# Thread: 2d10 Bell Curve vs d20 (need help from you math types).

1. ## 2d10 Bell Curve vs d20 (need help from you math types).

So I was thinking about these 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 ) 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!

2. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

3. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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 ).

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.

4. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

5. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

% 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.

6. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Sstoopidtallkid
% 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%

7. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Charity
*better math than me*
:-p wordiness

8. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

9. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

10. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Grynning
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.

11. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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...

12. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

^ 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.

13. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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?

14. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Grynning
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.

15. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by nagora
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.

16. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Grynning
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.

Originally Posted by Grynning
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%).

17. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

18. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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

19. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

20. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Kizara
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.

21. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

22. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Charity
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.

23. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Kizara
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.

24. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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

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.

Originally Posted by Kizara
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.

Originally Posted by Kizara
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

Originally Posted by Kizara
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.

25. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Kizara
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.
Originally Posted by Kizara
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.
Originally Posted by Kizara
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.
Originally Posted by Kizara
It is easier to use PA because you know more consistantly what range you will likely be rolling in.
That is true.
Originally Posted by Kizara
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?

26. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Sstoopidtallkid
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

27. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

28. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Kizara
*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.

29. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

Originally Posted by Sstoopidtallkid
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.

30. ## Re: 2d10 Bell Curve vs d20 (need help from you math types).

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.

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