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You roll a 100-sided die and can take the dollar amount shown or pay $1 to roll again, as often as you like. What is the game worth?

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You roll an 8-sided die and win the amount shown, or you may instead re-roll using a 12-sided die. How much should you pay to play?I roll a die up to three times. After each roll you may stop and take the number showing as your payoff. What is your strategy and what is the game worth?20-sided die, 100 rounds: each round either roll, or take the face value in dollars, after which the die is removed until you spend a round rolling again. How should you play?

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