At the casino in las vegas a customer can bet only in, Ask an Expert

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At THE CASINO in Las Vegas, a customer can bet only in dollar increments. Betting a certain amount is called ‘‘playing a round.'' Associated with each dollar bet on a round, the customer has a 40% chance to win another dollar and a 60% chance to lose his, or her, dollar. If the customer starts with $4 and wants to maximize the chances of finishing with at least $7 after two rounds, how much should be bet on each round? [Hint. Consider the number of dollars available at the beginning of each round as the state variable.]

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