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.

Spoiler

Show

-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?

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

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.

1. They need to be hit.
2. The hit needs to be debilitating.
3. They need to be hit again.
4. The second hit also has to be debilitating.
5. 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.

[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.

Spoiler

Show

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:

Spoiler

Show

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 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:

Spoiler

Show

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?