Three rolls, keep the last

Roll a die. You may keep its value or re-roll, up to 3 rolls total, and you keep whatever the final roll shows when you stop. Playing optimally, what is the expected payout? Give a decimal to two places.

Show hints (2)+
  1. Work backwards from the last roll.
  2. Keep a roll only if it beats the value of continuing.

Answer

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4.67 (± 0.03)

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Asked at: Jane Street, Optiver

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