YOUR MATH ARE WRONG If prisonners follow the last strategy, the dude number 0 as a probability of finding his hat of 50% and the dude number 1 000 000 50%. Why

YOUR MATH ARE WRONG If prisonners follow the last strategy, the dude number 0 as a probability of finding his hat of 50% and the dude number 1 000 000 50%. Why? because nobody knows how many times they will lose. Those who are sure to win are those close to infinity... This have nothing to do with Axiom of Choice. But only because almost all the mass of your distribution is near infinty. With or without Axiom of Choice this things exist.