Saturday, 7 July 2012

More AnyDice d6 Dice Pool Probabilities

Following my previous exciting and enigmatic post about d6 dice pool probabilities, I've also run the same combinations of dice pools through AnyDice to see what the probabilities are when you take the cumulative totals of the pools, rather than just the highest of either pool.   The results are (obviously) a lot different.

First though, here's the AnyDice code:

function: opposedhighestcume of A:n and B:n
      if A >= B { result: 1 }
      result: -1

output [opposedhighestcume of 1d6 and 1d6]
output [opposedhighestcume of 2d6 and 1d6]
output [opposedhighestcume of 3d6 and 1d6]
output [opposedhighestcume of 4d6 and 1d6]

output [opposedhighestcume of 1d6 and 2d6]
output [opposedhighestcume of 2d6 and 2d6]
output [opposedhighestcume of 3d6 and 2d6]
output [opposedhighestcume of 4d6 and 2d6]

output [opposedhighestcume of 1d6 and 3d6]
output [opposedhighestcume of 2d6 and 3d6]
output [opposedhighestcume of 3d6 and 3d6]
output [opposedhighestcume of 4d6 and 3d6]

output [opposedhighestcume of 1d6 and 4d6]
output [opposedhighestcume of 2d6 and 4d6]
output [opposedhighestcume of 3d6 and 4d6]
output [opposedhighestcume of 4d6 and 4d6]

That code outputs either -1 or 1, depending on which pool 'won':
•   1: Attacker's total is higher (or ties, which is also a win).
•  -1: Means that the second pool 'won' and the attack was unsuccessful.

Here are the results for the cumulative opposed checks, with ties resolved in favor of the attacker:

Attacker's pool
(down the left)
1d6 2d6 3d6 4d6
1d6 58% 16% 3% 0%
2d6 91% 56% 22% 6%
3d6 98% 85% 55% 26%
4d6 99% 96% 81% 54%

Here again are the previous results for the 'highest dice' opposed checks, with ties resolved in favor of the attacker:

Attacker's pool
(down the left)
1d6 2d6 3d6 4d6
1d6 58% 42% 34% 30%
2d6 75% 61% 53% 48%
3d6 83% 72% 65% 60%
4d6 88% 79% 73% 69%

That's all pretty boring, right?  

Well, hopefully it will make sense one day. :-)

Check out Heroes Against Darkness, which has a dice mechanic no one could call innovative: Heroes Against Darkness - Game Rules.


  1. Hello there,
    The system looks promising, especially because it is scalable, meaning that the attacker with 2d6 against a 1d6 has roughly the same chance as 4d6 against 3d6. This is very good to keep the game balanced and outcomes of challenges predictable. Counting these many dice however might end up being the problem.


    1. Hi Felix, I'm mainly focused on the lower numbers of dice, because I think that those areas give the better spread of opposed results (in both cases). I was originally thinking about 3d6 being 'normal', but now I think that 2d6 is a better statistically and probably easier in play.