85.Eight-Sided, Then Twelve-Sided
★★★optimal stoppingJane Street
You roll a fair eight-sided die numbered 1 to 8. You may keep that value, or discard it and instead roll a fair twelve-sided die numbered 1 to 12 and keep whatever it shows. Playing optimally, what is the expected payout?
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Work out what the twelve-sided option is worth on its own, then keep the first roll only when it beats that.
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