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Two armies of n attackers and m defenders do battle. If n=1, then there is 1 attacking die; if n=2 there are 2 attacking dice; if n \geq 3 there are 3 attacking dice. If m=1 there is 1 defending die; if m \geq 2 there are 2 defending dice. (You may recognize this as Risk, and you'd be right.)...

2 defending dice do battle with a attacking dice, where a can be any positive integer. The highest scoring defender die is paired with the highest scoring attacking die; the second-highest scoring defending die is paired with the second-highest scoring attacking die. If, in each pair, the...