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View Full Version : 2d10 Bell Curve vs d20 (need help from you math types).



Grynning
2008-09-15, 03:35 AM
So I was thinking about these (http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm) alternate rules when I was on my way home tonight from our M&M game. Tonight I had to roll way more d20's than I usually do as we had a skill/investigation focused session that culminated in my pool shark/kinetic controller character having a pool showdown with a luck controlling mobster. During the game (which was a series of opposed power-checks and dex checks), my rolls were all over the place, and it reminded me how frakkin random the d20 really is. I've always liked the idea of bell curve systems better since making routine checks (like making an easy pool shot) becomes more consistent and it seems like your stats make more of a difference than the luck of the die (without eliminating luck/probability/whatever as a factor). Of course, using a 3d6 curve for d20 games requires a fair amount of conversion since the range of numbers changes completely, so I was thinking, why not use 2d10 and have a compromise between the two? Does 2d10 skew the numbers too favorably or unfavorably, or what? I'm not good enough at math myself to figure it out (theatre and then communications major who never graduated :smalltongue:) so I was wondering if some of the calculator jockeys could tell me how well this would work.

I'd also like some help on how using 2d10 would change the mechanics of re-rolls, criticals, taking 20, etc. and how to modify them appropriately, somewhat like the published one I linked above does.

Also, I think it would be easier to use this change in 4th edition than in third, and in M&M than D&D in general. Thoughts?

Thanks guys!

Sstoopidtallkid
2008-09-15, 03:43 AM
A 1d20 has a mean of 10.5, with even odds of hitting any specific number. 2d10 has a mean of 11, with somewhat better chances of hitting numbers in the center of the curve, including reducing the odds of getting a 20 or a 1(2 on 2d10) from 5% to 1%. As I said, 1s become impossible, and if you retain the auto-miss rule, you'll have to adjust it to 2s instead. The primary rules issue I see is in crits, as the odds now favor high-range, low-multiplier crit weapons. A Greatsword has a 3% chance of critting for 2x damage, vs. a Greataxe which has a 1% chance of critting for x3. Much less useful. This doesn't even start of things like Burst and Keen weapons. UA had rules for 3d6, I would recommend just using those instead.

Grynning
2008-09-15, 03:46 AM
Is there a way to break down the specific % chance of hitting each particular number in the range? If you could just tell me how to calculate it that'd be great (or do it for me :smallwink:).

Also, my reasoning for wanting to use 2d10 is just because it seems like it would be more consistent with existing DC's/defenses and other target numbers. Granted you have a smaller chance of hitting the higher numbers just as you do with 3d6, but it seems like it would be *closer* to using a d20 with less of the fickleness.

Charity
2008-09-15, 04:01 AM
criticals will happen an awful lot less, this is an overall good thing to my mind (crits are much worse for players, I have killed a few characters this way), but those that love a keen weapon might be upset. (though what I would do is say that you only need one 10 to get a possible crit (which would make them about the same power they are now... However as crits would diminish dramatically in frequency it would make them relatively more powerful...

taking 20 could be replaced with you get 10 + 1d10 (instead of the 16/18 suggested) which would still leave the result a bit in question, but still heavily sway the result in their favour...

The other result would be that the third and fourth attacks in an itterative attack would have very little chance of connecting, and spells with high DC saves would be even more powerful... so essentially I fear this system might sway things even further in the casters favour... Might work for 4e, but I think it might punish melee types too much in 3e.

Sstoopidtallkid
2008-09-15, 04:02 AM
% chance for each number.
2d10

2=1%
3=2%
4=3%
5=4%
6=5%
7=6%
8=7%
9=8%
10=9%
11=10%
12=9%
13=8%
14=7%
15=6%
16=5%
17=4%
18=3%
19=2%
20=1%

There you go. I'll do it for 3d6 too, if you like.

Charity
2008-09-15, 04:07 AM
% chance for each number.
2d10

2=1%
3=2%
4=3%
5=4%
6=5%
7=6%
8=7%
9=8%
10=9%
11=10%
12=9%
13=8%
14=7%
15=6%
16=5%
17=4%
18=3%
19=2%
20=1%

There you go. I'll do it for 3d6 too, if you like.

