suitably flanked to Sneak Attack, approximately 75% of the time. (You can ignore this if necessary).
Assume 75% of enemies are evil, and none are resistant to fire or electricity.
Assume that I am not taking any further steps, via items, feats, etc. to increase damage per hit outside of the class levels, but will be looking to utilize Deadly Shot to the best of my ability.
Assume I have taken steps to negate any misfire chance.
I realize this is a large amount of calculations, so there is any additional information that might eliminate more variables involved, please let me know and I will provide further details/assumptions.

[Kane0]

Which is better:
1d8 damage with damage multiplied by 2 on a 20
or
1d6 damage with damage multiplied by 2.5 on a 20.
I'm aiming for some kind of balance here.

[Story]

The 1d8 is obviously a lot better. You need a much higher difference in multipliers since it only applies 5% of the time.

[warmachine]

Some feats and class features allow a d20 to be rolled twice and the best result chosen. For each number from 1 to 20, treating that as the minimum roll on a d20 to succeed, display the chance of success for 1d20, best of 2 d20s and equivalent bonus of the latter compared to the former (rounded to the nearest whole number). For example, 11 has 50% on 1d20, 75% on best of 2 d20s, making it equivalent to +5.

[Kane0]

The 1d8 is obviously a lot better. You need a much higher difference in multipliers since it only applies 5% of the time.

OK, will this apply to other die steps? Like:
1d4 at x2 and 1d3 at x2.5
1d6 at x2 and 1d4 at x2.5
1d10 at x2 and 1d8 at x2.5
I imagine it would.

Does changing the x2.5 to x3 change this much?
Changing the x2.5 to apply to 19s and 20s?
I have feats and weapon enchantments available to apply, so If I were to add them to both options you would end up with 1d8 (crit 19-20 x3) and 1d6 (crit 19-20 x3.5) does that even them out? Note, there is no confirmation roll for these.
Not counting bonus damage from strength, precision damage, etc.

Edit: I'm talking about base weapon damage, I just noticed I didn't actually say that.

[AttilaTheGeek]

Some feats and class features allow a d20 to be rolled twice and the best result chosen. For each number from 1 to 20, treating that as the minimum roll on a d20 to succeed, display the chance of success for 1d20, best of 2 d20s and equivalent bonus of the latter compared to the former (rounded to the nearest whole number). For example, 11 has 50% on 1d20, 75% on best of 2 d20s, making it equivalent to +5.

Well, there's a chart I came across in a thread (http://www.giantitp.com/forums/showthread.php?p=14602514). It was originally posted by 4th number.

http://i.imgur.com/8d8AT6c.png

[Proud Tortoise]

What is the average roll for 4d6b3?

[Story]

15869/1296 = 12.24...

The median is 12.

[warmachine]

Well, there's a chart I came across in a thread (http://www.giantitp.com/forums/showthread.php?p=14602514). It was originally posted by 4th number.
I was hoping for a table so I could compare the benefits of best of 2 d20, such as Rogue talent Wall Scramble (http://www.d20pfsrd.com/classes/core-classes/rogue/rogue-talents/paizo---rogue-talents/wall-scramble-ex), with feats such as Skill Focus (http://www.d20pfsrd.com/feats/general-feats/skill-focus---final). Guess I'll have to do the work myself.
Improvement of best of 2 d20s
{table]Min Roll|1d20|d20s x2|Improvement|Equivalent Bonus
1|100%|100.00%|+0.00%|+0
2|95%|99.75%|+4.75%|+1
3|90%|99.00%|+9.00%|+2
4|85%|97.75%|+12.75%|+3
5|80%|96.00%|+16.00%|+3
6|75%|93.75%|+18.75%|+4
7|70%|91.00%|+21.00%|+4
8|65%|87.75%|+22.75%|+5
9|60%|84.00%|+24.00%|+5
10|55%|79.75%|+24.75%|+5
11|50%|75.00%|+25.00%|+5
12|45%|69.75%|+24.75%|+5
13|40%|64.00%|+24.00%|+5
14|35%|57.75%|+22.75%|+5
15|30%|51.00%|+21.00%|+4
16|25%|43.75%|+18.75%|+4
17|20%|36.00%|+16.00%|+3
18|15%|27.75%|+12.75%|+3
19|10%|19.00%|+9.00%|+2
20|5%| 9.75%|+4.75%|+1[/table]

Best of 2 d20s compares favourably with a +3 Skill Focus except at the extremes, meaning easy or hard DCs for the character. This means little at the easy end with a near 100% success rate but is bad at the hard end where you need all the help you can get. It compares badly to a +6 (10 rank) Skill Focus.

[Yora]

Seeing the threads title, I was reading Attilas Death Mask. That would have made much more sense on this forum. :smallbiggrin:

[AttilaTheGeek]

I apologize for this off-topic non sequitur, but I had to share that I first read the title as "Attila's Death Mask".


Seeing the threads title, I was reading Attilas Death Mask. That would have made much more sense on this forum. :smallbiggrin:

I don't have a death mask, really!

[TuggyNE]

I don't have a death mask, really!

Dude, you clearly need to get one.

"Attila's death mask, now closed for intimidation!"

[Archmage1]

I am sort of hesitant to ask this, but then I thought of a slightly easier way
Essentially, how bad do opposed rolls get facing multiple opponents
Improved Question:
Can you provide a formula for determining the success/failure rate(as percent) of opposed rolls(that is, things like hide, move silently, listen, spot, bluff, sense motive...) that takes in the following
X: Character Skill(Increasing this increases success rate)
Y: Enemy Skill(Increasing this should decrease success rate)
Z: Number of enemies(assuming all get an equal skill value)
W: Number of rolls needed from character(X)(so, say, you need to pass hide and move silently to move on, or for a complex skill check)
V: Number of rolls needed from enemies(Z,Y)(since all NPC's always use both their standard and their move to spot player.

Using this, it should be possible to generate a table to convince DM's to make stealth encounters/bluff situations more balanced.(Currently, in my experience, DM's tend to vastly underestimate the difficulty that multiple opposed rolls cause)

Yes, there are a lot of variables, but, then, the equation is meant to be very variable.

Might be a good idea to provide a version that assumes W and V are both 1.

[AttilaTheGeek]

I actually have a Pathfinder question, and one that has been eating at me ever since I made a Gunslinger. I've been thinking of cross-classing, so I was wondering, if we assume 5-7 levels of Gunslinger (Musket Master), and 5-7 levels of Fighter or 5-7 levels of Rogue, which multiclass combination (Gunslinger/Fighter or Gunslinger/Rogue) produces the optimal damage output per round?
Assumptions:
Dex 20 (+5 to hit and damage), Half-Elf (if it makes a difference), will be carrying a +1 Holy, Flaming, Shocking, Distance Musket.
Assume he possesses the Deadly Aim, Rapid Reload, Point Blank Shot and Rapid Shot feats.
Assume he will constantly be within the first range increment for the musket.
Assume he will be using all Alchemical Cartridges, which when combined with Rapid Reload and Fast Musket, let him reload as a free action, meaning he can fire at his BAB.
Assume that he will be able to either catch the opponent flat-footed, or suitably flanked to Sneak Attack, approximately 75% of the time. (You can ignore this if necessary).
Assume 75% of enemies are evil, and none are resistant to fire or electricity.
Assume that I am not taking any further steps, via items, feats, etc. to increase damage per hit outside of the class levels, but will be looking to utilize Deadly Shot to the best of my ability.
Assume I have taken steps to negate any misfire chance.
I realize this is a large amount of calculations, so there is any additional information that might eliminate more variables involved, please let me know and I will provide further details/assumptions.

Alright. I will take on this challenge. I want to know what level I should run the test for (5, 6, or 7), what feats you'd have by then, what extra fighter feats you'd have, what rogue talents you would take, and what archetypes you'd take.

[Archmage1]

Hey... Just noticed, but nice sig, Atilla. :smallsmile:

[AttilaTheGeek]

Hey... Just noticed, but nice sig, Atilla. :smallsmile:

:smallbiggrin:

[yougi]

About the rolling 2d20b1, I got an average of 14 (3.5 higher average on 1d20). However, it also almost doubles the odds of a critical hit. My idea is to create a weapon enchantment that would allow you to do it, and to price it accordingly. How could I calculate the average damage of such a weapon?

[Randomguy]

One day, I hope to be able to do this math.


There's an exotic weapon in the 3.5 MM4 called the Minotaur Greathammer. It deals 1d12 damage with a threat range of 19-20 and a crit multiplier of x4.

What's the Minotaur Greathammer's average damage? How does it compare to the average damage of the greatsword, greataxe and falchion?


If you have a friendly wizard to cast Greater Mighty Wallop (http://dndtools.eu/spells/races-of-the-dragon--83/mighty-wallop-greater--3107/) on your minotaur greathammer each day, then how would the hammer's damage output compare to that of a heavy flail, if you also had the same wizard casting the spell on your flail?
Could I please get a comparison for caster levels 5, 8, 12 and 16 on the mighty wallop spell? Assume a medium sized wielder.

[Story]

What's your attack bonus and target AC? Critical hit damage depends strongly on what roll you need to confirm.

[TypoNinja]

What is the operation I need to preform to determine the probability of any one of two (or more) events happening.

For example, say I have two passive abilities that each have a 20% chance to activate in a combat round.

What about 3, or 4 abilities?

I know that I multiply the % together to get the odds of both happening, but I've no idea what operation or formula to apply in this case.

[Story]

If the events are independent and occur with probabilities p and q, then

The chance of both occuring is pq
The chance of neither occuring is (1-p)(1-q)
The chance of exactly one happening is p(1-q) + q(1-p).

If you want to know the probability of one or more events occuring with individual probabilities p1, p2, ...

Then it is 1 - (1-p1)(1-p2)(...)

[AttilaTheGeek]

One day, I hope to be able to do this math.

There's an exotic weapon in the 3.5 MM4 called the Minotaur Greathammer. It deals 1d12 damage with a threat range of 19-20 and a crit multiplier of x4.

What's the Minotaur Greathammer's average damage? How does it compare to the average damage of the greatsword, greataxe and falchion?

The set of rolls on 1d12 is {1,2,3...10,11,12}, which averages 6.5. In general, a roll of 1dX for any X will average 1/2*X + 1/2. A crit multiplier of x4 really means that x3 damage is added on a crit, because the first damage would have been done anyway. Like Story said, crit confirmation rolls depend on how likely you are to hit in the first place, which depends on your target AC and the attack bonus, B. (AC-B) is the number you need to roll on your d20 to hit, and (AC-B)/20 is the chance of rolling that number or below. For example, you have a 15/20 chance of rolling a 15 or below. 1 minus that is the chance of not rolling that number or below, but we add 1/20 bcause an equal attack hits, so the total chance of hitting is 1.05-(AC-B)/20. The extra damage added because of crits is the likelihood of a crit times the damage added. The chance of you getting a crit after you've already hit is the chance of threatening (2/20 for this 19-20 weapon) and confirming (times 1.05-(AC-B)/20), and the added damage is 3 times 6.5 makes 19.5. Then we multiply out to find that the damage added becaue of crits is 19.5*2/20*(1.05-(AC-B)/20.), or 2.0475-0.0975(AC-B). We add the base damage to that (6.5) to get total damage on hit of 8.5475-0.0975(AC-B) It may look strange, but the "reality check" gives it a pass- higher AC decreases damage, and because of the double negative, a higher attack bonus increases it.

A Greatsword hits for 2d6, averaging 7. Damage added because of crits is 7*2/20*(1.05-(AC-B)/20), which multiplies out to 0.735-0.035(AC-B). Added together, a Greatsword's average hit will do 7.7735-0.035(AC-B) damage.

A Greataxe's 1d12 averages to 6.5, and the damage added from crits is 6.5*2*1/20*(1.05-(AC-B)/20). That multiplies to 0.6825-0.0325(AC-B). Added together, a Greateaxe hits for 7.1825-0.0325(AC-B).

And, last but not least, the falchion. 1d4 averages 2.5, so 2d4 averages 5. It has a 3/20 chance to threaten a crit, adds 1 extra instance of 5 damage on a crit, and has the same chance to confirm a crit as every other weapon. 5*1*3/20*(1.05-(AC-B)/20) makes 0.7875-0.0375(AC-B). Added together, a falchon's damage is 5.7875-0.0375(AC-B).


If you have a friendly wizard to cast Greater Mighty Wallop (http://dndtools.eu/spells/races-of-the-dragon--83/mighty-wallop-greater--3107/) on your minotaur greathammer each day, then how would the hammer's damage output compare to that of a heavy flail, if you also had the same wizard casting the spell on your flail?
Could I please get a comparison for caster levels 5, 8, 12 and 16 on the mighty wallop spell? Assume a medium sized wielder.

Sure thing.Though I assume you meant CLs 4, 8, 12, and 16, because it scales every 4 levels.

{table=head]CL|Greathammer damage|Greathammer average damage|Flail damage|Flail average damage
None|1d12|8.5475-0.0975(AC-B)|1d10|6.0775-0.0275(AC-B)
4|3d6|12.705-0.105(AC-B)|2d8|9.945-0.045(AC-B)
8|4d6|16.94-0.14(AC-B)|3d8|14.9175-0.0675(AC-B)
12|6d6|25.41-0.21(AC-B)|4d8|19.89-0.09(AC-B)
16|8d6|33.88-0.28(AC-B)|6d8|29.835-0.135(AC-B)[/table]

The Greathammer wins. If you want to talk about math or ask for help, feel free to PM me :smallsmile:

[AttilaTheGeek]

What is the operation I need to preform to determine the probability of any one of two (or more) events happening.

For example, say I have two passive abilities that each have a 20% chance to activate in a combat round.

What about 3, or 4 abilities?

I know that I multiply the % together to get the odds of both happening, but I've no idea what operation or formula to apply in this case.

In addition to what Story said, if you have X abilities, and each of them has the same chance P of activating on any given weapon hit, then the chance of any one of them activating is 1-((1-P)^X). If you have four abilities that each have a 20% chance, the chance of getting at least one of them is 1-((0.8)^4), or 59.04%. For three abilities it's 48.8%, and for two it's 36%.

