Dice game, up to three rolls

You may roll a die up to three times. After the first or second roll you may keep the current value (forfeiting later rolls) or roll again; on the third roll you must keep the value. With optimal play, what is the expected value? (to 3 decimals)

Show hints (2)+
  1. Work backwards from the last roll.
  2. Keep only values above the continuation value.

Answer

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4.667 (± 0.01)

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Asked at: Citadel, DRW

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