132.Second Roll or Bust at Thirteen
★★★optimal stoppingJane Street
You roll a fair ten-sided die numbered 1 to 10. You may stop there, or roll a second time and add the two results together. Your payout in dollars is your final total if it is 13 or less, and nothing at all if the total exceeds 13. Playing optimally, what is the expected payout?
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Work first roll by first roll: compare keeping the number in front of you against the average value of rolling again, remembering that going over pays zero rather than costing only the excess.
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