82.Roll Until a Six Ruins You
★★★optimal stoppingJane Street
You roll a fair six-sided die repeatedly, accumulating the total of your rolls. You may stop at any point and keep the total, but if you ever roll a 6 your score drops to 0 and the game ends. Playing optimally, what is your expected score?
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From a running total s, one more roll risks everything for an average gain of 3. Compare the expected value of continuing against banking s, and find where the balance tips.
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