[Stouts]

About the rolling 2d20b1, I got an average of 14 (3.5 higher average on 1d20). However, it also almost doubles the odds of a critical hit. My idea is to create a weapon enchantment that would allow you to do it, and to price it accordingly. How could I calculate the average damage of such a weapon?

I haven't run numbers on damage output, but a quick look at the distribution (http://anydice.com/program/1e63) (click 'graph' for ease of viewing) shows that this would probably be better than +3 Enhancement for attack and better than Keen for damage. I'd ballpark it at +4.

[Pandoras Folly]

Ok easy one. My human character was just made a Large size character by dm fiat. What changes? I know I have a 10 foot reach, but I'm not real sure after that.

[Stouts]

Ok easy one. My human character was just made a Large size character by dm fiat. What changes? I know I have a 10 foot reach, but I'm not real sure after that.

The DM obviously is going to control the particulars, but it's likely that you just get the listed effects of enlarge person (https://sites.google.com/site/pathfinderogc/magic/all-spells/e/enlarge-person). Even if the DM doesn't give you the stat changes, though, large always carries a -1 hit to Attack and AC. You can also use that link as a reference for appropriately sized weapon damage.

[Twilightwyrm]

Alright. I will take on this challenge. I want to know what level I should run the test for (5, 6, or 7), what feats you'd have by then, what extra fighter feats you'd have, what rogue talents you would take, and what archetypes you'd take.

(Sorry it took so long to respond)
Sure, I can provide this. The level test should be for 12th level (assume Gunslinger 7/Fighter 5 or Gunslinger 5/Rogue 7).

By 12th level for the Gunslinger/Fighter Hybrid, I'm expecting the following: Archetypes: Musket Master (Gunslinger) and Weapon Master (Fighter)
Feats: Skill Focus (Stealth)*, Quick Draw, Gunsmithing**, Rapid Reload (Musket)***, Deadly Aim, Point Blank Shot**, Signature Deed (Deadeye), Improved Initiative, Rapid Shot****, Signature Deed (Targeting), Improved Critical****, Hammer the Gap, Snap Shot.

By 12th level for the Gunslinger/Fighter Hybrid, I'm expecting the following:
Archetypes: Musket Master (Gunslinger) and Sniper (Rogue)
Talents: Snap Shot, Bleeding Attack, Major Magic (Vanish)
Feats: Musket Master (Gunslinger) and Weapon Master (Fighter)
Feats: Skill Focus (Stealth)*, Quick Draw, Gunsmithing**, Rapid Reload (Musket)***, Deadly Aim, Point Blank Shot**, Rapid Shot, Signature Deed (Deadeye), Precise Shot, Improved Initiative
Additional Items: Sniper's Goggles (+2 damage per SA die (or +8 damage on SAs))

Note: Assume any other equipment, special abilities, or feats I've forgotten do not effect damage per round, and all other factors being equal.
Feel free to request additional information you might find pertinent.
*Half-Elf Bonus Feat
*Gunslinger Bonus Feat
***Musket Master Bonus Feat
****Fighter Bonus Feat

[AttilaTheGeek]

I haven't run numbers on damage output, but a quick look at the distribution (http://anydice.com/program/1e63) (click 'graph' for ease of viewing) shows that this would probably be better than +3 Enhancement for attack and better than Keen for damage. I'd ballpark it at +4.

(emphasis mine)

Actually, I had a hunch that wasn't true, so I decided to crunch some numbers. If you take C, the chance to Crit on 1d20, then the chance to not crit on 1d20 is (1-C). The chance to not crit on either of 2d20 is (1-C)^2, so the chance to crit on either of them is 1-(1-C)^2. However, the chance to confirm the critical is the chance to hit naturally, so let's call that H for Hit chance. The chance to confirm it with no enhancement or with Keen is H, but the probability of confirming a crit with advantage is 1-(1-H)^2.

{table=head]Crit range|Crit chance|With Keen|With Advantage|H must be
20-20|0.05*H|0.1*H|0.0975*[1-(1-H)^2]|97.4%
19-20|0.1*H|0.2*H|0.0199*[1-(1-H)^2]|94.7%
18-20|0.015*H|0.3*H|0.2775*[1-(1-H)^2]|91.8%[/table]

Then, I found out what the hit chance had to be for Advantage to be better. If every weapon swing hits, then every critical threat confirms, and Keen is better because Keen weapons have a larger chance to threaten. However, an Advantage weapon is probably more likely to hit, and so more likely to confirm the crit. I took the third column of each row in the table above and subtracted the second column to find the additional chance to crit that an Advantage weapon would have over a Keen weapon. Then, I graphed that as a function of H from 0 to 1. Wherever the function was positive, Advantage was better, and the value of that function was the extra damage added by Advantage over Keen in terms of the weapon's base damage. I then calculated the zero of the function to find out what the hit chance had to be for Advantage to be worse than Keen. That's how I generated the last column, what H must be for Keen to hit harder.


Conclusion: My hunch was wrong. Advantage is almost always better than Keen for damage. Assuming your initial attack roll hits, Keen only hits harder than Advantage when you have an 18-20 crit range and you can confirm the crit with a 3 on a d20 roll. A +4 price seems good.

[CockroachTeaParty]

What I'm taking away from this thread so far is that crit-fishing builds are probably a bad idea.

[AttilaTheGeek]

Oh yeah. It's common knowledge among optimizers that the 1d6 energy enhancements are solid but not great, and for an x4 crit weapon or an 18-20/x2 weapon every single hit needs to do over 20 damage for Keen to even catch up to that d6.

[Sugashane]

I love this idea.

Ok here is one that is confusing me, and please show the breakdown for me.

My large LVL 12 fighter with 30 STR (+10) using a large greatsword (3d6 +15)

Feats include:
Power attack (+12)
Shock trooper's heedless charge (why above can go to +12)
Leap attack modifier
Battle Jump (Unapproachable east)
________________________________

What would my average attack be if charging?
And would having a valorous weapon be more damaging or a magic item that allowed for pounce?

From what I understand the power attack is double with two hands (26 (12+2x2)) with the extra 2 being from charging which is "tripled" by leap attack (D&D math making it now a x4 multiplier) and again doubled by Battle Jump (so really x5). So would it be 3d6+ 70 (Bonus)+15 (STR) for an average of 95.5 damage?

Thank you, the errata and conflicting posts online have been frustrating to say the least.

[yougi]

I have a good one: what is the average of 5d6, keep the best 3? And while we're at it, when we roll 4d6 (Best 3) 8 times and keep the highest 6 scores, what would be the average of that? How do these methods compare, and what kind of point buy would they be equivalent to (assuming D&D Point buy, not PF).

[AttilaTheGeek]

I love this idea.

Ok here is one that is confusing me, and please show the breakdown for me.

I think that's beyond the scope of this thread. Because of the rules errata and conflicting rules, like you mentioned, that would go better in the simple Q&A thread, or perhaps in its own thread. I can tell you that the 3d6 averages 10.5, so you can add that to whatever constant you come out with to find out how hard you'll hit.

[Umbranar]

I have a question (D&D 3.5 btw):

My character has a two weapons to choose from:

+1 keen frost bastard sword - +16/+11 to hit 1d10+11 damage +1d6 frost
+2 Greatsword - +17/+12 to hit 2d6+12 damage

Knowing my avarage opponent has an AC of 24, which weapon is better and how great a penalty should I take with power attack to have the best effency (best damage per round)?

extra info for funz if you feel like it: im a dragon disciple and I have a bite attack which I add to full round attacks:

Bite - +10 to hit 1d6+3 damage

[CockroachTeaParty]

I was curious about something:

What over the long-term is statistically the superior one-handed exotic weapon in Pathfinder?

Bastard Sword: 1d10, 19-20/x2

Katana: 1d8, 18-20/x2

Falcata: 1d8, 19-20/x3

[yougi]

I have a question (D&D 3.5 btw):

My character has a two weapons to choose from:

+1 keen frost bastard sword - +16/+11 to hit 1d10+11 damage +1d6 frost
+2 Greatsword - +17/+12 to hit 2d6+12 damage

Knowing my avarage opponent has an AC of 24, which weapon is better and how great a penalty should I take with power attack to have the best effency (best damage per round)?

extra info for funz if you feel like it: im a dragon disciple and I have a bite attack which I add to full round attacks:

Bite - +10 to hit 1d6+3 damage

I can answer that.

As for which one is the best, well against an AC of 24:

Bastard Sword has average damage of 20 (5.5+11+3.5), and Greatsword has 19 (7+12) on a non-crit hit.

The bastard will deal an average of (13/20*20)+(4/20*13/20*16.5)+(8/20*20)+(4/20*8/20*16.5) = 24.465 points of damage per round.

The Greatsword will deal an average of (14/20*19)+(2/20*14/20*19)+(9/20*19)+(2/20*9/20*19)= 24.035 points of damage per round.

The difference is very small, but Bastard sword is better.

POWER ATTACK
Against a target with an AC of 24, considering you use the Bastard Sword from before, you're better off not power attacking on a full attack, and power attacking at -2 on a single attack.

Math:
FULL ATTACK
No Power attack (including bite): (13/20*20)+(4/20*13/20*16.5)+(8/20*20)+(4/20*8/20*16.5)+(7/20*6.5)+(1/20*7/20*6.5)= 26.853

Power Attack at -1: (12/20*22)+(4/20*12/20*18.5)+(7/20*22)+(4/20*7/20*18.5)+(6/20*7.5)+(1/20*6/20*7.5)= 26.775

So on a full attack, power attacking lowers you damage per round.

SINGLE ATTACK
No Power Attack: (13/20*20)+(4/20*13/20*16.5)= 15.145 pts of damage

Power Attack at -1: (12/20*22)+(4/20*12/20*18.5)= 15.42

Power Attack at -2: (11/20*24)+(4/20*11/20*20.5)= 15.455

Power Attack at -3: (10/20*26)+(4/20*10/20*22.5)= 15.25

So at -3, it starts going down again.

[AttilaTheGeek]

I was curious about something:

What over the long-term is statistically the superior one-handed exotic weapon in Pathfinder?

Bastard Sword: 1d10, 19-20/x2

Katana: 1d8, 18-20/x2

Falcata: 1d8, 19-20/x3

Math:Even if you always cofirm crits, the Falcata hits for 1d8 (4.5) times (1+ 2/20 * 2) = 5.4. The 1+ comes from the fact that it always does normal damage when it hits, the 2/20 is the crit chance, and the 2 is the extra weapon damage added by a crit.

The Katana is just worse than the Falcata because the katana's critical threat range adds 1x weapon damage 3/20 of the time (for a total of 3/20 extra damage before critical hit confirmation), whereas the Falcata's crit range adds 2x extra weapon damage 2/20 of the time for a total of 4/20 extra damage.

Even if the Bastard Sword never crit, its 1d10 damage still averages 5.5, which is above the Falcata's 5.4 even if it confirms all crits. Besides, rolling d10s is fun.

Conclusion: Bastard Sword, by a fairly large margin.

[TuggyNE]

Conclusion: Bastard Sword, by a fairly large margin.

This is only true if you have no extra damage that can be multiplied on a crit; it doesn't take all that much extra to make the falcata superior.

[AttilaTheGeek]

(Sorry it took so long to respond)
Sure, I can provide this. The level test should be for 12th level (assume Gunslinger 7/Fighter 5 or Gunslinger 5/Rogue 7).

I will, uh...get to it when I have a free two hours? :smalltongue:

My gut says the Fighter, but only because getting off 75% sneak attacks with a ranged weapon is nearly impossible unless you have a mechanic that can make people flat-footed, like Dazzling Display and Shatter Defenses. Do you want me to model it with something more realistic, or are you confident in the 75% sneak attacks? If you are, it's going to be a close race.

[AttilaTheGeek]

This is only true if you have no extra damage that can be multiplied on a crit; it doesn't take all that much extra to make the falcata superior.

Oh. Right. I forgot about that. And he did say "long-term". I'm going to make the assumption that our character needs an 8 on a d20 roll to hit because it's reasonable across most levels and lets us get an answer just in terms of how much damage you need for the falcata to be better.

Our damage is in terms of the Bonus damage, B. The Bastard Sword does 5.5+B damage on a normal hit with an additional 5.5+B on a crit, which happens (2/20) * (12/20), or 24/400 of the time. Adding those together, we get 5.5+B + 24/400 * 5.5+B, or (5.5+B)*424/400. That multiplies to 5.83+1.06B damage on a hit.

The Falcata hits for 4.5+B, and an extra 9+2B when a crit is threatened and confirmed on (3/20)*(12/20) of hits, or 36/400 of all hits. 4.5+B+ (9+2B)*36/400 multiplies to 4.5+B+0.81+0.18B. Adding that all together, we get 5.31+1.18B damage on hit.

Then, to find out what damage we need to make the falcata more powerful, we put them into an inequality and solve.
5.31+1.18B > 5.83+1.06B
0.12B > 0.52
B>4.3
You were right. As long as you add 5 or more damage to every attack, the Falcata is better. So, in the long run, the Falcata is the winner, not the Bastard Sword.

[Umbranar]

I can answer that.

As for which one is the best, well against an AC of 24:

Bastard Sword has average damage of 20 (5.5+11+3.5), and Greatsword has 19 (7+12) on a non-crit hit.

The bastard will deal an average of (13/20*20)+(4/20*13/20*16.5)+(8/20*20)+(4/20*8/20*16.5) = 24.465 points of damage per round.

The Greatsword will deal an average of (14/20*19)+(2/20*14/20*19)+(9/20*19)+(2/20*9/20*19)= 24.035 points of damage per round.

The difference is very small, but Bastard sword is better.

POWER ATTACK
Against a target with an AC of 24, considering you use the Bastard Sword from before, you're better off not power attacking on a full attack, and power attacking at -2 on a single attack.

Math:
FULL ATTACK
No Power attack (including bite): (13/20*20)+(4/20*13/20*16.5)+(8/20*20)+(4/20*8/20*16.5)+(7/20*6.5)+(1/20*7/20*6.5)= 26.853

Power Attack at -1: (12/20*22)+(4/20*12/20*18.5)+(7/20*22)+(4/20*7/20*18.5)+(6/20*7.5)+(1/20*6/20*7.5)= 26.775

So on a full attack, power attacking lowers you damage per round.

