I really wish I still had my Combinatorics textbook. (The drawback of borrowing textbooks to try and save money)

There is a major drawback to "Dice Pools", where you roll many dice, but aren't summing them together. Apparently you can actually get into issues where rolling more dice, decreases your chances. I had a conversation once about it with someone far better at stats than I am, and I think he referenced the White Wolf system as having this flaw as you gain levels. I think it was your chance of total failure or bad botch rose as you gained level/skill, and thus threw more dice, but minor failure decreased or something. Hopefully someone more familiar with the mechanics knows of this issue and can chip in with a better understanding.


The tool at the website anydice.com seems to work very well for showing you the stats.

For 3d6, you get numbers like this: Number rolled followed by its chance of being rolled out of 100.
3 0.46

4 1.39

5 2.78

6 4.63

7 6.94

8 9.72

9 11.57

10 12.50

11 12.50

12 11.57

13 9.72

14 6.94

15 4.63

16 2.78

17 1.39

18 0.46

As you can see, nearly half the time you can expect to roll a 9, 10, 11, or 12. This is a reason why I'm not the biggest fan of rolling 3 or more dice to get a sum: Your results are too predictable. However they can be great if that is what you want in your system; a wide range of possible options, but a more narrow predictable range it is most likely to fall in.

When you compare types of dice rolls you need to consider a few things: What do the numbers actually mean in your system? What do your rolls mean? "Roll X or higher?" or "Roll higher than X", vs "Roll exactly X" makes how you look at your chances a lot different.

If you are rolling a value or better than it, then you look at the target number, and take the sum of the percentages of those values that would beat it. You can then roughly compare that to a dice roll over a similar range. Such as comparing d20 to a 2d12. If you graph the probability you get a triangle for 2d12, and a flat line for the d20. (3 or more dice gets you a proper bell curve.)
If you compare your "Chance to roll X or Higher", you actually get better chances in 2d12 till you get at the upper range. (Past where the d20 can actually roll into) Your chances of rolling a 20 in d20 are a lowly 5%, but over 10% in 2d12. (Of course, you're around 0.7% to roll a 24, far worse to roll absolute max.)

Also remember that while your PCs are more likely to hit at given number in a system, it usually means your NPCs get the same effect. So be careful if you have defenses that creep too high on either side. A game where no one hits anything tends to be boring. As is a game where one side gets the advantage in bonuses that lets them usually hit vs the other side almost never hitting.