2013 HMMT Guts #15: Expected Amount of Tenus
Source:
March 26, 2013
HMMTprobabilityexpected value
Problem Statement
Tim and Allen are playing a match of tenus. In a match of tenus, the two players play a series of games, each of which is won by one of the two players. The match ends when one player has won exactly two more games than the other player, at which point the player who has won more games wins the match. In odd-numbered games, Tim wins with probability , and in the even-numbered games, Allen wins with probability . What is the expected number of games in a match?