SINGLE ATTACK
No Power Attack: (13/20*20)+(4/20*13/20*16.5)= 15.145 pts of damage

Power Attack at -1: (12/20*22)+(4/20*12/20*18.5)= 15.42

Power Attack at -2: (11/20*24)+(4/20*11/20*20.5)= 15.455

Power Attack at -3: (10/20*26)+(4/20*10/20*22.5)= 15.25

So at -3, it starts going down again.


I thank you very much, now maybe for an extra: We have a bard who manages to boost our attack by +6 to hit +7 damage (inspirational boost, masterwork instrument, words of creation and badge of valor). How does this change the math. Also I have boots of Speed or I am regularly buffed with haste. How does that change things :smallbiggrin:

[Squirrel_Dude]

A pretty simple one, i think, but I don't want to try and do it.


What's the chance of a Level 20 monk in Pathfinder hitting a Pit Fiend (AC 38) 4 times using flurry.
- Monk has 28 strength
- +5 Amulet of Might Fists
What is the most likely number of times that the monk will hit the Pit Fiend?

What's the chance of a Level 20 Fighter in Pathfidner hitting a Pit Fiend 4 times using his full attack.
- Fighter has 28 Strength
- Fighter has +5 bonus to attacking with this weapon (weapon focus + weapon training 1)
What is the most likely number of times that the fighter will hit the Pit Fiend?

[CockroachTeaParty]

As long as you add 5 or more damage to every attack, the Falcata is better. So, in the long run, the Falcata is the winner, not the Bastard Sword.

Interesting. Thanks for the maths!

Now, which one to pick for my character... he's a STR-based, shocking grasp-channeling magus, by the way, so I'm not sure if that changes anything.

[AttilaTheGeek]

Interesting. Thanks for the maths!

Anytime. :smallsmile:


Now, which one to pick for my character... he's a STR-based, shocking grasp-channeling magus, by the way, so I'm not sure if that changes anything.

In that case, I'd probably go with the Katana, because 50% more crits on your ridiculous, ridiculous Shocking Grasp is what you want. The Falcata would still be better, except for this:


This attack uses the weapon's critical range (20, 19–20, or 18–20 and modified by the keen weapon property or similar effects), but the spell effect only deals ×2 damage on a successful critical hit, while the weapon damage uses its own critical modifier.

With Shocking Grasps reaching into the bajillions, the weapon damage is pretty much negligible in comparison, so the 19-20/x3 crit range really acts like 19-20/x2.

[CockroachTeaParty]

When he hits 6th level or so, he'll be able to make his weapon Keen with his Arcane Pool.

So I might actually be looking at a 15-20/x2 with the katana. However, it looked like reliance on critical hits was ill-advised based off some of the earlier calculations.

I guess spellstriking shocking grasp changes all of that?

[AttilaTheGeek]

Well, say you do 10 damage on a hit and an extra 10 damage on a crit. A +1 damage increases your damage by 10%, but getting more crits doesn't do much.

But say you hit for 1000, with an extra 1000 on a crit. At that point, an extra +1 damage is almost negligible, and you really want that extra thousand damage on a crit. You also want to hit as often as you can, because each miss is a wasted thousand or two damage.

[CockroachTeaParty]

The magus guides I've been reading favored high-crit threat weapons, so this would make sense.

Now, do I pick a katana, or an urumi, which is statistically the same, but a friggin' 5-foot long razor-sharp metal death whip? Picture one of these (http://www.youtube.com/watch?v=E42rUlxRZH8) covered in lightning!

[AttilaTheGeek]

Why would you ever not pick the Urumi?

I guess if you wanted to take the rocket launcher instead.

[Twilightwyrm]

I will, uh...get to it when I have a free two hours? :smalltongue:

My gut says the Fighter, but only because getting off 75% sneak attacks with a ranged weapon is nearly impossible unless you have a mechanic that can make people flat-footed, like Dazzling Display and Shatter Defenses. Do you want me to model it with something more realistic, or are you confident in the 75% sneak attacks? If you are, it's going to be a close race.

That's cool, I'd imagine it is a lot of numbers to crunch.

The 75% SA chance is just a number I pulled off the top of my head to account for what percentage of the time I expect my strategy will not be working. The DM doesn't seem terribly inclined to use SA immune/resistant monsters, and I'm expecting invisibility and greater invisibility support much of the time if I go that route. I was not, however, under the presumption that I would be getting off SAs off 100% or even 90% of the time, hence the 75% estimation. It can be amended to something else, if you think that would be a better model for what such a build would be facing. I wonder though: do you predict the gap would be that wide without 75% or higher sneak attack chances?

[Squirrel_Dude]

A pretty simple one, i think, but I don't want to try and do it.

What's the chance of a Level 20 monk in Pathfinder hitting a Pit Fiend (AC 38) 4 times using flurry.
- Monk has 28 strength
- +5 Amulet of Might Fists
What is the most likely number of times that the monk will hit the Pit Fiend?

What's the chance of a Level 20 Fighter in Pathfidner hitting a Pit Fiend 4 times using his full attack.
- Fighter has 28 Strength
- Fighter has +5 bonus to attacking with this weapon (weapon focus + weapon training 1)
What is the most likely number of times that the fighter will hit the Pit Fiend?I think I mostly answered my own question but I would hope that someone else would be kind enough to check my math.

The monk has a 21% chance to hit an enemy 4 times
- I didn't determine the likeliest number of hits

The fighter has a 3% chance to hit an enemy with all 4 attacks
- The fighter is most likely to hit the enemy two times (46%)

[TuggyNE]

I think I mostly answered my own question but I would hope that someone else would be kind enough to check my math.

The monk has a 21% chance to hit an enemy 4 times
- I didn't determine the likeliest number of hits

The fighter has a 3% chance to hit an enemy with all 4 attacks
- The fighter is most likely to hit the enemy two times (46%)

That doesn't seem to be quite right, but it is close. Assuming the fighter has a plain (non-masterwork, non-magical weapon), he hits 1.78% of the time, and the monk hits 24.65%. However, if we assume a +5 weapon for the fighter, that goes up to 16.96%. Full details (http://anydice.com/program/1e93). (As usual, I adapted my baseline AnyDice attack code to suit the situation.)

[Squirrel_Dude]

That doesn't seem to be quite right, but it is close. Assuming the fighter has a plain (non-masterwork, non-magical weapon), he hits 1.78% of the time, and the monk hits 24.65%. However, if we assume a +5 weapon for the fighter, that goes up to 16.96%. Full details (http://anydice.com/program/1e93). (As usual, I adapted my baseline AnyDice attack code to suit the situation.)Thank you.

Ah, I see the error now. I was making 28 Str = to +7 modifier instead of +9 for some reason.

[classy one]

I have a math question; well it's more of a cost benefit question.
You have established that vicious gives the most bang for the buck, but what if it was combined with vampiric (MIC pg 45). Provides +1d6 damage and heals for that same amount but it costs +2. Would +3d6 for +3 cost be under priced or even? My DM is refusing to let me have this weapon but I think it should be okay.

[AttilaTheGeek]

I have a math question; well it's more of a cost benefit question.
You have established that vicious gives the most bang for the buck, but what if it was combined with vampiric (MIC pg 45). Provides +1d6 damage and heals for that same amount but it costs +2. Would +3d6 for +3 cost be under priced or even? My DM is refusing to let me have this weapon but I think it should be okay.

A +3d6 weapon priced at +3 is just the same as a Flaming, Frost, Shocking weapon. In other words, a good choice, but not super powerful. If you can afford a +3 weapon, Dancing is recommended, or Speed if you don't have anyone who can cast Haste.

[Razanir]

"1d100": 60.5

Just as a nit-picky thing, that should be 50.5


I'm sorry. I meant, I wanted to know the distribution of the varrious scores (ability scores, saves, melee and ranged attack bonuses, hp, and the three types of AC) among the characters found linked in the first table I presented.

If this still makes no sense, or is utterly useless, or is a waste of time, I appologize for making you expend even a thought on it.

Actually, if you could point me to a decent (and free and easy to use) statistics engine (is that the term I want? I mean a program or website I can plug data points into and get a statistical breakdown of the set as output.) I'd be grateful. I searched, but I only found links to data analysis suites for sale.


Other than that, I can't really help you, sorry.

Attila, I can handle this one.


By what method would you go about contrasting the damage of a longsword (1d8) and a falchion (2d4) over the course of an encounter? It would seem that on a single swing, the Longsword (average damage 4.5) is outclassed by the Falchion (statistical probability of rolling 5) but I know my logic is faulty in that instance. But over the course of an encounter in which each hits, say, 20 times, the longsword has an increased chance of rolling either 1 or 8 damage. So which is optimal, if we ignore criticals?

And is the same formula directly applicable to a Greataxe (1d12) and a Greatsword (2d6)?

Apologies in advance for the garbled question.

You're really asking two questions here. Which does more damage on average and which does damage more consistently. The falchion wins on both accounts.

Math:
Not going to bother showing that the expected values are 4.5 and 5


Var(1d8) = E((1d8)²) - E(1d8)² = 25.5 - 20.5 = 5
Var(2d4) = 2 * Var(1d4)
Var(1d4) = E((1d4)²) - E(1d4)² = 7 - 6.25 = .75
Var(2d4) = 2 * .75 = 1.5

Summary of the math. We all know the expected values of 1d8 and 2d4 are 4.5 and 5 respectively. So the falchion does more damage on average. It also has a lower variance (1.5 compared to 5), so it does that damage more consistently. Overall, I would recommend the falchion because while it doesn't do insanely high damage as often, it does decent damage more reliably.

Math for the greataxe and greatsword:

Var(1d12) = E((1d12)²) - E(1d12)² = 54.17 - 42.25 = 11.92
Var(2d6) = 2 * Var(1d6)
Var(1d6) = E((1d6)²) - E(1d6)² = 15.17 - 12.25 = 2.92
Var(2d6) = 2 * 2.92 = 58.7

The same logic holds with the greatsword and the greataxe.

EDIT: My math is under the very reasonable assumption that all theoretical die rolls are independent. Otherwise there'd be a nasty covariance term

[Squirrel_Dude]

There is already great information (http://www.darkshire.net/~jhkim/rpg/dnd/abilities.html) on average value for ability scores in a 4d6 drop lowest. I don't like the 4d6-lowest x 6 version of generation, and I'm thinking of making so that you fill out the six scores by doing 4d6-lowest 8 times.


What would be the effect on the average values for abilities scores in a 4d6-lowest generation if you were allowed to pick from 8 rolls of the dice instead of 6?

[Story]

That depends on whether you're still using reroll rules. Under the standard 4d6 drop 1, you reroll if your highest score is below 14 or your total bonus is 0 or below.

[AttilaTheGeek]

What would be the effect on the average values for abilities scores in a 4d6-lowest generation if you were allowed to pick from 8 rolls of the dice instead of 6?

I'm sure there's some way to do that using anydice, but having absolutely zero experience with it I really couldn't tell you.

[Metahuman1]

For 3.5 D&D, with no setting specific material and no Leadership feats or variants, and not counting str mod (If you can add other ability scores, that's fine though.).

How can I get a +6 to hit for less then 6K gold?

And then how can I keep that scaling up so that every additional level I get an additional +1 to hit?(IE, +7 at 7th lvl, +8 at 8th lvl, so on.)

[Story]

Assuming no rerolling, choosing out of 8 for 4d6 gives you the following probabilities of getting at least one score of x or more

18: 12.25%
17: 37.93%
16: 67.30%

If you were only rolling 6 times, it'd be 9.35%, 30.07%, and 56.76% respectively. Note that this is without rerolling. Under standard rules, the odds of getting an 18 are actually a little over 10%.

[AttilaTheGeek]

For 3.5 D&D, with no setting specific material and no Leadership feats or variants, and not counting str mod (If you can add other ability scores, that's fine though.).

How can I get a +6 to hit for less then 6K gold?

And then how can I keep that scaling up so that every additional level I get an additional +1 to hit?(IE, +7 at 7th lvl, +8 at 8th lvl, so on.)

I'm a Pathfinder player, so I'm probably missing quite a few, but...

+1 from a +1 weapon
+1 from Weapon Focus
+2 from Inspire Courage
+1 (I think) from some Dragon Shaman aura, if it stacks
and at that point you'd be looking at +4 or +5 from STR, but without that I don't know of any more.

[Squirrel_Dude]

Assuming no rerolling, choosing out of 8 for 4d6 gives you the following probabilities of getting at least one score of x or more

18: 12.25%
17: 37.93%
16: 67.30%

If you were only rolling 6 times, it'd be 9.35%, 30.07%, and 56.76% respectively. Note that this is without rerolling. Under standard rules, the odds of getting an 18 are actually a little over 10%.Interesting. Thank you.

May I ask how you got those number, if you can sum it up in short, or if you used Any Dice how you did it.

[Bowbreaker]

I have a question for you:
What are the lowest requirements to make the Feycraft weapon template (DMG II p.275) actually worth its cost, damage wise? I'd like to have this calculated once taking into regards the Weapon Finesse feat and once without taking any feats into acount.

[AttilaTheGeek]

I have a question for you:
What are the lowest requirements to make the Feycraft weapon template (DMG II p.275) actually worth its cost, damage wise? I'd like to have this calculated once taking into regards the Weapon Finesse feat and once without taking any feats into acount.

Just to make sure I'm understanding you correctly, you're asking "How expensive does the Dancing special quality have to be for the 10% off it from Feycraft to exceed the 1,500 gp Feycraft cost"?

If that's what you're asking, then it's always worth it. The least you can pay for Dancing is 30,000 gp by upgrading a +1 weapon to a +1 Dancing weapon. At that cost, paying 1,500 gp for Feycraft gives a 10% discount of 3,000 gp off, saving 1,500 gp.

It gets even better at high levels too. Upgrading a +5 weapon to a +5 Dancing weapon costs 78,000 gp, and adding on Feycraft first saves 6,300 gp.

[Zweisteine]

First, I'll say that I got lazy and didn't read the whole thread, so this may have been brought up before.

On the first page, you made a recommendation for +1 weapon enchantments. You recommended an enchantment granting 1d6 extra damage. I have heard from some friends of mine (who are extraordinary at math), that just getting a +1 enhancement is better than increasing the actual damage (more hits deal more damage than bigger hits).
Is that true?

