And what if the person running the game said "No thanks" to that offer? What is the top amount you would be willing to pay to play? Keep in mind that the expected value is infinite. Also keep in mind that the only way to obtain this expected value is to flip an infinite number of tails in a row, which is something you will not be able to do in a finite amount of time. (And you will presumably die in a finite amount of time.)Since the question is what I would pay, I would pay zero, so that any winnings would be pure profit.