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Consider a game of chance with the following characteristics: A person repeatedly bets $1 each play. If he wins, he receives $1. If he goes broke, he stops playing. Also, if he accumulates $3, he stops playing. On each play the probability of winning is 0.432 and of losing 0.568. If the gambler begins with $2, what is the expected number of times that he will play before quitting? (Round your answer to 3 decimal places.)

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