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A gambler has $4, and he can bet up to 4 times with the goal of maximizing the probability of ending with exactly $8. In

A gambler has $4, and he can bet up to 4 times with the goal of maximizing the probability of ending with exactly $8. In each bet, the probability of winning is 0.6 and the probability of losing is 0.4. If the gambler wins the bet, he gets twice the value of the bet back, but if he loses, he gets nothing back (including the bet). In addition, the gambler can only bet value up to what he has available at the beginning of each betting time

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