[AttilaTheGeek]

First, I'll say that I got lazy and didn't read the whole thread, so this may have been brought up before.

On the first page, you made a recommendation for +1 weapon enchantments. You recommended an enchantment granting 1d6 extra damage. I have heard from some friends of mine (who are extraordinary at math), that just getting a +1 enhancement is better than increasing the actual damage (more hits deal more damage than bigger hits).
Is that true?

It depends on how hard you hit. If you hit for a million, you really want to not miss, but if you only hit for 1d6, adding another d6 doubles your damage.

[Zweisteine]

But, in general, those who can afford anything better than a +1 weapon are dealing more than 1d6 damage, and more hits will deal more damage, and every +1 counts when you are attacking.
Also, at those levels, the damage dealt by the dice will be considerably less than the bonus, and more hits is more damage.
Every +1 to attack means you'll hit 5 percent more often. (incomplete thought)

(Now I'll have to all my friend and get the actual math...)


Warning: The above and below thoughts are rather disorganized and/or incomplete.

Edit: And if you're dealing only 1d6 damage, yoy have no business getting a weapon better than +1.

[ddude987]

Hello! So I was wondering if you could work some mathomagics on a probobility for the feat Lightning Mace. I don't think it has been done (or my google-fu just sucks). Currently with a crit range of 15-20/x4 and 4 attacks, though a variable number of attacks would be sweet. I tried to figure this one out for a while but I'm not the best learned at math. If you can help thanks!

[AttilaTheGeek]

Hello! So I was wondering if you could work some mathomagics on a probobility for the feat Lightning Mace. I don't think it has been done (or my google-fu just sucks). Currently with a crit range of 15-20/x4 and 4 attacks, though a variable number of attacks would be sweet. I tried to figure this one out for a while but I'm not the best learned at math. If you can help thanks!

Sure thing. Can you specify weapon damage, attack bonus, and target AC, or should I leave it variable? If I do, it'll be a general formula full of [W], AC, and B terms and very messy.

[ddude987]

Sure thing. Can you specify weapon damage, attack bonus, and target AC, or should I leave it variable? If I do, it'll be a general formula full of [W], AC, and B terms and very messy.

Actually I was just looking for the average number of attacks... if you don't mind taking the time to do a general formula then that would be awesome! However, if you just want to do the average number of attacks in a formula that would be sweet to. For example, I have 5 attacks from itterive and whatever else, how many attacks will I make on average?

[lynessawarblade]

Hi! I'm ddude987's girlfriend :)

I wrote a Java program to determine the average number of attacks with the lightning mace feat for any number of main attacks and any crit range.


//LynessaWarblade 3.6.2013
import javax.swing.JOptionPane;

public class AverageAttacks {
public static double probCrit;
public static double notCrit;
public static int mainAttacks = -1;

public static void main(String[] args) {
int lowestCritNum = -1;
while(lowestCritNum == -1) {
try {
lowestCritNum = Integer.parseInt(JOptionPane.showInputDialog(null,"What is the lowest number you crit on?","Input Box",JOptionPane.OK_OPTION));
if(lowestCritNum < 1 || lowestCritNum > 20) {
lowestCritNum = -1;
JOptionPane.showMessageDialog(null,"Enter a number between 1 and 20.","Error",JOptionPane.ERROR_MESSAGE);
}
}
catch (Exception e) {
JOptionPane.showMessageDialog(null,"Enter an integer.","Error",JOptionPane.ERROR_MESSAGE);
}
}
probCrit = calcCritProb(lowestCritNum);
notCrit = 1-probCrit;
while(mainAttacks == -1) {
try {
mainAttacks = Integer.parseInt(JOptionPane.showInputDialog(null,"How many attacks do you normally make?","Input Box",JOptionPane.OK_OPTION));
if(mainAttacks < 1) {
mainAttacks = -1;
JOptionPane.showMessageDialog(null,"Enter a number >= 1.","Error",JOptionPane.ERROR_MESSAGE);
}
}
catch (Exception e) {
JOptionPane.showMessageDialog(null,"Enter an integer.","Error",JOptionPane.ERROR_MESSAGE);
}
}


if(probCrit == 1) {
System.out.println("infinity");
System.exit(0);
}
double lastProb = 1;
int numAttacks = mainAttacks;
double avgAttacks = 0;
while(lastProb*(numAttacks-1) > .00000001) {
lastProb = calcProb(numAttacks);
avgAttacks += lastProb*numAttacks;
numAttacks++;
System.out.println((numAttacks-1) +" "+ lastProb);
}
System.out.println("\n"+avgAttacks);
}
public static double calcCritProb(int lowCrit) {
return .05*(21-lowCrit);
}

public static double calcProb(int attacks) {
int choices = calcWays(mainAttacks,attacks-mainAttacks);
if(choices == 0) {
System.out.println("eep");
return (Math.pow(notCrit,mainAttacks)*Math.pow(probCrit,( attacks-mainAttacks)));
}
return (Math.pow(notCrit,mainAttacks)*Math.pow(probCrit,( attacks-mainAttacks)))*choices;
}
public static int calcWays(int max, int extra) {
if(extra == 0) {
//System.out.println(max+"C"+extra);
return 1;
}
if(extra < 0) {
System.out.println("error in calcWays");
return -1;
}
int ways = 0;
for(int i = 1; i <= max && i <= extra; i++) {
int currentIter = choose(max,i);
int extraAttacks = extra-i;
currentIter *= calcWays(i,extraAttacks);
ways += currentIter;
}
return ways;
}

public static int choose(int total, int toChoose) {
//System.out.print(total+"C"+toChoose+" ");
return fac(total)/(fac(total-toChoose)*fac(toChoose));
}
public static int fac(int num) {
if(num < 0) {
System.out.println("factorial of negative?");
return -1;
}
if(num <= 1) {
return 1;
}
return num*fac(num-1);
}
}

It would be less obnoxiously long without the error catching.

[RFLS]

Actually I was just looking for the average number of attacks... if you don't mind taking the time to do a general formula then that would be awesome! However, if you just want to do the average number of attacks in a formula that would be sweet to. For example, I have 5 attacks from itterive and whatever else, how many attacks will I make on average?

It's just


([W] + ([W] * [Range/20])) + (([W] * [Range/20]) *[Range/20])

where [W] is the initial number of attacks per round you're taking and Range is your crit range. With 4 attacks a round and a crit range of 15-20, you end up with, on average, about 5.56 attacks every round.

EDIT: Disclaimer: My formula isn't exact. You iterate downwards, but after the second iteration, it stops mattering, really. Mine'll get you pretty darn close, though.

[RFLS]

And, just because I want to see if I can inflict some suffering, a question: Can you provide a generic formula that will tell me whether I should choose 1 point of to-hit chance or 1 point of damage on my weapon roll, for an arbitrary initial to-hit, initial weapon damage (within the range of Core weapons, of course), and initial AC? You can choose to standardize the weapon damage in the formula.

[Story]

Hi! I'm ddude987's girlfriend :)

I wrote a Java program to determine the average number of attacks with the lightning mace feat for any number of main attacks and any crit range.

It would be less obnoxiously long without the error catching.

Have you considered learning Python? Java's pretty much the worst language you could pick for stuff like this.

[lynessawarblade]

And, just because I want to see if I can inflict some suffering, a question: Can you provide a generic formula that will tell me whether I should choose 1 point of to-hit chance or 1 point of damage on my weapon roll, for an arbitrary initial to-hit, initial weapon damage (within the range of Core weapons, of course), and initial AC? You can choose to standardize the weapon damage in the formula.

damage ? (hitProb*(1+probCrit))/((improvedHitProb-hitProb)*(1+probCrit))

hitProb: The probability that you hit w/o the bonus = (AC-atkBonus+2)/20
probCrit: The probability that you crit = (21-minCrit)/20
improvedHitProb: The probability that you hit w/ the bonus = (AC-atkBonus+3)/20

so all together...

damage ? ((AC-atkBonus+2)/20*(1+(21-minCrit)/20))/(((AC-atkBonus+3)/20-(AC-atkBonus+2)/20)*(1+(21-minCrit)/20))

If damage > [snip], choose +1 to hit. Otherwise choose +1 to damage.

Note: This doesn't account for 20s autohitting nor for confirming crits.

[RFLS]

Have you considered learning Python? Java's pretty much the worst language you could pick for stuff like this.

Seconded for great truth!

[lynessawarblade]

Have you considered learning Python? Java's pretty much the worst language you could pick for stuff like this.

I already know python. It's just I didn't feel like downloading the IDE.

[Story]

What IDE? Unlike Java, you don't need an IDE for Python. Though Sublime Text 2 is nice.

[Bowbreaker]

Just to make sure I'm understanding you correctly, you're asking "How expensive does the Dancing special quality have to be for the 10% off it from Feycraft to exceed the 1,500 gp Feycraft cost"?

If that's what you're asking, then it's always worth it. The least you can pay for Dancing is 30,000 gp by upgrading a +1 weapon to a +1 Dancing weapon. At that cost, paying 1,500 gp for Feycraft gives a 10% discount of 3,000 gp off, saving 1,500 gp.

It gets even better at high levels too. Upgrading a +5 weapon to a +5 Dancing weapon costs 78,000 gp, and adding on Feycraft first saves 6,300 gp.

I actually was asking something more akin to "What is the simplest/earliest situation where spending the money to make a weapon Feycraft is worth it?"
I didn't actually know that it always gave a discount to the dancing enhancement, so its probably always worth it at the stage where you'd try to get that. But what about earlier? Is the 1500 gp cost coupled to the damage reduction ever worth the Finesse related stuff (and the weight reduction I guess) for specific weapons during specific times in the game or is there always a more efficient way to go for any kind of normal melee build that would benefit from that in the first place.

[AttilaTheGeek]

What finesse stuff? I didn't see anything there. As for weapon weight, if you're actually carrying a meelee weapon, you have enough strength to not worry about weight.

[Archmage1]

Feycraft grants weapon finesse, if the weapon was already light.

[Urpriest]

Ooh, hadn't seen this thread before. I've got a problem to suggest, actually:

At what point (in terms of the save bonuses of opponents, and assuming that stagger is as bad as being unable to act for the opponents in question) does Waves of Ecstasy (http://www.d20pfsrd.com/magic/all-spells/w/waves-of-ecstasy) beat Persistent (http://www.d20pfsrd.com/feats/metamagic-feats/persistent-spell-metamagic) Greater Command (http://www.d20pfsrd.com/magic/all-spells/c/command)?

[AttilaTheGeek]

Feycraft grants weapon finesse, if the weapon was already light.

Oh.
...Derp.

You can't really give Weapon Finesse a value, though. It doesn't do anything but make you MAD if you don't have a way to get dex to damage. The benefits of being SAD exist, but they're hard to quantify. Or if you meant it lets you get another feat slot? Again, for that, I'd have to find the one feat that adds the most damage and compare them (Power attack doesn't work for light damage), but there's no way I'm hunting through every sourcebook ever for the most damaging feat.

[Archmage1]

Probably craven, at +1 per hd, but does require a SA.

[Bowbreaker]

Feycraft Weapon also lets the actual feat Weapon Finesse aply to one-handed weapons that aren't light. So a Feycraft Longsword, Trident or Warhammer for instance could benefit from your dexterity through your Weapon Finesse Feat.
I'd really like to see some lithe Elf Rogue elegantly swinging his delicate Feycraft Warhammer :smallbiggrin:.

[Tokuhara]

I am planning on buildin a Dwarf TWF Barbarian build themed around axes. I'm kind of wondering on two things:

1. Battle Axe vs Dwarven Waraxe. Normally, I'd lean with the Waraxe as my main-hand weapon, but since I can equally choose either, which is better for two-weapon fighting with a handaxe (to my knowledge, the only "Light" axe available)

2. We are using a 28 Point-Buy with stats starting at 8. If I want to TWF, what is the "ideal" option for the 28 PB?

[AttilaTheGeek]

I am planning on buildin a Dwarf TWF Barbarian build themed around axes. I'm kind of wondering on two things:

1. Battle Axe vs Dwarven Waraxe. Normally, I'd lean with the Waraxe as my main-hand weapon, but since I can equally choose either, which is better for two-weapon fighting with a handaxe (to my knowledge, the only "Light" axe available)

The Waraxe hits for 1d10 and the Battleaxe hits for 1d8, and everything else is the same. No contest.


2. We are using a 28 Point-Buy with stats starting at 8. If I want to TWF, what is the "ideal" option for the 28 PB?

Sorry, I'm gonna pass on actually mathing out every combination. Way too much work. As far as I know, though, the best thing to do is to dump STR and pump DEX with two Agile (http://www.d20pfsrd.com/magic-items/magic-weapons/magic-weapon-special-abilities/agile) weapons.

[Scizor]

This is a 3.5e question

So, I have another "Weapon enhancement comparison" request. Could you compare the Soulknife's enhancements on his mind blade? Here's a link (http://www.d20srd.org/srd/psionic/classes/soulknife.htm#mindBladeEnhancement)
Also, which of the shapes (short sword (possibly TWF), longsword or Bastard sword) are most optimal/cost-effective?
Assumptions:
Level 6 Soulknife with 18 strength, Weapon foucs (mind blade), +1 enhancement already.
The to-hit AC is... varying. Pick a number.

Thanks in advance!

[Addi]

This is a very nice resource - thanks.
I hope, my question is not too complicated. I try to include every necessary detail.

I've got a magus working pretty well in a current campaign but at the moment I can't seem to decide how to approach our next opponent - a Great Wyrm Red Dragon

The Dragon (Spell Resistance: 33/ Armor Class: 39 (Touch: 0)/ Cold vulnerability/ Ref-Save:+14)

Magus:
Shocking Grasp --> +23 against SR / 60 + 5d6 Damage
Pure Cold-Damage with his Dwarven Waraxe
(optional Empowered Cone of Cold --> +19 agains SR)
Attack: +24/+24/+19/+14 (hasted)
Weapon Damage: 1d10+18 (cold damage)

My Options are:
1.) Shocking Grasp + Full Attack
2.) Shocking Grasp channeled through weapon + Full Attack (This gives one more additional weapon damage at a +24 vs. normal AC)
3.) Emp. Cone of Cold for more Damage (x1.5 cold vulnerability), but lower probability of piercing the SR + Full Attack

What is the best option agains this foe?

