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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?

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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?A rolls a 30-sided die and B a 20-sided die; the higher roll wins (B wins ties) and the loser pays the winner the number on the winner's die. What is the game worth to A?You roll two dice and receive their sum, unless both show the same number, in which case you receive nothing. What is the game worth?

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