In D&D you are not looking for an exact number just a > number, your table should reflect that.
2=100%
3=99%
4=97%
5=94%
6=90%
7=85%
8=79%
9=72%
10=64%
11=55%
12=45%
13=36%
14=28%
15=21%
16=15%
17=10%
18=6%
19=3%
20=1%

Sstoopidtallkid
2008-09-15, 04:12 AM
*better math than me*:-p wordiness

Charity
2008-09-15, 04:28 AM
Hey, you did all the work, I just added up some numbers.

I do think it will skew things, especially where you can adjust your hit chance (power attack etc) it adds a lot of swing to your hit chance, as much as 10% for a +1 damage... or as little as 1% for the same.

Grynning
2008-09-15, 04:28 AM
Ok, so I did the math in my slow, ghetto-tastic fashion and here's are the percentages that I came up with:

2 - .91
3 - 1.82
4 - 2.73
5 - 3.64
6 - 4.55
7 - 5.46
8 - 6.37
9 - 7.28
10 - 8.19
11 - 9.1
12 - 8.19
13 - 7.28
14 - 6.37
15 - 5.46
16 - 4.55
17 - 3.64
18 - 2.73
19 - 1.82
20 - .91

On the criticals thing:

Modifying the crit ranges slightly could fix that, and in 4th edition, all weapons are pretty much equal in the crit department, so no big deal there. Just make the "standard" crit range 19-20 (2.73% chance of a crit by my calculations) or 18-20 (5.46% chance, higher than a d20), whichever you prefer. For 3.x you would just shift the table for 3d6 a little bit.

You could also have criticals have a chance to occur whenever both dice came up the same number, or when ever one die showed a 10, but this would mean eliminating all critical modifying stuff altogether and replacing it with something else.

nagora
2008-09-15, 04:31 AM
Ok, so I did the math in my slow, ghetto-tastic fashion and here's are the percentages that I came up with:

I don't know what you did, but those are wrong; Charity/Sstoopidtallkid's posts have the correct values.

Grynning
2008-09-15, 04:33 AM
how exactly do you do the math?

also, I don't really understand Charity's table, could someone explain that to my poor liberal arts and codeine-addled brain?

(by the way, it's prescription, for my bronchitis, not recreational...as to why it hasn't knocked me out, I can only guess that quitting smoking is causing massive insomnia).

Edit: You're totally right, somehow I was calculating their fraction out of 91 instead of 100...not sure how I arrived at that...

Charity
2008-09-15, 04:36 AM
^ OK the chance of rolling a 2 or more is 100%, chance of rolling a 15 or more is 21% etc...
It comes from the number of outcomes that satisfy the required sum.
All numbers on each die give you a sum of 2 or more, however there are only 21 results of the total 100 different results that add up to 15 or more


Erm... I'm not sure what you are showing there, there is no crit confirmation in 4e so to keep a 5%ish crit rate you just need to crit on a 18-20.
In 3e it is different depending on what you need to hit, but for a 20 crit it is easy- crit chance depending on number required to hit.

2=1.00%
3=0.99%
4=0.97%
5=0.94%
6=0.90%
7=0.85%
8=0.79%
9=0.72%
10=0.64%
11=0.55%
12=0.45%
13=0.36%
14=0.28%
15=0.21%
16=0.15%
17=0.10%
18=0.06%
19=0.03%
20=0.01%

a 19-20 crit would be 3x these values 18-20 6x these values etc.

Grynning
2008-09-15, 04:39 AM
You still roll to confirm crits in 4th - you just don't multiply damage, it just does maximum damage for what you would roll.
Edit: Whoops, no you don't...guess we've been doin it wrong.

Your last table confused me even more, what is that all about?

nagora
2008-09-15, 04:41 AM
how exactly do you do the math?
In a piece of paper, make a table with the numbers 1 to 10 across the top and down the side. At each intersection write the total of the top number and the side number. Then count the number of times each separate number appears on the table. Since there are 100 entries on the table, you now have a bunch of odds out of 100 (AKA percentages) for each number from 2 to 20. Tah-da!

You can then make a list of those percentages and add them up as they run from 2 to 20, thus giving the cumultive chance to roll each number or less as well as the chance of rolling a specific number.

Sstoopidtallkid
2008-09-15, 04:44 AM
In a piece of paper, make a table with the numbers 1 to 10 across the top and down the side. At each intersection write the total of the top number and the side number. Then count the number of times each separate number appears on the table. Since there are 100 entries on the table, you now have a bunch of odds out of 100 (AKA percentages) for each number from 2 to 20. Tah-da!

