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. :-)

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