Forthcoming in the Journal of Philosophy A New Twist To The St. Petersburg Paradox Martin Peterson In this paper I explain why Mark Colyvanʹs proposed resolution of the Petrograd paradox does not work. 1 The Petrograd paradox is derived from the Petrograd game, which is a slightly modified version of the well‐known St Petersburg game. 2 The difference is that, in the Petrograd game, the player always wins one additional utile no matter how many times the coin has been tossed. See Table 1. Probability 1/2 1/4 1/8 ... St Petersburg 2 4 8 ... Petrograd 1 2 + 1 4 + 1 8 + ... Table 1. Everybody agrees that the Petrograd game should be preferred to the St Petersburg game. The challenge is to explain why, without giving up the principle of maximising expected utility. Clearly, the expected utility of both games is ∞ . The Petrograd game dominates the St Petersburg game. However, the problem is not only that the dominance principle and the expected utility principle give different recommendations. The problem is more complex, as shown by the Leningrad game. This game is identical to the Petrograd game, except that in some very improbable state the player receives one utile less than in the St Petersburg game. The Leningrad game does not dominate the St Petersburg game. Nevertheless, the intuition is that it is worth more: `After all, the Leningrad game almost dominates the St. Petersburg game and the probability of finding oneself in the non‐dominant state is, by construction, very low.ʹ 3 Colyvan proposes that the paradoxes posed by the Petrograd and Leningrad 1 ʹRelative Expectation Theoryʹ, Journal of Philosophy, 105 (January 2008): 37–44. 2 In the St Petersburg game a fair coin is tossed n times until it lands heads up. The player then receives a prize worth n 2 utiles. 3 Colyvan, op. cit., p 38.