217.Bank Before You Bust
★★★optimal stoppingJane Street
You roll a fair six-sided die repeatedly, adding each result to a running total. You may stop at any point and keep the total, but if the total ever reaches 7 or more you score nothing. Playing optimally, what is your expected score?
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Work backwards from a total of 6. At each total compare stopping against rolling, remembering that any roll pushing you past 6 scores zero.
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