edit: As noted in your other comment, the expectation with a standard utility function is actually negative, thus the premise for part of the below is incorrect

edit: As noted in your other comment, the expectation with a standard utility function is actually negative, thus the premise for part of the below is incorrect, and therefore so are its conclusions. A more faithful reproduction of Peters' argument is that EE recovers the correct solution without requiring the addition of an arbitrary utility function, and corresponding appeals to irrationality. original comment: Yes, you are correct that in the initial framing it is just a single gamble, but of course the point is that an individual's life is made up of many gambles. Expected utility assures us that this bet has a positive expectation, and so naively we might think that iterating it also produces a positive expectation sequence, but it does not, as we saw. We can recover a correct answer by considering the expected utility of the whole sequence, but there is nothing in the problem to suggest that we should do so, unless we acknowledge the cause of the issue, which is that the ergodic hypothesis does not hold. The point of the whole "parallel universe" thing is that even though the expectation in a single step may be positive, an individual never realises that ensemble average - they only ever realise a time average. Thus, the time average is the more useful object of study.