You can then make a list of those percentages and add them up as they run from 2 to 20, thus giving the cumultive chance to roll each number or less as well as the chance of rolling a specific number.Or you can do it the easy way, and just mentally count how many different rolls on one die have a number rollable on the second die that will add up to the target amount, then multiply by .1. That gave you my chart, which gives the odds of rolling any individual number. Charity's chart gave the odds of rolling a specific number or more, which is better for crit calculations.

Charity
2008-09-15, 04:45 AM
You still roll to confirm crits in 4th - you just don't multiply damage, it just does maximum damage for what you would roll.
No you don't there is no crit confirmation in 4e.


Your last table confused me even more, what is that all about?

Sorry to muddy the water, that is the chance of getting a crit on a specific hit chance so for example if you have a 20 crit range and you nedd a 15 to hit the chance of rolling a 20 followed by a 15 or higher is the number given in the table (0.21%).

potatocubed
2008-09-15, 04:47 AM
As a general rule of thumb, the more dice you roll the closer to the mean average each result will be. This has the gameplay effect of emphasising character skill over luck.

The actual maths, I will leave to people who like maths. :smalltongue:

Grynning
2008-09-15, 04:48 AM
Ok, thanks, those last couple posts cleared a lot up for me.

Sorry I'm so easily confused right now - like I said earlier, there are several factors contributing but I can't sleep - and the boards are a good way to kill time until I can :smallsigh:

Kizara
2008-09-15, 04:49 AM
See the link in my sig for my thread discussing this. I use 2d10 for my RPing. It somewhat messes the critical system but the reduction of luck-based gameplay is wroth it.

Charity
2008-09-15, 04:52 AM
See the link in my sig for my thread discussing this. I use 2d10 for my RPing. It somewhat messes the critical system but the reduction of luck-based gameplay is wroth it.

How does it work out with itterative attacks, spell DC's and things like power attack?
From the math it seems likely to punish those much beleaguered meleers.

Grynning
2008-09-15, 04:55 AM
I had actually read that thread earlier, Kizara, and I was interested that you had it working in a game. I just hadn't seen you post in quite a while so I wasn't sure that discussion of it was still ongoing.

The other reason I started a new thread is because if I ever use this it's more likely to be for 4th ed. or Mutants and Masterminds, neither of which have the issues of iterative attacks and widely varying crit ranges, so I was more looking for a straight breakdown of the chances to roll a combination to compare to target numbers.

Kizara
2008-09-15, 05:10 AM
How does it work out with itterative attacks, spell DC's and things like power attack?
From the math it seems likely to punish those much beleaguered meleers.

I'd like to know how people could think having a better bell-curve nerfs iteritive attacks.

If you are more consistant with your attack rolls, it is easier for you to hit things. Also, your high AC as a fighter is more consistantly valuable. It is easier to use PA because you know more consistantly what range you will likely be rolling in.

Also, since you are likely to roll 9-14 you are unlikely to fail sane spell DCs. This rolling system, all by itself, goes a ways to reign-in save-or-screws.


Thus, not only does this rolling system reduce luck and empathsize player/character skill but it also helps to address the caster/non caster discrepency.


Mind you, I have alot more to say about what needs to be done to balance the system. And not just say, show in what work I've done.

Grynning
2008-09-15, 05:17 AM
I'd like to know how people could think having a better bell-curve nerfs iteritive attacks.


Iterative attacks go down by 5 with each attack - meaning that the number you need to roll on the die goes up with each one. If you're less likely to roll higher numbers, you are less likely to hit with each iterative attack. It's a valid point.

Edit: A possible solution would be to have iterative attacks break on every 4 points of BAB rather than 5 - yes, this means people would have more of them with a better bonus, but they probably would hit about as often as 3.5 iteratives do. I'm not a fan of them in the first place, though, hence my preference for 4th and the Green Ronin games.

Charity
2008-09-15, 05:28 AM
I'd like to know how people could think having a better bell-curve nerfs iteritive attacks.

http://www.fontys.nl/lerarenopleiding/tilburg/engels/Toetsing/bell_curve2.gif
Anything more than 1 standard deviation away from the middle has substatially reduced odds compared with a flat probability if you take 5/10/15 from a hit roll you are likely to inhabit that area of the graph, hence reduced chance of landing itterative attacks.





