ILL 1985 Problem 45

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 ?