MathDB

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\in \{1,..,6\}

and

10a + b \le 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?

Problem Statement