If you are more consistant with your attack rolls, it is easier for you to hit things. Also, your high AC as a fighter is more consistantly valuable. It is easier to use PA because you know more consistantly what range you will likely be rolling in.
Itterative attacks are not consistant.
I agree it does make AC more valuable, but as you can see it reduces the monsters chance to hit, why can't you see how it can similarly affect the characters?
Power attach has diminishing returns on the RHS of the graph and inreasing returns on the LHS... I'm not seeing how this is easier.


Also, since you are likely to roll 9-14 you are unlikely to fail sane spell DCs. This rolling system, all by itself, goes a ways to reign-in save-or-screws. There are no sane DC's saves (especially for melee classes) tend to fall outside that range in my experiance



Thus, not only does this rolling system reduce luck and empathsize player/character skill but it also helps to address the caster/non caster discrepency.
I'm not seeing this really, if it works for you thats dandy, but I can't see why it works out mathematically.

Sstoopidtallkid
2008-09-15, 05:44 AM
I'd like to know how people could think having a better bell-curve nerfs iteritive attacks.At level 14, you have an attack at +14(which because of scaling should hit on a 5+), an attack at +9(needs a 10+), and an attack at +4(which needs a 15). Under a 2d10 or 3d6 system, that 3rd attack might as well not exist.
If you are more consistant with your attack rolls, it is easier for you to hit things.No, it is easier to predict if you can hit something, but if that thing has an AC even a bit better than you expect, it becomes much harder when the dice are less random.
Also, your high AC as a fighter is more consistantly valuable.When has a Fighter had good AC? A Rogue's AC is only a point lower, most of the time, depending on how they spent their gold.
It is easier to use PA because you know more consistantly what range you will likely be rolling in.That is true.
Also, since you are likely to roll 9-14 you are unlikely to fail sane spell DCs. This rolling system, all by itself, goes a ways to reign-in save-or-screws.Define 'sane'. A first-level Wiz is going to have a save DC of 16. 15 without Spell Focus, but at low levels I always take SF. A Fighter is going to have a Will Save of anywhere from +1 to -2. That means he only has a 30% chance of making, under favorable conditions and the d20 system. 2d10 drops that to 21%. How is that supposed to help, exactly?

nagora
2008-09-15, 06:02 AM
Or you can do it the easy way, and just mentally count how many different rolls on one die have a number rollable on the second die that will add up to the target amount, then multiply by .1.
Yes, that's er... the easy way :smalleek:

Kizara
2008-09-15, 06:14 AM
I suppose my houserules and playstyle unduely cloud my preceptions, my appologies.

High stats + high wealth + ban alot of the more imba items (metamagic rods, alot of the MIC stuff, etc) = weapon-based characters have a much easier time.

Your saves are better cause you got a cloak of resist +5 at level 5, etc.

Your attacks and AC are better cause your weapon focus gives you +2, you have expensive armor, and maybe you took armor feats to further improve this.


Randomness is one of the things that makes it harder as an weapon-based character. You don't have to roll to succed at your spells, and when you do that rolls are stupidly easy (touch attacks, Concentration vs low DCs). Lowering this randomness thus helps you.

Also, recall the many times in the DMG where it says that increasing randomness hurts PCs and lowering it help them, it is true for this too.


Anyways I'm exhausted and will talk about this later, Kizara out.

Sstoopidtallkid
2008-09-15, 06:22 AM
*stuff*Resistance +5 at level 5?!? Okay, that explains a lot. Like, a lot a lot. Wow, yeah, that may be the one Save-or-Die nerf that works, but doesn't hurt anything. Still doesn't help against a lot of the better spells, but it does help.

Kizara
2008-09-15, 07:15 AM
Resistance +5 at level 5?!? Okay, that explains a lot. Like, a lot a lot. Wow, yeah, that may be the one Save-or-Die nerf that works, but doesn't hurt anything.

I suppose I was exagerating slightly even by my own standards. Cloak +4 is more reasonable at around that level, if they are willing to spend the majority of their wealth.


Still doesn't help against a lot of the better spells, but it does help.

Some spells need to be re-worked, a small few need to be removed, but in general some basic rules are:

1) If a spell effects your status n any way and is below 5th level, it allows a save. FULL STOP. None of this "touch AC is a defense!" nonsense. Rays are still plenty good anyways.

2) Effects that mitigate spell resistance beyond Spell Penetration feat and archmage abilities are removed. No Assay Resistance, for example.

3) Effects that mitigate spell level adjustment on metamagic are largely removed. Circumventing a major balance mechanic is not a good idea.

4) Concentration is opposed by your opponents attack skill, and spell level is still factored in. Yes, that means its hard to cast in melee. That's the point.