(I don't dare to ask for Power Attack :smallsmile:)

[Blackadam]

i was redirected here because i'm just awesome i think :P

well i posted this question on here and was told i should try this thread really

"I was wondering if anyone knows or if there is available or will be available a program where you can create your character and that it can calculate the math for you (BAB, Saves skills points, ability modifiers, number of feats, spells, etc) to cut down on character creation time? I use to use E-tools but honestly I found it only useful for making mass simple characters as appose and very limiting to making intricate characters where you would need to sift through 8 books to explain how you can do half of what the character is able to do. (i'm looking for something i can use with 3.5 and possible pathfinder)"

In a bit more detailed of what i'm looking for which i'm not sure if it is out there or something close to it
like chose race
enter the level for your toon
either roll stats with your dm and input them or have it roll stats for you and you arrange them.
it will say okay you have X non epic feats Y epic feats
and once you select how you chose your levels and pick your feats it will say okay you have "Blah" skill points go use them
etc

This is where i spend the bulk of my time checking and rechecking all the math so that i either have it right or with the least amount of math errors. the ni have 3 people check it for me to be sure its good

sorry for rambling i do that at times :/

[AttilaTheGeek]

You posted
lol okay thanks where exactly should i post this??

And I replied
Things specific to 3e, 3.5, Pathfinder, or other d20 systems go in the 3e/3.5/d20 (http://www.giantitp.com/forums/forumdisplay.php?f=59) forum.

which was intended to redirect you to the d20 forum, not to the link in my sig, which led you here.

Psliontech's answer still stands.


Here's what you might be looking for. (http://bit.ly/10mrKO9)

[AttilaTheGeek]

This is a very nice resource - thanks.
I hope, my question is not too complicated. I try to include every necessary detail.

I've got a magus working pretty well in a current campaign but at the moment I can't seem to decide how to approach our next opponent - a Great Wyrm Red Dragon

The Dragon (Spell Resistance: 33/ Armor Class: 39 (Touch: 0)/ Cold vulnerability/ Ref-Save:+14)

Magus:
Shocking Grasp --> +23 against SR / 60 + 5d6 Damage
Pure Cold-Damage with his Dwarven Waraxe
(optional Empowered Cone of Cold --> +19 agains SR)
Attack: +24/+24/+19/+14 (hasted)
Weapon Damage: 1d10+18 (cold damage)

My Options are:
1.) Shocking Grasp + Full Attack
2.) Shocking Grasp channeled through weapon + Full Attack (This gives one more additional weapon damage at a +24 vs. normal AC)
3.) Emp. Cone of Cold for more Damage (x1.5 cold vulnerability), but lower probability of piercing the SR + Full Attack

What is the best option agains this foe?

(I don't dare to ask for Power Attack :smallsmile:)

First off, why would you ever not channel the Shocking Grasp through spellstrike? All else nonwithstanding, option (2) gives a free extra weapon attack over option (1). In the same vein, options (2) and (3) both have a full attack included, so there's no reason to bother mathing it out if it's added to both. Edit: herp derp. Calculus I can do, reading not so much. Option (1) is against touch AC 0. Well, for that, you need to calculate your THAC0 stat. Math spoiler:
Option (1) adds 60+5d6 (average 77.5) with a touch attack against AC 0, which always hits. That's a very simple formula.

1 * 77.5 = 77.5 damage

Option (2) adds a weapon attack and 60+5d6 (average 77.5) damage over a full attack. Your chance to hit Spellstrike is a +24 attack against AC 39. You need to roll at least a 15, so you have a 6/20 chance to hit. Weapon damage averages 23.5, but multiplied by 1.5 it's 35.25 damage. Shocking Grasp has +23 piercing against SR 33, so you need at least a 10, and you have an 11/20 chance to get it through. The damage comes down to this.

6/20 * [ 35.25+ 11/20 * 77.5] = 23.362 damage

Option (3) adds 15d6 (averaging 52.5) *1.5 from empowered * 1.5 vulnerability for an average of 118.125 damage if it pierces SR. You have +19 against SR 33, so you need to roll a 14 and you have a 7/20 chance of getting it through. However, you don't also have to hit with a weapon attack, so the formula is simpler.

7/20 * 118.125 = 41.313 damage

You'll do roughly 3/4 more additional damage with Cone of Cold over Maximized Intensified Empowered Shocking Grasp. (Note that it's not 3/4 more total damage, but 3/4 more added.) Edit: forgot that (1) hits against its touch AC of 0. Since it always deals its damage and always hits, it wins by a very large margin. CoC still beats the channeled version, though, because even though CoC has a lower chance to beat SR, Shocking Grasp has to beat SR and AC.

I also want to commend you on the way you phrased the question. I wish all my questions had that much given in such a convenient way. :smallbiggrin: And good luck slaying the dragon!

[Razanir]

I'm sorry. I meant, I wanted to know the distribution of the varrious scores (ability scores, saves, melee and ranged attack bonuses, hp, and the three types of AC) among the characters found linked in the first table I presented.

If this still makes no sense, or is utterly useless, or is a waste of time, I appologize for making you expend even a thought on it.

Actually, if you could point me to a decent (and free and easy to use) statistics engine (is that the term I want? I mean a program or website I can plug data points into and get a statistical breakdown of the set as output.) I'd be grateful. I searched, but I only found links to data analysis suites for sale.

Finally getting around to this. (It's the pre-Spring Break lull in homework) Can you get me a table with their hit dice? I feel like those would lead to a more interesting distribution than just looking at hp. Like how the hydra lists 11d12+88 not just 149 hp. Or the couatl having 10d10+1d8+33. I'd need it for the Yeti, Behir, Androsphinx, Spider and Pseudodragon.

[Talakeal]

Recent discussion in the 5E thread has gotten me curious, does anyone know the exact odds of an underdog winning an opposed skill test?

Assuming 1d20 + modifier, highest roll wins, reroll ties.

I know that if the characters have even skills the odds are of course 50 / 50, and if one character has more a 20 or more point advantage they are guaranteed victory.

I think the odds of overcoming a 19 point advantage are 1/400 but I am not sure, and beyond that I have no clue.

Any help for a 1-18 point advantage? (and 9-20 if I am wrong above)

(BTW, I did not read through the whole thread. If someone has already answered this question here or someplace else a point in the right direction will do me fine).

Thanks!

[Story]

How far did you read? I answered that exact question in the third post in this thread.

Edit: My table assumes attacker wins ties, but it's easy to adjust for rerolling ties.

[Talakeal]

How far did you read? I answered that exact question in the third post in this thread.

Edit: My table assumes attacker wins ties, but it's easy to adjust for rerolling ties.

Clearly not far enough :smallsmile: Honestly I was going to start a new thread for it and then I saw this one was already here and just read the OP.

Forgive my badness, but how do I adjust it to account for rerolling ties or actual draws on a tie?

[Addi]

..... And good luck slaying the dragon!

Thanks a lot! The information will really help me in doing so and now I even understand, how to calculate this. :)
There is one more question though. My rudimentary mathematical skills don't allow me to calculate the impact of the granted save for Cone of Cold.
Spell DC would be 21 and the Reflex save bonus of the dragon +14.
I guess it's something like 41.313 - 0.3 * 41.313/2

Now you encouraged me to do this stuff myself - thanks.
Next one is the inclusion of natural hits and misses :)

Keep up the good work!

[Saito Takuji]

okay, i have one, here

was wondering on ways to have my players roll for stats, and wanted to have them have 2 superior ability scores, 2 that would likeley be a bit above average, and 2 that would be average- a bit below average.

was thinking someting along the lines of (2) times each


so ultimatley i was wondering about what sort of rolls would get the types of results i would want

something with a general average fo like 15-17 or so

something with a general average from about 12-14

and the last 2 i would be using the standard 3d6

so any advice on what sorts of die rolls to use for the first 2 sets?

[AttilaTheGeek]

okay, i have one, here...

Perhaps you might find these to your liking?

These (http://anydice.com/program/1f37)are possible distributions for the high score- 3d6+6 and 5d6b4. They both average around 16.

These (http://anydice.com/program/1f39) distributions (8d6b6 divided by 2, 4d6b3, and 4d8b2) might work for the average stat.

For the low stat, you might want to try 1d6+6, which rolls between 7 and 12, giving you a little more reliability in your "bad but not too bad" stat.

[Story]

Well, I don't know about distributions, but 6d6, reroll 1s, drop highest and 2 lowest will give you an average very close to 13. It could be useful for your 'average' stats.

For the 'good' stat, 8d6, reroll 1s, drop 5 lowest gives you an average very close to 16.

[Saito Takuji]

sounds about good, will go with that likeley then

[Bowbreaker]

I have another question. How much is the average damage per turn of a +1 Keen Rapier and how much that of a +1 Fiery Rapier? Assume Weapon Finesse, 14 Dexterity and 10 Strength.

[yougi]

I have another question. How much is the average damage per turn of a +1 Keen Rapier and how much that of a +1 Fiery Rapier? Assume Weapon Finesse, 14 Dexterity and 10 Strength.

What is your BAB? And what is your average enemy AC? And by Fiery, do you mean Flaming or Fiery Burst?


okay, i have one, here

was wondering on ways to have my players roll for stats, and wanted to have them have 2 superior ability scores, 2 that would likeley be a bit above average, and 2 that would be average- a bit below average.

was thinking someting along the lines of (2) times each


so ultimatley i was wondering about what sort of rolls would get the types of results i would want

something with a general average of like 15-17 or so

something with a general average from about 12-14

and the last 2 i would be using the standard 3d6

so any advice on what sorts of die rolls to use for the first 2 sets?

If you want to keep the max at 18, (4d6b2)+6 is a pretty solid 15-17. And 4d6b3 is a good 12-14.

[Bowbreaker]

I only have a BAB of 1 and the enemies are whatever is considered normal for a group of five 6th level city adventurers I guess. Flaming was what I meant. Always confuse the two :smallredface:.

[Kornaki]

I only have a BAB of 1 and the enemies are whatever is considered normal for a group of five 6th level city adventurers I guess. Flaming was what I meant. Always confuse the two :smallredface:.

How do you have a BAB of 1 and you're level 6? :smallconfused:

[Jack Zander]

I've got one for you! In 3.5, will you get more damage from a driud wildshaped into a dire lion (http://www.d20srd.org/srd/monsters/direLion.htm) using pounce, or a rhino (http://www.d20srd.org/srd/monsters/rhinoceros.htm) with it's charge attack?

What if we put Power Attack (http://www.d20srd.org/srd/feats.htm#powerAttack)/Shock Trooper (http://dndtools.eu/feats/complete-warrior--61/shock-trooper--2614/) in the mix?

P.S. What other typical options will make one better than the other in terms of damage output?

[Bowbreaker]

How do you have a BAB of 1 and you're level 6? :smallconfused:

By being multiclassed into a total of three classes with Rogue-like BAB progression... I'm not a primary combatant. I have 115 skill points freely distributed though. And that while being non-optimized for IC flavor reasons. Else I'd have 11 more.

[Story]

See if you can get the fractional BAB and save rules instated. It makes multiclassing much fairer.

[Bowbreaker]

I rather like my +9 Reflex :smallcool:. And isn't having no XP penalty already making multiclassing stronger than designed? I'll think about it though.

[Story]

Well the multiclassing penalty is poorly designed. All it does is shaft melee without affecting spellcasters at all. It also has the unintentional side effect of forcing you to dip as much as possible once you've started mutliclassing, leading to 15 class monstrosities.

[Urpriest]

I rather like my +9 Reflex :smallcool:. And isn't having no XP penalty already making multiclassing stronger than designed? I'll think about it though.

You'd keep that, though. Fractional Saves doesn't get rid of the +2 from entering a new class.


Ooh, hadn't seen this thread before. I've got a problem to suggest, actually:

At what point (in terms of the save bonuses of opponents, and assuming that stagger is as bad as being unable to act for the opponents in question) does Waves of Ecstasy (http://www.d20pfsrd.com/magic/all-spells/w/waves-of-ecstasy) beat Persistent (http://www.d20pfsrd.com/feats/metamagic-feats/persistent-spell-metamagic) Greater Command (http://www.d20pfsrd.com/magic/all-spells/c/command)?

Bringing this up again in case it got missed.

[AttilaTheGeek]

Bringing this up again in case it got missed.

It did. Sorry about that. If P is the probability of a creature making a 5th-level save, then P-0.1 is the chance of that creature making a 7th-level save. For Persistent Greater Command to be better, 1-P^2 > P-0.1.
1.1-P^2 > P
-P^2 -P+1.1>0
*quadratic formula crunch crunch*
P < 0.66

If the minimum number rolled on a d20 needed to save is below a 13, then Persistent Greater Command is better.

Let me make that a little easier to interpret. I'm assuming the caster has a 26 in their casting stat, which is reasonable for 14th level (18 base + 6 headband + 2 level-up), putting Persistent Greater Command at DC 23 two times versus Waves of Ecstasy at DC 25. With a 14th-level caster, the creature needs to have less than a +10 Will save for Persistent Greater Command to be better.

[avr]

Also Waves of Ecstasy still staggers targets for one round on a successful save. That's got to make it better ... barring the slight awkwardness of a cone shaped effect rather than one target/level.

[AttilaTheGeek]

Also Waves of Ecstasy still staggers targets for one round on a successful save. That's got to make it better ... barring the slight awkwardness of a cone shaped effect rather than one target/level.

How many targets can you reliably hit in a 30' cone without hitting any allies?

How much can you count on your party member making a will save? If your BSF has a bad Will save at level 14, 10 WIS, and a Cloak of Resistance +4, then (s)he has an 85% chance to be taken out of the fight with your own Waves of Ecstasy. That is, unless you get him/her to move out of the way and take a whole bunch of attacks of opportunity.

[Urpriest]

It did. Sorry about that. If P is the probability of a creature making a 5th-level save, then P-0.1 is the chance of that creature making a 7th-level save. For Persistent Greater Command to be better, 1-P^2 > P-0.1.
1.1-P^2 > P
-P^2 -P+1.1>0
*quadratic formula crunch crunch*
P < 0.66

If the minimum number rolled on a d20 needed to save is below a 13, then Persistent Greater Command is better.

