 Is the Petrograd game worth more than the St. Petersburg game because the outcomes of the Petrograd game dominate those of the St. Petersburg game? In this context, dominance means that the player will always win $1 more regardless of which state of the world turns out to be the true state, that is, regardless of how many times the coin is flipped. The problem is that it is easy to imagine versions of the Petrograd game to which the dominance principle would not be applicable. Imagine, for instance, a version of the Petrograd game that is exactly like the one in  Table 1  except that for some very improbable outcome (say, if the coin lands heads for the first time on the 100th flip) the player wins 1 unit less than in the St. Petersburg game. This game, the Petrogradskij game, does not dominate the St. Petersburg game. However, since it is almost certain that the player will be better off by playing the Petrogradskij game a plausible decision theory should be able to explain why the Petrogradskij game is worth more than the St. Petersburg game.