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You roll a fair six-sided die up to three times, stopping whenever you like and taking the value you stopped on; the third roll must be accepted. What is the game worth?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

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You roll a fair six-sided die up to three times, stopping whenever you like and taking the value you stopped on; the third roll must be accepted. What is the game worth?

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