A gambler has $ 1 and needs to increase it to $ 5 in a hurry. He can play a game

Question

A gambler has $ 1 and needs to increase it to $ 5 in a hurry. He can play a game with the following rules: a fair coin is tossed; if a player bets on the right side, he wins a sum equal to his stake, and his stake is returned; otherwise he loses his stake. The gambler decides to use a bold strategy ini which he stakes all his money if he has $ 2 or less, and otherwise stakes just enough to increase his capital, if lie wins, to $ 5. What is the probability that the gambler achieve his aim? What is the expected number of tosses until the gambler either achieves his aim or loses his capital?

Explanation / Answer

A gambler has $ 1 and needs to increase it to $ 5 in a hurry. He can play a game

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