 You might object that the utility of money decreases as you obtain more of it: if the rate of this decrease is sufficiently large, then the expected value of playing the game is finite. Daniel Bernoulli argued that utility goes by the logarithm of the amount of money, and indeed replacing the dollar amounts with their logarithms yields a finite expected utility. However, we can retell the story in terms of utilities themselves. And we can retell it with super-exponential escalation of the value of the payoffs: taking logarithms then gives us exactly the original expected utility. (See Menger 1967/1934.) In fact, as long as utilities are unbounded, we can fashion a version of the game that has infinite expected utility.