AnyDice vs. a d6 Dice Pool Mechanic

I've been mulling over a set of super-simple RPG rules for kids (maybe from 4 and up).   As part of this I've been thinking about a simple (but playable) dice mechanic that involves opposed pools of d6s, with only the highest dice counting for each of the participants (and ties resolving in favor of the attacker, although this could change).

I've finally managed to get AnyDice to spit out the probabilities I was after for the opposed dice pool mechanic (gosh I hate it when people get excited about their 'new' dice mechanics).

This code for AnyDice spits out the amount by which the highest dice of the first dice pool is equal to or greater than than the highest dice of the second dice pool:

---

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

output [opposedhighest of 1@1d6 and 1@1d6]
output [opposedhighest of 1@2d6 and 1@1d6]
output [opposedhighest of 1@3d6 and 1@1d6]
output [opposedhighest of 1@4d6 and 1@1d6]

---

•  -1: Means that the second pool 'won' and the attack was unsuccessful.
•  0: Means the highest dice of each pool were tied, which can be resolved in favor of the attacker or the defender.
•  1+: Higher numbers represent the disparity between the attacker's highest dice against the defender's highest dice.

Here are the results for the 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%

And, here are the results with ties resolved in favor of the defender:

Attacker's pool (down the left)	1d6	2d6	3d6	4d6
1d6	42%	26%	17%	13%
2d6	58%	39%	28%	21%
3d6	66%	47%	35%	27%
4d6	71%	53%	40%	31%

What does it mean?   Which one is better?   

I'm not sure yet, but I'll let you know!

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