Probability in the boardgame Risk
Just for my own amusement I've been trying to work out the probability of winning a dice roll in Risk. For those of you who've never played it, here's the set up:
1) The attacker has 3 dice, the defender has 2. Both sides roll all their dice.
2) The attacker's highest die is compared with defender's highest die, and whichever is higher wins, and whichever is lower is discarded.
3) This is repeated for the attacker's second highest against the defender's second highest. Any ties are awarded to the defender.
There's more to it than this, depending on how many armies each side has got etc, but all I really want to do is work out the probabilities of each side winning for one roll of the dice.