You roll a fair 10-sided die with faces 0 to 9 again and again, adding each roll to a running total, but a 0 wipes out the total and ends the game. When should you stop?
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You roll a fair 10-sided die with faces 0 to 9 repeatedly. Each roll adds its face to a running total, but rolling a 0 wipes out the whole total and ends the game. After each roll you may stop and keep the total. What is the optimal strategy?
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