A and B alternate rolling a pair of dice, stopping either when A rolls the sum 9 or when B rolls the sum 6. Assuming that A rolls first, find the probability that the final roll is made by A.
The Attempt at a Solution
A rolls a sum 9 on each roll with prob 1/9
B rolls a sum 6 on each roll with prob 5/36
Given that A wins, he will win on an odd number of turns. (since A starts)
Let E be the event that the game finishes on an odd number of turns
Then P(E) = (1/9)(1-5/36)(1/9)(1-5/36)....
Where do I go from here?