*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 defending die has a greater or equal score to the attacking die, the defending die wins (conversely, if the attacking die has a greater score than the defending die, the attacker wins that pair).

In terms of

*a*, how do we calculate the probability that i) the defending dice will win both pairs, ii) the attacking dice will win both pairs, iii) 1 pair will be won by a defending die and the other by an attacking die?

I see I'm required to show work, but I really don't know how to start! I solved the problem for when there is only 1 defending die and it's paired up with the highest attacking die. I landed up realizing that P(Defending die wins pair)=(1/6)*Sigma(i=0 to 6)[(i/6)^a]. (Please excuse the lack of LaTeX - my abilities do not reach far enough so far to write sigma functions in LaTeX) but how do I find a function for this problem now there are 2 defending die?