Jane StreetInternInternshipQuestion #592

You are given a ten-sided die (values 1-10) and are allowed to roll it once or twice. After your first roll, you may choose to roll again. If you roll a second time, you add both values for your final score. If your total is 13 or less, you receive that amount in pounds as a payout. If your total exceeds 13, you receive nothing. What is the optimal strategy, and how did you arrive at your answer?

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