 Let us also mention another, quite simple variation of the original St. Petersburg game, which is played as follows (see Peterson 2015: 87): A manipulated coin lands heads up with probability 0.4 and the player wins a prize worth \(2^n\) units of utility, where n is the number of times the coin was tossed. This game, the Moscow game, is more likely to yield a long sequence of flips and is therefore worth more than the St. Petersburg game, but the expected utility of both games is the same, because both games have infinite expected utility. It might be tempting to say that the Moscow game is more attractive because the Moscow game stochastically dominates the St. Petersburg game. (That one game stochastically dominates another game means that for every possible outcome, the first game has at least as high a probability of yielding a prize worth at least u units of utility as the second game; and for some u, the first game yields u with a higher probability than the second.) However, the stochastic dominance principle is inapplicable to games in which there is a small risk that the player wins a prize worth slightly less than in the other game. We can, for instance, imagine that if the coin lands heads on the 100th flip the Moscow game pays one unit less than the St. Petersburg game; in this scenario neither game stochastically dominates the other. Despite this, it still seems reasonable to insist that the game that is almost certain to yield a better outcome (in the sense explained above) is worth more. The challenge is to explain why in a robust and non-arbitrary way.