You have three dice: Die A, Die B, and Die C. They are non-standard, but arranged such that A tends to roll higher than B, B tends to roll higher than C, and C tends to roll higher than A (a non-transitive set, like Efron’s dice). If you pick one die and I pick another, each roll, what is the probability that the non-transitive cycle yields a win for the first die on average?
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