Let me make that a little easier to interpret. I'm assuming the caster has a 26 in their casting stat, which is reasonable for 14th level (18 base + 6 headband + 2 level-up), putting Persistent Greater Command at DC 23 two times versus Waves of Ecstasy at DC 25. With a 14th-level caster, the creature needs to have less than a +10 Will save for Persistent Greater Command to be better.

Your math is off. It should be 1-P^2 > 1.1-P, if we're comparing the same thing. With that correction, Persistent Greater Command is better for 0.11<P<0.89, so unless the opponent only can succeed on a 19 or can succeed even on a 2, Persistent Greater Command is better.

Does this change noticeably if we factor in duration? Say that combat lasts three rounds, and one is trying to maximize the number of rounds that the opponents are affected. I was mostly wondering how much of a disadvantage offering saves every round is when the risk is lowered due to Persistent. What about the fact that Waves of Ecstasy has a one-round effect even on a passed save?

[AttilaTheGeek]

Your math is off. It should be...

Yes, you're right, sorry. It's been a long day.

[yougi]

I have another question. How much is the average damage per turn of a +1 Keen Rapier and how much that of a +1 Fiery Rapier? Assume Weapon Finesse, 14 Dexterity and 10 Strength.

CR6 has an average AC of 19 (18.88), but probably between 15 and 23, so let's start with those digits. From what I get, you have +4 to hit with either rapier.

Hypothesis: If you crit, you double 1d6+1. With a flaming weapon, you always add 1d6 when you hit. For some reason, I believe the flaming weapon will be much better. And that the overall damage will suck.

KEEN:
AC15 Avg Dmg: (10/20*4.5)+(6/20*10/20*4.5)=2.925
AC19 Avg Dmg: (6/20*4.5)+(6/20*6/20*4.5)=1.755
AC23 Avg Dmg: (2/20*4.5)+(2/20*2/20*4.5)=0.495

FLAMING
AC15 Avg Dmg: (10/20*8)+(3/20*10/20*4.5)= 4.3375
AC19 Avg Dmg: (6/20*8)+(3/20*6/20*4.5)=2.6025
AC23 Avg Dmg: (2/20*8)+(2/20*2/20*4.5)=0.845

So against all enemies (except those with negative ACs, and even then), Flaming is 50% better.

[Talakeal]

You'd keep that, though. Fractional Saves doesn't get rid of the +2 from entering a new class.



Bringing this up again in case it got missed.

You sure it doesn't? I remember playing 3.0 in taking a dip every level and ending up with saves three or four times higher than the rest of the party who didn't exploit that. I thought it was stupid then and still do, I can't believe that is still how people play, let alone still raw even when using the more rational variant, but then again....

[Philistine]

You sure it doesn't? I remember playing 3.0 in taking a dip every level and ending up with saves three or four times higher than the rest of the party who didn't exploit that. I thought it was stupid then and still do, I can't believe that is still how people play, let alone still raw even when using the more rational variant, but then again....

That's how it was printed in UA, so… yep.

[Urpriest]

You sure it doesn't? I remember playing 3.0 in taking a dip every level and ending up with saves three or four times higher than the rest of the party who didn't exploit that. I thought it was stupid then and still do, I can't believe that is still how people play, let alone still raw even when using the more rational variant, but then again....

Remember, PrCs have the +2 included too, despite usually being intended to be entered by classes that already have that save high. Other WotC-published d20 systems do it differently, having only base classes get that +2, so clearly its inclusion was intentional.

[Gazzien]

Dice question; what's the difference in odds of rolling each number between:
1d10
2d10 low
2d10 high
2d10 average of the two?
-Results of X.5 are acceptable, if it's easier, or you can round up. Or down. Whatever you find the easiest, really. (If you could do both rounding up and rounding down, that would be really nice)

EDIT: I mean, for 1d10, it's a 10% chance for each number. For 2d10 average, I know it's a 1% chance for a 1, and 1% for a 10 (if you're not rounding), but past there, I'm stuck.

[yougi]

Dice question; what's the difference in odds of rolling each number between:
1d10
2d10 low
2d10 high
2d10 average of the two?
-Results of X.5 are acceptable, if it's easier, or you can round up. Or down. Whatever you find the easiest, really. (If you could do both rounding up and rounding down, that would be really nice)

EDIT: I mean, for 1d10, it's a 10% chance for each number. For 2d10 average, I know it's a 1% chance for a 1, and 1% for a 10 (if you're not rounding), but past there, I'm stuck.

Comes down to this.

{table="head"]Result| 1d10 | 2d10L1 | 2d10B1 |2d10Avg (Round down)|2d10Avg (Round up)
1| 10% |19%|1%|3%|1%
2| 10% |17%|3%|7%|5%
3| 10% |15%|5%|11%|9%
4| 10% |13%|7%|15%|13%
5| 10% |11%|9%|19%|17%
6| 10% |9%|11%|17%|19%
7| 10% |7%|13%|13%|15%
8| 10% |5%|15%|9%|11%
9| 10% |3%|17%|5%|7%
10| 10% |1%|19%|1%|3%
[/table]

Sorry about edits, math was wrong on my first try.

[TuggyNE]

{table="head"]Result| 1d10 | 2d10L1 | 2d10B1 |2d10Avg (Round down)|2d10Avg (Round up)
1| 10% |19%|1%|3%|1%
2| 10% |17%|3%|7%|5%
3| 10% |15%|5%|11%|9%
4| 10% |13%|7%|15%|13%
5| 10% |11%|9%|19%|17%
6| 10% |9%|11%|17%|19%
7| 10% |7%|13%|13%|15%
8| 10% |5%|15%|9%|11%
9| 10% |3%|17%|5%|7%
10| 10% |1%|19%|1%|3%[/table]

Just to check, I whipped this up in AnyDice (http://anydice.com/program/1f66/graph) (I'm addicted to that thing, seriously), and it seems to agree with you. :smallsmile:

[Gazzien]

Comes down to this.

{table="head"]Result| 1d10 | 2d10L1 | 2d10B1 |2d10Avg (Round down)|2d10Avg (Round up)
1| 10% |19%|1%|3%|1%
2| 10% |17%|3%|7%|5%
3| 10% |15%|5%|11%|9%
4| 10% |13%|7%|15%|13%
5| 10% |11%|9%|19%|17%
6| 10% |9%|11%|17%|19%
7| 10% |7%|13%|13%|15%
8| 10% |5%|15%|9%|11%
9| 10% |3%|17%|5%|7%
10| 10% |1%|19%|1%|3%
[/table]

Sorry about edits, math was wrong on my first try.
Thank you very much!

[Ardantis]

Attilla~

LOVE the math thread.

I've always heard how unreliable grappling can be, and I know from experience that even a strong grappler may be screwed over by poor relative rolls.

Here's my question-

What Str score must a lvl 13 Medium-sized character with full BAB progression need in order to have even odds of winning a grapple check against a young adult Red Dragon?

EDIT: This also includes making the touch attack to initiate the grapple, so I really need a better than even chance of winning the grapple check itself to make up for the imperfect chance of initiating the grapple. Not sure of the math here

http://www.d20srd.org/srd/combat/specialAttacks.htm#grapple

http://www.d20srd.org/srd/monsters/dragonTrue.htm#redDragon

How about a Large character? How about against a two-legged creature with the same stats?

I really just need to know how much Str/Attack Bonus/Grapple Bonus I'd need to make this possible.

Because every epic fantasy grappler needs to be able to wrassle Dragons at their CR. Even if they must "Inukchuck" to do it.

[yougi]

Just to check, I whipped this up in AnyDice (http://anydice.com/program/1f66/graph) (I'm addicted to that thing, seriously), and it seems to agree with you. :smallsmile:

Well, that's what I used, so it's actually agreeing with itself! :smallbiggrin:



What Str score must a lvl 13 Medium-sized character with full BAB progression need in order to have even odds of winning a grapple check against a young adult Red Dragon?

EDIT: This also includes making the touch attack to initiate the grapple, so I really need a better than even chance of winning the grapple check itself to make up for the imperfect chance of initiating the grapple. Not sure of the math here

http://www.d20srd.org/srd/combat/specialAttacks.htm#grapple

http://www.d20srd.org/srd/monsters/dragonTrue.htm#redDragon

How about a Large character? How about against a two-legged creature with the same stats?


(I'm kind of highjacking Attila's thread... oh well!)

Well, a YA Red Dragon has a touch AC of 8, so that means that with full BAB and enough Strength to reliably grapple it, you only miss on a 1 (and even then, if your DM use nat 1 = -10 rule, that will not be the case).

Now, the dragon's grapple modifier is +37, +8 for Huge size, so +45. That's your target to have even chances of succeeding. To achieve that with a +13 BAB, you'd need a +32 Strength bonus, or a 74-75 Strength score. If you were Large, OR if you have Imp. Grapple, you'd only need 66-67; if you have both large size and Imp. Grapple, you'd only need 58-59. To be sure you'd make it (instead of even odds), you'd need 40 more strength than what's listed.

And, as far as I know, number of legs don't affect grapples, do they?

[Preaplanes]

What is the curve on a "3d6, reroll 1s and 2s until there are none, drop lowest, add 6, best of two sets" stat line?

[Talakeal]

Remember, PrCs have the +2 included too, despite usually being intended to be entered by classes that already have that save high. Other WotC-published d20 systems do it differently, having only base classes get that +2, so clearly its inclusion was intentional.

Hmm, I always thought I was cheesing the system with my character who had 1 level dips in 20 different classes and ended up with obscene saving throws. To find out that is not only still the case, but still the case with optional rules and intentional makes me lose a lot respect for D&D.

So if using the fractional variant, do good progression classes add +2.5 at first level or just +2? And do bad saving throw classes at first level add 1/3 or just +0?

[Urpriest]

Hmm, I always thought I was cheesing the system with my character who had 1 level dips in 20 different classes and ended up with obscene saving throws. To find out that is not only still the case, but still the case with optional rules and intentional makes me lose a lot respect for D&D.

So if using the fractional variant, do good progression classes add +2.5 at first level or just +2? And do bad saving throw classes at first level add 1/3 or just +0?

+2.5 and +1/3, respectively.

[NM020110]

I've got a question for you. Not strictly d&d, but somewhat related.

Gapland players, please don't open this spoiler. Doing so will be considered metagaming, and may invoke penalties.

Stats are denoted by a quantity and a quality, denoted n and l. The dice for resolving an action are nd6+nl. For each six that is rolled, the result of that die has one subtracted, and an additional 1d6+l is rolled.

If it would be possible and not overly inconvenience you, I would like to request a bit of help is calculating the average value and standard deviation for different values of n and l.


Thank you.

[Sugashane]

Math question if you don't mind.

Level 12 Large character with 30 Str and large masterwork greatsword

Combining only Power Attack, Heedless Charge, and Leap Attack would give 3d6+15+48+1.
Since nothing has been doubled yet, a critical Hit on that attack would deal 6d6+128

But what happens when I use Rhino's Rush from Spell Compendium? My understanding is that it would be 3d6*2+30+60(+5 per -1)+1

How would this be affected by a Valorous weapon?
My numbers came to 3d6*3+45+72(+6 per -1)+1?

[Story]

I've got a question for you. Not strictly d&d, but somewhat related.

Gapland players, please don't open this spoiler. Doing so will be considered metagaming, and may invoke penalties.

Stats are denoted by a quantity and a quality, denoted n and l. The dice for resolving an action are nd6+nl. For each six that is rolled, the result of that die has one subtracted, and an additional 1d6+l is rolled.

If it would be possible and not overly inconvenience you, I would like to request a bit of help is calculating the average value and standard deviation for different values of n and l.


Thank you.

According to my calculations,

mean = (6x-2)n
st dev = sqrt((2+6*x^2)n)

Where x = 1 + l/5

[AttilaTheGeek]

What is the curve on a "3d6, reroll 1s and 2s until there are none, drop lowest, add 6, best of two sets" stat line?

The "3d6, reroll 1s and 2s until there are none" bit really just makes it 3(1d4+2) or 3d4+6. By "drop lowest, add 6", this makes it "[highest 2 of 3d4] +6+6" According to Anydice (http://anydice.com/program/1f7a), the most common value is 18 and roughly half the values are 17, 18, or 19.

That is, unless I'm misunderstanding your generation method?

[AttilaTheGeek]

Math question if you don't mind.

Of course I don't mind! :smalltongue:


Combining only Power Attack, Heedless Charge, and Leap Attack would give 3d6+15+48+1.
Since nothing has been doubled yet, a critical Hit on that attack would deal 6d6+128

But what happens when I use Rhino's Rush from Spell Compendium? My understanding is that it would be 3d6*2+30+60(+5 per -1)+1

How would this be affected by a Valorous weapon?
My numbers came to 3d6*3+45+72(+6 per -1)+1?

I don't have the Spell Compendium, and it doesn't appear to be on dndtools.eu. Neither does Valorous. What do they do?

[Amphetryon]

Of course I don't mind! :smalltongue:



I don't have the Spell Compendium, and it doesn't appear to be on dndtools.eu. Neither does Valorous. What do they do?

Rhino's Rush doubles damage from the first attack on a successful charge. A Valorous weapon doubles the damage dealt from a charge attack.

[Preaplanes]

The "3d6, reroll 1s and 2s until there are none" bit really just makes it 3(1d4+2) or 3d4+6. By "drop lowest, add 6", this makes it "[highest 2 of 3d4] +6+6" According to Anydice (http://anydice.com/program/1f7a), the most common value is 18 and roughly half the values are 17, 18, or 19.

That is, unless I'm misunderstanding your generation method?

Well this is a theoretical generation method I considered using for a high-power campaign, in the Evil half of a campaign where the players take over the mostly-sunshine-and-butterflies world before the Good half where they set things right again and fight against their old PCs turned Epic NPCs.

Something's wrong in your assumptions because 19s are completely impossible.

Say you rolled three sixes. Drop the lowest, that gives you twelve. Add six, that gives you 18. I suppose it's "lowest roll becomes a 6".

