IMO 1985 LL ITA45
Two persons, X and Y , play with a die. X wins a game if the
IMO 1985 LL ITA45
Origin: ITA
Problem
Two persons, X and Y , play with a die. X wins a game if the outcome is 1 or 2; Y wins in the other cases. A player wins a match if he wins two consecutive games. For each player determine the probability of winning a match within 5 games. Determine the probabilities of winning in an unlimited number of games. If X bets 1, how much must Y bet for the game to be fair?