Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever has the higher number wins, when there is a tie X wins. What is the probability that Y wins this game?
I even couldn't start computing probabilities since X's decision is based on Y's decision. I assume that they are both rational. How can we proceed?
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