Jane Street–styleInternSummer InternQuestion #641

I have a 12-sided die and you have a 20-sided die. Each of us gets up to two rolls, and on either roll, we can choose to stop and keep the number from that roll. Whoever has the higher number wins, with ties going to the person with the 12-sided die. What is the probability that the person with the 20-sided die wins this game?

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