Anyways, I'm ranting/rambling and derailing your thread. Sorry, I'll shut up now.

Sstoopidtallkid
2008-09-15, 07:24 AM
See, the problem with giving any spell a save is how do you justify a save v. Solid Fog? And how often is the save rolled? Every 5 feet? Every turn? Once? Does Magic Missile give a save? The Orb spells? Black Tentacles?

And you still don't get rid of some great ones. Grease and Glitterdust are still good, even into high levels. Summon Monster 3, Haste, every Cleric self-buff. It's like Pathfinder. It moves towards balance but misses the point.

only1doug
2008-09-15, 08:29 AM
I suppose I was exagerating slightly even by my own standards. Cloak +4 is more reasonable at around that level, if they are willing to spend the majority of their wealth.
woah, spend every gp they have to own a +4 resistance cloak, then get killed by melee as they have no AC or offensive weaponry... yup that balances out magic...



Some spells need to be re-worked, a small few need to be removed, but in general some basic rules are:

1) If a spell effects your status n any way and is below 5th level, it allows a save. FULL STOP. None of this "touch AC is a defense!" nonsense. Rays are still plenty good anyways.

self buffs and weapon buffs? "the giant dwarf cleric hit me harder so therefore his spell effects my status, i'll make a save against it!"


2) Effects that mitigate spell resistance beyond Spell Penetration feat and archmage abilities are removed. No Assay Resistance, for example.
yes, because when you have a monster with spell resistance why allow the PC casters a chance to effect it at the cost of tying up one (or more) of their spell slots and choosing to cast a spell on it before they cast their save/suck or save/die.


3) Effects that mitigate spell level adjustment on metamagic are largely removed. Circumventing a major balance mechanic is not a good idea.
OK, seems a sensible enough plan.


4) Concentration is opposed by your opponents attack skill, and spell level is still factored in. Yes, that means its hard to cast in melee. That's the point.
this seems a little awkward, you are changing a fixed target number to one that varies dependant on circumstances, extra bookkeeping isn't necessarily an advantage. it is also unclear as to how you would implement it:

Existing: Combat casting DC=15+spell level, concentration check DC=10+ spell level + damage received (or 1/2 of continuous damage received)

you would change that to:
Combat casting DC=spell level + BAB of most dangerous opponent or DC=spell level + attack bonus with current weapon of most dangerous opponent or
DC= spell level + BAB of all opponents or
DC= spell level + attack bonus of all opponents or
DC= 15 + spell level + BAB of most dangerous opponent or
DC= 15 + spell level + attack bonus of most dangerous opponent or
DC= 15 + spell level + BAB of all opponents or
DC= 15 + spell level + attack bonus of all opponents

Tengu_temp
2008-09-15, 08:52 AM
Several days ago I was pondering should I use 2d10 instead of d20 for my 4e game (since my players tend to have horrible luck with dice), changing the standard crit chance from 20 (5%) to 18-20 (6%), and today this thread appears. Another proof that either I'm emitting brainwaves that other people receive and subconsciously take the ideas contained in them as their own, or the other way around.

I really should get that tinfoil hat.

Charity
2008-09-15, 08:56 AM
^^ I think you may have missed his point here, Kizara says these are the methods he uses to balance out his games... that he runs... and he therefore is implying he does not follow the WBL guidelines.

I can't say I endorse his methods, but they work for his group.


^ I can see it working better for 4e as it goes, though it would make death saves really harsh.

http://lolcats.com/images/u/07/24/lolcatsdotcomiy0hwr7nqv87ch3g.jpg

Sstoopidtallkid
2008-09-15, 08:59 AM
^^ I think you may have missed his point here, Kizara says these are the methods he uses to balance out his games... that he runs... and he therefore is implying he does not follow the WBL guidelines.

I can't say I endorse his methods, but they work for his group.But they also color his balance advice, apparently, which does need to be brought up in a balance discussion.

only1doug
2008-09-15, 09:06 AM
^^ I think you may have missed his point here, Kizara says these are the methods he uses to balance out his games... that he runs... and he therefore is implying he does not follow the WBL guidelines.

I can't say I endorse his methods, but they work for his group.


^ I can see it working better for 4e as it goes, though it would make death saves really harsh.

<snipped img>

But he also says it would eat up the majority of their cash, which implies not leaving much for other magic items. magical defense is only one aspect of defense and defense should take about 1/3 to 1/2 your budget, not "most" (3/4 maybe?).