[NM020110]

According to my calculations,

mean = (6x-2)n
st dev = sqrt((2+6*x^2)n)

Where x = 1 + l/5

Thank you very much. That should help quite a bit with setting target values.

[Story]

Keep in mind that for small values of n, the probabilities may not be adequately characterized by the mean and variance.

To pick an extreme example, with n=1 and l=100, we have a mean of 124, but the odds of actually getting a 124 or better are only 1 in 6.

[Sugashane]

Rhino's Rush doubles damage from the first attack on a successful charge. A Valorous weapon doubles the damage dealt from a charge attack.

Exactly, thank you. Valorous states that it doubles charge damage like the Spirited Charge feat. And as Amphetryon said Rhino's Rush does say it double's damage on "the first charge attack" after the spell is cast.

[Gazzien]

Well this is a theoretical generation method I considered using for a high-power campaign, in the Evil half of a campaign where the players take over the mostly-sunshine-and-butterflies world before the Good half where they set things right again and fight against their old PCs turned Epic NPCs.

Something's wrong in your assumptions because 19s are completely impossible.

Say you rolled three sixes. Drop the lowest, that gives you twelve. Add six, that gives you 18. I suppose it's "lowest roll becomes a 6".

He used +6+6, where it should have been [Best 2 out of 3d4]+[b]4+6, because you drop one of the d4+2 (or the d6 reroll 1, reroll 2, if you like). Simply lower all the numbers he gave you by 2.

In other words, it's essentially 3d4b2+10

[AttilaTheGeek]

He used +6+6, where it should have been [Best 2 out of 3d4]+[b]4+6, because you drop one of the d4+2 (or the d6 reroll 1, reroll 2, if you like). Simply lower all the numbers he gave you by 2.

In other words, it's essentially 3d4b2+10

My apologies; this is correct. According to anydice (http://anydice.com/program/1f84), the most common value is a 16, and each stat has a roughly 50% chance to be either 16 or 17.

[Skysaber]

Not sure what's the best choice? I can help you out.

Not quite a "is this better than that" but I've got a D&D fortress that's a really odd shape, a great dodecahedron actually, based on a pentagon whose dimensions are:
a (side length) = 3836.14 ft
r (inradius) = 2640 ft
R (circumradius) = 3263.22 ft
A (area) = 25,318,600 ft2
P (perimeter) = 19180.7 ft
x (interior angle) = 108°
y (exterior angle) = 72°

And now I need to know surface area and volume. What's more, if that wasn't awkward enough I based the whole thing on an Alexander's Star, where if you removed all of the little mobile bits, basically sheered off the stars on each face, at the core there is a little nugget in the shape of an ordinary twelve-sided die, and I'd labeled that as my "inner keep" - only now my DM wants to know the dimensions of it, and I am at a loss as to how to go about calculating them.

Is this the sort of problem you could help with?

P.S. I won't even ask, but there is magic getting tossed around that could potentially "double all internal dimensions" of the caster's house, or even "Add two sub-basements" which is a pretty odd thing on a flying fort, but that's wild magic surges for you.

[AttilaTheGeek]

Not quite a "is this better than that" but I've got a D&D fortress that's a really odd shape, a great dodecahedron actually, based on a pentagon whose dimensions are:
a (side length) = 3836.14 ft
r (inradius) = 2640 ft
R (circumradius) = 3263.22 ft
A (area) = 25,318,600 ft2
P (perimeter) = 19180.7 ft
x (interior angle) = 108°
y (exterior angle) = 72°

And now I need to know surface area and volume.

Sure thing. According to wikipedia, the surface area and volume of a dodecahedron (http://en.wikipedia.org/wiki/Dodecahedron#Area_and_volume) are too obnoxious to type out here (nothing is fun like nested root signs), but they simplify to constants and I can plug and chug for you.

Surface Area ≈ 20.6457*s² =3.038 *10^8 = 303,800,000 square feet.

Volume ≈ 7.6631*s^3 = 4.326 * 10^11 = 432,600,000,000 cubic feet.

For a little bit of context, the distance from any vertex of your keep to the vertex opposite it is more than two miles*. I really hope you can fly, or that's a whole lot of wasted space.

*The radius of a circumscribed sphere of a dodecahedron (that touches all the vertices) is 1.4012s, so the diameter of that sphere is 2.802s. Multiplying by side length s=3836.14 feet gives 10,748.86 feet from one vertex to the one across it, or 2.036 miles.


What's more, if that wasn't awkward enough I based the whole thing on an Alexander's Star, where if you removed all of the little mobile bits, basically sheared off the stars on each face, at the core there is a little nugget in the shape of an ordinary twelve-sided die, and I'd labeled that as my "inner keep" - only now my DM wants to know the dimensions of it, and I am at a loss as to how to go about calculating them.

Is this the sort of problem you could help with?

Wikipedia saves the day again (http://en.wikipedia.org/wiki/Pentagram#Geometry). The ratio between your outer keep side length and your inner keep side length is the golden ratio cubed (man, isn't geometry cool?), so for outer side length s and inner side length l:

s = φ^3*l = (1.6180)^3*l = 4.2360*l
l= (1/4.2360)s = 0.2361s = 905.7127 feet.

So then we do the formulas again.

Surface Area ≈ 20.6457*l² = 16,935,987 square feet.

Volume ≈ 7.6631*l^3 = 5,693,454,646 cubic feet.


P.S. I won't even ask, but there is magic getting tossed around that could potentially "double all internal dimensions" of the caster's house, or even "Add two sub-basements" which is a pretty odd thing on a flying fort, but that's wild magic surges for you.

That's not really how geometry works. You can't double all the dimensions at the same time because they're proportional to different powers. For example, you could double the side length, which would multiply the volume by 8, or you could double the volume, but that would only multiply the side length by 1.260 (cube root of 2)...

The sub-basements one is really vague because it doesn't say anything about size.

[Kornaki]

That's not really how geometry works. You can't double all the dimensions at the same time because they're proportional to different powers. For example, you could double the side length, which would multiply the volume by 8, or you could double the volume, but that would only multiply the side length by 1.260 (cube root of 2)...

On the other hand if you want to create a building that has surreal geometry, just draw a normal building and then declare all dimensions are doubled. So the 10x10 room looks like it has 20 feet to a side, but only eight people can fit in it at a time for some reason.

[AttilaTheGeek]

On the other hand if you want to create a building that has surreal geometry, just draw a normal building and then declare all dimensions are doubled. So the 10x10 room looks like it has 20 feet to a side, but only eight people can fit in it at a time for some reason.

Oh yes. (http://en.wikipedia.org/wiki/Non-Euclidean_geometry)

[Skysaber]

Sure thing. According to wikipedia, the surface area and volume of a dodecahedron (http://en.wikipedia.org/wiki/Dodecahedron#Area_and_volume) are too obnoxious to type out here (nothing is fun like nested root signs), but they simplify to constants and I can plug and chug for you.

Surface Area ≈ 20.6457*s² =3.038 *10^8 = 303,800,000 square feet.

Volume ≈ 7.6631*s^3 = 4.326 * 10^11 = 432,600,000,000 cubic feet.

Thank you so much.

Just to clarify, however, are those numbers for a regular dodecahedron, or a
Great Dodecahedron (hhttp://en.wikipedia.org/wiki/Great_dodecahedron)?

http://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Great_dodecahedron.png/240px-Great_dodecahedron.png

Frankly, if it's too much trouble to do the more complex design, I'll change the fortress layout to match your current figures rather than the other way around.


For a little bit of context, the distance from any vertex of your keep to the vertex opposite it is more than two miles*. I really hope you can fly, or that's a whole lot of wasted space.

I was always intending to divide it into levels, say with 40ft ceilings, and let people rent out sections, sort of like a giant, flying shopping mall. That's part of why the inner keep was important, as that was going to stay as my private 'royal reserve' of space for palace and parks and libraries and all of the workshops for the sort of stuff an archmage can get up to to while away the centuries. Along with generous accomodations for eventual children and grandchildren, etc.

But yes, I can fly.



That's not really how geometry works. You can't double all the dimensions at the same time because they're proportional to different powers. For example, you could double the side length, which would multiply the volume by 8, or you could double the volume, but that would only multiply the side length by 1.260 (cube root of 2)...

I'm pretty sure what they meant was side length, height, breadth, width, etc, when they were talking about 'all dimensions'.


The sub-basements one is really vague because it doesn't say anything about size.

If it ever comes up I'll propose the same dimensions as any other level above it.

Thanks for your help!

[AttilaTheGeek]

Thank you so much.

Just to clarify, however, are those numbers for a regular dodecahedron, or a
Great Dodecahedron (hhttp://en.wikipedia.org/wiki/Great_dodecahedron)?

Frankly, if it's too much trouble to do the more complex design, I'll change the fortress layout to match your current figures rather than the other way around.

Those numbers are for the great dodecahedron EDIT: This was a typo. Both sets are for a regular dodecahedron.


I was always intending to divide it into levels, say with 40ft ceilings, and let people rent out sections, sort of like a giant, flying shopping mall. That's part of why the inner keep was important, as that was going to stay as my private 'royal reserve' of space for palace and parks and libraries and all of the workshops for the sort of stuff an archmage can get up to to while away the centuries. Along with generous accomodations for eventual children and grandchildren, etc.

That sounds so cool.


I'm pretty sure what they meant was side length, height, breadth, width, etc, when they were talking about 'all dimensions'.

Right.


Thanks for your help!

Anytime! :smallsmile:

[Razanir]

Just to clarify, however, are those numbers for a regular dodecahedron, or a
Great Dodecahedron (hhttp://en.wikipedia.org/wiki/Great_dodecahedron)?

Frankly, if it's too much trouble to do the more complex design, I'll change the fortress layout to match your current figures rather than the other way around.

The formulas linked to are for a regular dodecahedron.

Here (http://mathworld.wolfram.com/GreatDodecahedron.html) are the great dodecahedron formulas.

Volume = 2.9270 * s³
SA = 20.6457 * s²

Swordsage'd by Attila, and am surprised that the formulas were apparently already for the great version

[Valwyn]

Not sure if the desk is still open, but...

I'm planning a level 14 character for a 3.5 game. He has Str 22, Dex 17, Con 16, Cha 13, and BAB 14. He is a fire elf, with 1 level in Barbarian and 2 in Wildrunner (Races of the Wild 139). Right now I'm thinking of giving him a guisarme or other reach polearm (longspear is another choice).

Wildrunner gives you a rage-like ability called Primal Scream, which normally stacks with other rage-like effects. What would you say is better, regular Rage, Ferocity (Cityscape Web Enhancement), or Whirling Frenzy (Unearthed Arcana 66, specifically states that it doesn't stack with other rage-effects)? He has Combat Reflexes, Bounding Asault, and Improved Trip (though I'm considering trading it for Improved Disarm/Sunder (I don't think he'll mind sundering stuff, even if it's loot, though using wooden weapons makes it harder)).

I can post the modifiers for each effect, if you want.

Thanks for your help. :smalltongue: Advice in general is welcome as well.

[AttilaTheGeek]

Not sure if the desk is still open, but...

It totally is. :smallsmile:


Wildrunner gives you a rage-like ability called Primal Scream, which normally stacks with other rage-like effects. What would you say is better, regular Rage, Ferocity (Cityscape Web Enhancement), or Whirling Frenzy (Unearthed Arcana 66, specifically states that it doesn't stack with other rage-effects)? He has Combat Reflexes, Bounding Asault, and Improved Trip (though I'm considering trading it for Improved Disarm/Sunder (I don't think he'll mind sundering stuff, even if it's loot, though using wooden weapons makes it harder)).

I can post the modifiers for each effect, if you want.

Thanks for your help. :smalltongue: Advice in general is welcome as well.


I don't actually own any 3.5 books; I mainly play Pathfinder and use dndtools.eu for any 3.5 material I need. Up until now, it's worked out fine, but I wasn't able to find Ferocity or Whirling Frenzy. If you could provide links or paraphrases of what they do, that would be great.

That being said, Primal Scream is a free action, so you can activate it along with rage.

[Valwyn]

If you could provide links or paraphrases of what they do, that would be great.

No problem. :smalltongue:

Primal Scream (3+Cha/day): free action, +2 Str, +6 Dex, 1d6 bite attack, 6 rounds (3+Con)
Rage (1/day): free action, +4 Str, +4 Con, +2 Will,-2 AC, 8 rounds (3+Con), end up fatigued
Ferocity (1/day): immediate action, +4 Str, +4 Dex, -2 ranged attacks, 7 rounds (4+Con), end up sickened
Whirling Frenzy (1/day): free action, +4 Str, +2 Ref, +2 dodge AC, -2 attack, extra attack per round (all attacks have a -2 penalty), 6 rounds (3+Con), end up fatigued, doesn't stack with rage and similar stuff

Here's the sheet (http://www.myth-weavers.com/sheetview.php?sheetid=544370), if it helps. (It uses lots of house rules)

[Jon_Dahl]

Two characters are trying to swim 5940 ft. They need DC 10 swim checks to swim 15 ft. per round. However, their swimming modifiers are negative, so they are unable take 10. They need to roll every single check.

How to resolve the swimming time with simple mathematics which take the random factor of bad/good rolls into account?

A character who is able take 10 (in other words, does not have a negative swim modifier) is able to swim this distance in 39 minutes.
Formula: 6*(5940 / 15) = 2376 seconds = 39.6 minutes.


Not sure what's the best choice? I can help you out.


I know that my question is not the type you wanted, but I'd appreciate if you could take the time to answer the this one, please :smallsmile:

[TypoNinja]

Two characters are trying to swim 5940 ft. They need DC 10 swim checks to swim 15 ft. per round. However, their swimming modifiers are negative, so they are unable take 10. They need to roll every single check.

How to resolve the swimming time with simple mathematics which take the random factor of bad/good rolls into account?

A character who is able take 10 (in other words, does not have a negative swim modifier) is able to swim this distance in 39 minutes.
Formula: 6*(5940 / 15) = 2376 seconds = 39.6 minutes.



