354.Risky Second Roll
★★★optimal stoppingCh. 6 — Random Variables and Expectation444+ Problems in Probability
You roll a fair 6-sided die. You may keep the roll and receive its value in dollars — or roll again, in which case: if the two rolls sum to at least 7 you pay your first roll's value, and if the sum is less than 7 you receive the second roll's value. Under optimal play, what is your expected payout?
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Compute the re-roll EV as a function of your first roll — note that higher both shrinks the safe range and raises the penalty.
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