 Bartha (2016) proposes a more complex version of Colyvan’s theory designed to address the worry outlined above. His suggestion is to ask the agent to compare a “problematic” game to a lottery between two other games. If, for instance, Petrograd+ is the game in which the player always wins 2 units more than in the St. Petersburg game regardless of how many times the coin is tossed, then the player could compare the Petrograd game to a lottery between Petrograd+ and the St. Petersburg game. By determining for what probabilities p a lottery in which one plays Petrograd+ with probability p and the St. Petersburg game with probability \(1-p\) is better than playing the Petrograd game for sure one can establish a measure of the relative value of Petrograd as compared to Petrograd+ or St. Petersburg. (For details, see Sect. 5 in Bartha 2016. See also Colyvan and Hájek’s 2016 discussion of Bartha’s theory.) 