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On a trip to Las Vegas, you stopped over at a casino to play a game of chance. You have $10, and each play costs

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On a trip to Las Vegas, you stopped over at a casino to play a game of chance. You have $10, and each play costs $2. You have 1/3 chance to win $5, and 2/3 chance to win nothing. You just want to play as long as you have enough money. How many games do you expect to play in total? Be careful! If you cannot give the exact answer, give upper and lower bounds.

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