Games and stopping · Dice game
Keep or reroll
You roll a fair 6-sided die and are paid its face value. After each roll you may keep it, or roll again, up to 1 rerolls in total; you must keep the last roll. Playing optimally, what is your expected payout?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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