262.A Die With One Reroll
★★★optimal stoppingJane Street
You roll a fair six-sided die and are paid the number shown. After seeing the result you may, if you wish, discard it and roll once more, in which case you are paid whatever the second roll shows. Playing optimally, what is the expected payout?
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Rerolling is worth it exactly when the roll in front of you is below what a fresh roll is worth on average.
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