One re-roll allowed

Roll a die once. You may keep its value or re-roll exactly once and keep the second value. Playing optimally, what is the expected payout? Give a decimal to two places.

Show hints (2)+
  1. Compare the first roll to the value of re-rolling.
  2. Re-roll only when the first roll is below 3.5.

Answer

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4.25 (± 0.01)

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Asked at: Optiver, Akuna Capital

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