434.Push Your Luck on a d10
★★★optimal stoppingCh. 6 — Random Variables and Expectation444+ Problems in Probability
Adam rolls a fair 10-sided die repeatedly. Each non-10 roll adds its face value to his bank; rolling a 10 wipes the bank to zero and ends nothing — he may stop at any time and keep the bank. Playing optimally, Adam should stop once his bank reaches at least . Find .
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Compare the marginal EV of one more roll at bank : what do you gain on average, and what do you risk?
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