Holocron Coder
2008-09-15, 09:09 AM
As for the death saves in 4e with a 2d10, you can just adjust as you would for the normal critical (18-20 recovers). Otherwise, you still have a 50/50 chance of declining vs nothing/recovering, if I have my numbers right.

Charity
2008-09-15, 09:19 AM
But doug was on about raw WBL and the such, which Kizara was clearly not endorsing...
Anyhow I was just trying to keep your thread on track... I know, I know a bit of a departure for me.

It is possible that Kizara's strange cocktail works out just nicely but I would be reticent about replacing the d20 in the d20 system.

I can't see the same problems for 4e favouring the middle of the graph as it does.


But he also says it would eat up the majority of their cash, which implies not leaving much for other magic items. magical defense is only one aspect of defense and defense should take about 1/3 to 1/2 your budget, not "most" (3/4 maybe?).

Tru dat... well I'll just let him defend his stuff himself, I'm sure he'll make a better job of it..


I wasn't (see above post)

yeah got that

only1doug
2008-09-15, 09:27 AM
But doug was on about raw WBL and the such, which Kizara was clearly not endorsing...
<snip>

I wasn't (see above post)

Tengu_temp
2008-09-15, 09:33 AM
^ I can see it working better for 4e as it goes, though it would make death saves really harsh.


Here we'd replace 20 with 18-20 too, of course.

Charity
2008-09-15, 09:36 AM
As for the death saves in 4e with a 2d10, you can just adjust as you would for the normal critical (18-20 recovers). Otherwise, you still have a 50/50 chance of declining vs nothing/recovering, if I have my numbers right.

Counter intuative but quite correct. 2d10 might well work for 4e with a little bit of adjustment, I'd need to have played it a bit more to be sure.

Grynning
2008-09-15, 11:12 AM
So, if one were to try to implement this, would you borrow from the UA variant and replace re-rolls with roll 3 drop lowest?

Also, I was thinking that for 4th edition, some monster AC and hit bonuses may need to be adjusted slightly downwards, since a lot of monsters have significantly better to-hit and AC than the players do in 4th ed.

Charity
2008-09-15, 11:53 AM
Or you could just leave monsters rolling d20's, no reason that it should be the same for both.

Grynning
2008-09-15, 11:57 AM
I was thinking of somebody's chart about the AC of monsters vs. player attack bonus - most monsters would probably need a 1-2 pt. AC nerf for players to be able to hit with any regularity, since a lot of the monsters need higher than 12 to hit in 4th ed.

I could still use a d20 for monster attacks, that's not a bad idea. NPC's and BBEG's might get moved to the 2d10 system since they're supposed to be closer to PC ability.

Edit: Can't remember who made that chart - I thought it was Frosty for some reason but a search has found nothing :smallconfused:

EditEdit: Oh, it was you, Tengu! Linky (http://www.giantitp.com/forums/showthread.php?t=89993). Y'know...looking at it again, I guess adjustment wouldn't really be required, the average numbers to hit aren't as high as I remembered them being.

Yakk
2008-09-15, 12:28 PM
Yum, math.

So there are a number of cute tricks you can do with double-dice rolls.

Critical tricks -- these exploit the fact that on a given die roll, you are throwing away information when you merely add them up. We use this information to generate "is this hit a critical hit"!

There are 4 levels of critical hit, as follows:
Crit on even pairs. (5% chance)
Crit on any pair. (10% chance)
Roll an extra 'crit' die (different color). Crit on even pairs. (~15% chance)
Roll an extra 'crit' die (different color). Crit on any pair. (~30% chance)

Crits never happen if you don't hit.

Improved Critical and Keen moves you 1 notch up the table.

Note that a 19-20 weapon with improved critical under this system only hits a ~15% chance, not the ~20% chance under core. Other than that, it works out really well.

-------------

The second thing about 2d10 is we can use the variance (well, sqrt of the variance) to say what the impact of a +/- 1 modifier is, compared to a d20.

The square root of Variance is known as the Standard Deviation. If you take a random die roll (or set of die rolls), subtract the average, then divide by the standard deviation, and plot the points....

Regardless of what set of dice you started with, you end up with a graph that looks very similar. Adding more dice make it curvier and make the "tail" at each end tailier -- but that tail tends to fall within the 5% ends of the probabilities, so...

The variance and standard deviation of dice is relatively easy to calculate.

