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A die game with paid re-rolls · Part 2 of 3
You roll a fair six-sided die and are paid the face value in dollars. After seeing a roll you may stop, or pay to roll again, under the rules in each part.
Now you may re-roll as many times as you like, paying $1 each time. What is the game worth under the best strategy?
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
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