I know that my question is not the type you wanted, but I'd appreciate if you could take the time to answer the this one, please :smallsmile:

That may be a fatal trip. Failure of 5 or more has them sinking, don't ask me for much math at 5 am, but if a d20 represents a 5% per face, even at only a -1 swim check, they are going to be underwater 30% of the time. Failure by 4 or less means no progress at all, so that's about 800 rolls, or 80 minutes of swimming, not including time lost recovering from sinking.

I'm not sure what the odds of them rolling low enough twice in a row (or more) to sink are, but with 800 rolls to cover, its virtually certain it'll happen, more than once.

[Jon_Dahl]

That may be a fatal trip. Failure of 5 or more has them sinking, don't ask me for much math at 5 am, but if a d20 represents a 5% per face, even at only a -1 swim check, they are going to be underwater 30% of the time. Failure by 4 or less means no progress at all, so that's about 800 rolls, or 80 minutes of swimming, not including time lost recovering from sinking.

I'm not sure what the odds of them rolling low enough twice in a row (or more) to sink are, but with 800 rolls to cover, its virtually certain it'll happen, more than once.

Thank you, this is exactly what I mean. I didn't remember that thing about sinking, but we are thinking about the same thing here. But... how to resolve the math? Is it impossible? I guess I'm asking too much, but... I still do :smallbiggrin: Please :smallwink:

[TuggyNE]

Thank you, this is exactly what I mean. I didn't remember that thing about sinking, but we are thinking about the same thing here. But... how to resolve the math? Is it impossible? I guess I'm asking too much, but... I still do :smallbiggrin: Please :smallwink:

The problem is that you have to resolve:

Whether they make progress
Whether they sink
Whether they have to make Con checks
Whether they succeed at those increasing DCs, or swim to the surface once more


That's a lot of rolls, and it's extremely difficult or impossible to simplify that meaningfully.

Incidentally, if they have only a -1 or -2 penalty, they might best be served by simply trying to Aid Another on their swim checks as a standard action and swim as a move action; they'll still fail sometimes, but it'll be less often. (Of course, that's at the price of one and a half times the rolls and half the speed.)

[TypoNinja]

Thank you, this is exactly what I mean. I didn't remember that thing about sinking, but we are thinking about the same thing here. But... how to resolve the math? Is it impossible? I guess I'm asking too much, but... I still do :smallbiggrin: Please :smallwink:

There's probably a better way, but I just eyeballed it. You never mentioned what they actually need to roll, so lets stick with them only having a -1.

-1 means they need to roll an 11 or higher. That's 10 numbers 11-20. 10x5% is 50%. So 50% chance they'll make progress. 20% chance they go nowhere, and 30% chance they sink.

They need 400 successes to make it, and 50% of 800 is 400. So 800 rolls/rounds at -1.

They'll spend 160 rounds making no progress, 240 rounds sinking, and 400 rounds swimming. If a decent portion of those sinking round happen close together we get a fatality. I'll take an average of 2 rolls to recover from one sink roll, so as little as 2 sinks in a row get you 4 rolls to recover,, but on balance one of those 4 rolls should also still be a "sink". You can see how a little bit of bad luck all in once place could be lethal.

Even at -2, that skews the odds to 45% swim, 20% nowhere, 35% sink and ~900 rolls instead of 800.

At -3 I'd call it straight up suicidal. It'd be 40% 20% 40%. That means you are just as likely to sink more as you are to recover from sinking. You are more likely to be under water than not, and more likely to stay there.

The biggest problem left is determining how long they spend sinking and recovering from sinking, the method I used just shows how many rolls they need to get the required number of successes, but enough failures could cause them to lose progress.

But me brains mush at this point, so you'll have to wait for somebody more alive than me to wake up and finish it off. :P

[qwertyu63]

What are the odds of 1d6 beating 2d6, drop lowest? What about 1d6 vs 3d6, drop lowest two? Or 2d6, drop lowest vs 3d6, drop lowest two? Thank you in advance.

[Razanir]

What are the odds of 1d6 beating 2d6, drop lowest? What about 1d6 vs 3d6, drop lowest two? Or 2d6, drop lowest vs 3d6, drop lowest two? Thank you in advance.

Attilla's offline, so I'll take this one.

First off, are you really sure you mean odds? In statistics, there's a distinction between the odds and the probability. The probability measures the ratio of successes to total outcomes, whereas the odds measure the ratio of sucesses to failures. The other issue is that you don't say how to handle ties. I'll go with a literal interpretation, and assume you want ONLY cases where 1d6 > 2d6b1

1d6 is easy enough to roll. It's a uniform discrete distribution with 6 outcomes. 2d6b1, on the other hand, uses what's called a binomial distribution, which measures the probability of getting so many successes out of a set number of trials. Here, we need each die to be less than 1d6, so a success is being less than it, the probability is (1d6 - 1)/6, and we need two successes. Multiply each by the probability of the 1d6 value, sum them up, and we have our answer. 3d6b1 works in the same way, just with 3 successes

P(1d6 > 2d6b1) = 55/216 = .2546, Odds(1d6 > 2d6b1) = 55/161 = .3416
P(1d6 > 3d6b1) = 25/144 = .1736, Odds(1d6 > 3d6b1) = 25/119 = .2101

The last part's a bit more complicated. 3d6b1 will work the same way, but the probability distribution for 2d6b1 when we aren't just checking for under a value is weirder. It's technically now a multinomial distribution. We want at least one case of it being at a number, and no cases of it being greater. THANKFULLY, though, there's a known number of dice. Otherwise it would be much nastier. This way, I can just write P(die 1 = X) * P(die 2 <= X) * P(2,2) <- that last term is how many ways we can organize the two dice

P(2d6b1 = X) = X/18

Unfortunately, the corresponding sum hits quartic quations, which I can't manually sum. At least not with shortcuts. So I used WolframAlpha instead :smallbiggrin:

P(2d6b1 > 3d6b1) = 301/972 = .3097, Odds(2d6b1 > 3d6b1) = 301/671 = .4476

[Thurbane]

Not sure if this really belongs here, but...can someone please help me figure out the attack routine/bonuses of a Half-Farspawn Athach with the Multiattack and Multiweapon Fighting feats? It's doing my head in.
BAB +8, STR 28, 3 morningstars (iterative attacks with the first), 1 bite, and 2 tentacles?

[TypoNinja]

Not sure if this really belongs here, but...can someone please help me figure out the attack routine/bonuses of a Half-Farspawn Athach with the Multiattack and Multiweapon Fighting feats? It's doing my head in.
BAB +8, STR 28, 3 morningstars (iterative attacks with the first), 1 bite, and 2 tentacles?

first things first. Your base to hit is +8 BAB and +9 Str, so +17.

MultiWeapon Fighting is just like TWF expect more arms. Alas, the Morningstar inst a light weapon so you take -4 to each. You could lower that to only -2 with a light weapon in your off hands.

So your 3 weapons are going to be Main hand +13+8 and +13 +13 for each of your two off hands.

Using a manufactured weapon makes all your natural weapons secondary attacks, at -5 usually, but with multiattack -2. So All three of your natural attacks are at +15.

Your full attack will look like this;

3xMorning stars +13/+8 +13 +13, Bite +15 2x tentacle +15.

Immproved Multi-Weapon Fighting never got updated to 3.5 as far as I know, but the SRD Epic Feats lists has updated versions listed.

This of course assumes that the manufactured weapons you are holding don't interfere with your natural attacks. You couldn't for example, claw with the same hand that swung a sword.

[Thurbane]

Sweet, thanks man. I couldn't reconcile my figures with the SRD stats for the Athach, but it was the -4 penalty for a non-light weapon that I wasn't accounting for. :smallwink:

[TypoNinja]

Sweet, thanks man. I couldn't reconcile my figures with the SRD stats for the Athach, but it was the -4 penalty for a non-light weapon that I wasn't accounting for. :smallwink:

I'm not familiar with either your base race, or the template, so hopefully they don't have any racials that matter, for instance a Marlith multiweapon fights at no penalty at all, just because.

[HurinTheCursed]

I've a big excel sheet that I use to calculate the impact of the malus on power attack for mean damage depending on feats, bonus, extra dice...
I'm still not satisfied with the layout but when it is I'll share with you guys.

For the question now, is it possible to find an analytic function to find the best power attack value knowing that:
- by seeing the values for the [-20;20] interval, the function isn't monotonous and may have local max (obviously other than the global max)
- the base function isn't continuous, so I can't derive it to get the mean damage

What I look for takes as input (total attack value without power attack - expected AC) and gives back the best power attack value: PA(3) = 8.21

[AttilaTheGeek]

For the question now, is it possible to find an analytic function to find the best power attack value knowing that:
- by seeing the values for the [-20;20] interval, the function isn't monotonous and may have local max (obviously other than the global max)
- the base function isn't continuous, so I can't derive it to get the mean damage

I would just take the derivative anyway, have it note the values where it's inconsistent, and have a little bit of formula code that says "if it is one of these values, then throw an error". I can't say more without seeing what you have.

[dascarletm]

I've a big excel sheet that I use to calculate the impact of the malus on power attack for mean damage depending on feats, bonus, extra dice...
I'm still not satisfied with the layout but when it is I'll share with you guys.

For the question now, is it possible to find an analytic function to find the best power attack value knowing that:
- by seeing the values for the [-20;20] interval, the function isn't monotonous and may have local max (obviously other than the global max)
- the base function isn't continuous, so I can't derive it to get the mean damage

What I look for takes as input (total attack value without power attack - expected AC) and gives back the best power attack value: PA(3) = 8.21
Ah, yes I have a few of these. I made a large reference table, that automatically highlights the Highest PA value for each AC value.

[AttilaTheGeek]

Ah, yes I have a few of these. I made a large reference table, that automatically highlights the Highest PA value for each AC value.

But damage also depends on crit chance, crit confirmation chance, and crit multiplier.

[dascarletm]

But damage also depends on crit chance, crit confirmation chance, and crit multiplier.

Yes, I have one for each character that is PA dependent.

I took a simple, yet probably wrong route.

I just treated it as though all possible outcomes would happen, added the damage, then divided by the total. For each crittable # you need to calculate in 20 possibilities rolling (1-20) and divide by that. To the side of the reference table you can just have each of those crit related numbers (multiplier, etc.) referenced by the mother formula with $'s. Example A$5$ since you don't want that number to change when you pull the formula across the area.

[HurinTheCursed]

I guess it's rather similar to dascarletm's

So far, it works but it's rather dirty:
- by knowing the BAB, I get the number of attacks
- I add as input all modifiers for hitting, damaging, feats, criticals... (I added a combo box where you can pick previously entered weapons like +1 holy longsword)
- I calculate probability to hit for each couple base roll to hit / PA malus (you still have to guess the enemy's AC)
- I calculate the mean damage for one attack for that AC
- I get the full attack damage from iterating the single attack damage for a normal sequence (no snap kick, celerity...)
- The user has to find the optimal value by finding the colored cell in the line for the chosen base roll needed or by reading an histogram

It doesn't work against not critable opponents, some variable dice (holy, flaming...) when weapons don't work as usual.

[dascarletm]

I guess it's rather similar to dascarletm's

So far, it works but it's rather dirty:
- by knowing the BAB, I get the number of attacks
- I add as input all modifiers for hitting, damaging, feats, criticals... (I added a combo box where you can pick previously entered weapons like +1 holy longsword)
- I calculate probability to hit for each couple base roll to hit / PA malus (you still have to guess the enemy's AC)
- I calculate the mean damage for one attack for that AC
- I get the full attack damage from iterating the single attack damage for a normal sequence (no snap kick, celerity...)
- The user has to find the optimal value by finding the colored cell in the line for the chosen base roll needed or by reading an histogram

It doesn't work against not critable opponents, some variable dice (holy, flaming...) when weapons don't work as usual.

If you have all of your crit information available you can just set the crit multiplier to 1 to see on non-crittables. I also am thinking of putting in 2 base damage values, critable and non. You could then adjust those as needed

[AugustNights]

I have a math request, if I may.

I am struggling to ascertain which would be superior; 1d12+1d8+4, or Roll (1d12+1d8) and distinctly separate (1d12+1d8) and take the superior outcome.

[TuggyNE]

I have a math request, if I may.

I am struggling to ascertain which would be superior; 1d12+1d8+4, or Roll (1d12+1d8) and distinctly separate (1d12+1d8) and take the superior outcome.

You can implement that in AnyDice as a one-liner: `output 1d12+1d8+4 > [highest of 1d12+1d8 and 1d12+1d8]`

Or a two-liner:
output 1d12+1d8+4
output [highest of 1d12+1d8 and 1d12+1d8]

Either way, the first one is better; it has a higher average, a higher minimum, and a higher maximum. It's also tidier.

[AugustNights]

Thanks, tuggyne.

[Phelix-Mu]

Hi Attila! Fan of the thread, here, and confirmed lifelong mathematician (if a bit rusty:smallwink:).

Here's my question, and it might be a bit raw, so if you need to refine it or simplify it to make the numbers easier to figure, go for it. I'm interested to see how you model it. If you already solved this in one of the pages I skipped, a link or page number would be great.

So, here's the premise:
A 20th level shaper psion and his 17th level psion(telepath) cohort.

Assume infinite wealth and unlimited experience points to spend; neither are limiting factors.

The Question:
How many iterations of psychic chirurgery, Expanded Knowledge, and psychic reformation would be needed for them to teach each other all of the powers in Expanded Psionics and Complete Psionics (excepting the 9th level powers on the other discipline lists...though there may be a trick to net those, too)?

A total cost of experience points is key here. A time amount would be great too, but once you've figured the iterations, it's not hard to get these other number. I'm obviously looking to optimize the trick, so as few iterations as possible in the ideal pattern would be great.

(If you have a quick number for the total published # of psionic powers in 3.5, use that).

Good luck. If there's a reason that I haven't sussed out why this doesn't work, please tell me.

[AttilaTheGeek]

Hi Attila! Fan of the thread, here, and confirmed lifelong mathematician (if a bit rusty:smallwink:).

Thanks!


The Question:
How many iterations of psychic chirurgery, Expanded Knowledge, and psychic reformation would be needed for them to teach each other all of the powers in Expanded Psionics and Complete Psionics (excepting the 9th level powers on the other discipline lists...though there may be a trick to net those, too)?

Okay, a few clarifications.

Can you link or quote all three powers?

Also, how many powers are there that are applicable?