Variance = (n^2-1)/12 (n is the number of sides).
Standard Deviation = square root of Variance

The Variance of multiple dice ... adds linearly. Standard Deviation, naturally, does not. :-)

Variance of d20 = 33.25
Variance of 2d10 = 2* Variance of 1d10 = 2*8.25 = 16.5

Taking the sqrt of both:
SD of 2d10 = ~4.06
SD of 1d20 = ~5.77

With SD of 1d20 being about 1.42 times the SD of 2d10.

What does that mean? Well, it means that using a d20, your modifiers are about 1/1.42 times less important than under 2d10. As are changes in your target number.

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If you like the 2d20 system, you can make an even stronger version of it by changing D&D slightly.

Attribute modifiers go from (stat-10)/2 to (stat-10).
BaB in 3e goes up by +2 per level for full-BaB classes, +1.5 for 3/4 BaB classes, and +1 per level for 1/2 BaB classes.

"Good" saves are +4+1 per level.
"Poor" saves are +2/3 levels.

DCs for spells is (twice spell level)+10+casting attribute.

Weapon Focus adds +2 to your to hit roll.

In short, double all modifiers to d20 rolls.

For skill DCs, first subtract 10, then double the number, then add 10, to generate new "rescaled" DCs.

Double the to-hit bonuses of magic weapons. Double the magic AC bonuses of armor. Double the max dex value of armor. Double the AC of armor (well, actually, I'd do the following: Enchantment Bonuses on Light armor is +2 AC per level. Enchantment Bonuses on Medium armor is +3 AC per level. Enchantment Bonuses on Heavy armor is +4 AC per level.)

Chronos
2008-09-15, 12:59 PM
Regardless of what set of dice you started with, you end up with a graph that looks very similar. Adding more dice make it curvier and make the "tail" at each end tailier -- but that tail tends to fall within the 5% ends of the probabilities, so...You need more than two dice before you really start getting a bell curve. With just two dice, you get a triangular "curve", that just ramps up uniformly to the middle value, and then ramps back down. And if you don't have (approximately) a Gaussian distribution (the classic "bell curve"), the standard deviation isn't the most relevant of measures.

It is true that, when you're rolling multiple dice, your modifiers become more significant compared to luck, but for small numbers of dice (like 1 or 2), it's hard to quantify exactly how much more significant they are.

Tsotha-lanti
2008-09-15, 01:23 PM
Indeed, with dice, you have set "minimum" and "maximum" values. With a Bell curve and a Gaussian distribution, you just have smaller and smaller percentages the further into the ends of the curve you go.


2d10 / 3d6 don't work too well if you're doing "roll dice, add modifier, exceed goal number" - D&D's mechanic. It works much better if you're doing "roll dice equal to or under goal number, possibly with slight modifiers to goal number" - GURPS' mechanic. (In GURPS, skills of 15 are pretty much the upper limit of usefulness for unmodified tests; someone with a skill of 18 has almost the same chance of success, but has a dramatically improved chance of success if the task has a -5 modifier to the skill.)

Yakk
2008-09-15, 02:57 PM
You need more than two dice before you really start getting a bell curve. With just two dice, you get a triangular "curve", that just ramps up uniformly to the middle value, and then ramps back down. And if you don't have (approximately) a Gaussian distribution (the classic "bell curve"), the standard deviation isn't the most relevant of measures.
Chronos, have you actually looked at the graph of the CDF of each distribution, mangled as I mentioned it?

It really really really looks very similar, from 2 dice through to 4 dice. 1 die looks somewhat different, in that the curve even outside of the tails lacks ... a curve. But even then, the main impact is at the tails.

You aren't going to make me post images, are you?

Yakk
2008-09-15, 04:02 PM
The image that displays what I'm talking about:
http://theorem.ca/~afn/xd10.png
The vertical axis it the probability that you roll that value or higher.

The horizontal axis is the number of standard deviations the target number is away from the average.

The lines correspond to 1d10, 2d10, 3d10 and 4d10.

The marks on the lines correspond to particular target numbers. Using different die sizes (say, 1d20 instead of 1d10) wouldn't change the shape of the line all that much: the main effect would be to put more notches on the line.

In effect, I compensated for the change in average, and the change in "central tendency".

The 1d10 curve looks quite distinct from the other curves, but even there it is not that different beyond the "very end" of the curve. 2d10 through 4d10 look nearly identical, once you properly scale modifiers and target numbers.

