The points problem
(The Problem of the Points) Ari and Ben flip coins. If the coin shows head, Ari gets a point. If the coin shows tail, Ben gets a point. The player who is the first to get N points wins the game. After they have been playing for a while, Ari notices: „I still need n points to win.” Ben replies: „I need m points to win.”
What is the probability that Ari wins the game?
Hint: Ari suggests: „Let’s flip another n+m‐1 coins, even if one of us wins the game before that.”
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player's guess his bet will be doubled. It costs 1 dollar to play
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long as there is the available bank amount.
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