336.Dollar Re-Rolls
★★★optimal stoppingCh. 6 — Random Variables and Expectation444+ Problems in Probability
Alice rolls a fair 6-sided die. After seeing the face she may stop and receive its value in dollars, or pay to roll again — with no limit on re-rolls. Under optimal play, what is her expected payout?
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Let be the value of the game. Then — solve the fixed point.
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