The main difference between 2d10 and 4d10 lies in the 'tails' of the distribution -- but, they have on the order of 3% to 5% chance of coming up during any given role, and people seem to be reasonably comfortable with having a special mechanism for rare critical hits.

Chronos
2008-09-15, 04:25 PM
I was just referring to the distribution functions themselves, not the cumulatives. On thinking about it, though, you're right: The cumulatives are much more relevant in most RPGs.

Kizara
2008-09-15, 04:35 PM
See, the problem with giving any spell a save is how do you justify a save v. Solid Fog? And how often is the save rolled? Every 5 feet? Every turn? Once? Does Magic Missile give a save? The Orb spells? Black Tentacles?

And you still don't get rid of some great ones. Grease and Glitterdust are still good, even into high levels. Summon Monster 3, Haste, every Cleric self-buff. It's like Pathfinder. It moves towards balance but misses the point.

Solid Fog gives a strength check to move through it, albeit at reduced speed. It ends up being a sort of powered-up entangle.

Magic Missile doesn't, as it doesn't effect status. I don't have a problem with it being able to do an inferior amount of damage but gaurenteed.

It is my current opinion that orb spells are fine as-is, but that may change when I have a more through look at them.

Black Tentacles are already opposed by grapple checks, and are a random effect.

Greese is a bit of an issue I'm still trying to deal with myself.

Glitterdust is a 3rd level spell that allows a Fortitude save (its completely absurd that it's Will in the first place. I disbelieve my eyes have dust in them? Wtf is that?)

Why is Summon Monster 3 particularly imba? Summons are rarely used in my group, so I'm likely naive to it. Please explain.

Haste is fine.

Some of the cleric buffs need to be nerfed a bit, like:

-Divine Favor is a 2nd-level spell and has a duration of 1min/level.
-Find Traps is removed from the normal list, still exists as a Domain spell.
-Divine Power now has a casting time of 1 round.
-Freedom of Movement grants a bonus equal to your caster level to resist grapple attempts and all Escape Artist checks, instead of immunity. It still grants immunity to the listed magical effects.

That is hardly the extent of all my cleric spell revisions, only the major buff ones that stood out to me.


Regarding the Concentration as an opposed check, you are looking at it the wrong way. And your confusion is understandable, as if I tried to do what you are suggesting it would be mechanically terrible. This is my skill revision:

Concentration:

-Casting Defensively: When you attempt to cast defensively in combat to avoid an Attack of Opportunity, your Concentration check is opposed by your opponent’s attack roll. Essentially, you still provoke but your Concentration check serves as your AC, with a penalty of the spell level of the spell you are trying to cast (but not twice the spell level, as with other Concentration checks). Your opponent must still hit your normal AC to hit you.

-Double the spell level (instead of merely the spell level) is added to any DCs that involve the spell level.
-Any Concentration check made to cast a spell, whether from damage, motion or distraction, adds the spell level of the spell being attempted to the DC. Thus, it adds twice the spell level.


woah, spend every gp they have to own a +4 resistance cloak, then get killed by melee as they have no AC or offensive weaponry... yup that balances out magic...

Regarding the Cloak +4 at level 5 example: I was throwing it out there to make a point.
I generally give 1.5-2x the recomended WBL to my characters, and much higher stat arrays (because it gives you the freedom to make more rounded and heroic characters, you don't have to 'dump' Cha or Wis to be decent at your job, for instance).

So, while a 16k item at level 5 would be probably be almost all of their wealth just then, and I wouldn't expect people to do that, they could afford a +3 more reasonably. Also, in a few levels (when those really nasty spells and effects start comming into play) they will easily have enough for a +5 if they are worried about their defense.


self buffs and weapon buffs? "the giant dwarf cleric hit me harder so therefore his spell effects my status, i'll make a save against it!"

You are taking it a bit out of context, although I suppose I should've said "directly negatively effects your status and I don't consider straight HP damage to be 'status' ", but I was tired and was not as concise as I could've been.
No, this isn't 4e, you don't Save vs enemy buffs.


yes, because when you have a monster with spell resistance why allow the PC casters a chance to effect it at the cost of tying up one (or more) of their spell slots and choosing to cast a spell on it before they cast their save/suck or save/die.

Because sometimes magic shouldn't have an easy solution? Maybe you need to use conjuration effects, or buff party members to fight it in combat.
SR is a balancing factor for magic, and thus shouldn't be easily circumvented.