Consider a game with n ∈ N participants which are somehow ordered (P1, P2, ..., Pn). The game starts with the first numbered player (P1) tosses a fair coin until the first “Tail” appears. By x1 we denote the number of flips made by P1. Player P1 is eliminated from the game if x1 < y. In this case, the second player tosses a fair coin until the first “Tail” appears. Similarly, by x2 we denote the number of flips made by P2. Player P2 is eliminated from the game if x1 + x2 < y. The game proceeds this way until either the total number of coin flips attains y, or all players are eliminated. All those players who are not eliminated at the end of the game are winners. Find the expected number of tosses for a player i (E(xi)) assuming there is no limit on the total number of flips (y).
Consider a game with n ∈ N participants which are somehow ordered (P1, P2, ..., Pn). The game starts with the first numbered player (P1) tosses a fair coin until the first “Tail” appears. By x1 we denote the number of flips made by P1. Player P1 is eliminated from the game if x1 < y. In this case, the second player tosses a fair coin until the first “Tail” appears. Similarly, by x2 we denote the number of flips made by P2. Player P2 is eliminated from the game if x1 + x2 < y. The game proceeds this way until either the total number of coin flips attains y, or all players are eliminated. All those players who are not eliminated at the end of the game are winners.
Find the expected number of tosses for a player i (E(xi)) assuming there is no limit on the total number of flips (y).
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