Players A and B play the following game. Each of them throws a dice, and if the outcomes are x and y respectively, a list of all two digit numbers 10a+b with a,b∈{1,..,6} and 10a+b≤10x+y is created. Then the players alternately reduce the list by replacing a pair of numbers in the list by their absolute difference, until only one number remains. If the remaining number is of the same parity as the outcome of A’s throw, then A is proclaimed the winner. What is the probability that A wins the game? probabilitygamecombinatorics