From St. Petersburg to Monte Carlo: A Resolution Rediscovered and Affirmed

Abstract

The St. Petersburg paradox has served as an intriguing pedagogical device for almost 300 years, since it was first described by Daniel Bernoulli in 1738. Many explanations of the paradox have been offered, most involving either theories of individual behavior or the practical limitations of playing the game. We do not revisit any of the conventional explanations. Rather, we endeavor to demonstrate that the premise underlying the paradox – that the St. Petersburg game’s expected value is infinite – is mistaken. The analysis focuses on how the probability distribution of the game’s duration determines and limits the expected value. We do not claim precedence on so fundamental a resolution of the paradox. Our analysis is guided by the approach first described by the mathematician William Feller in 1945. We conduct a massive array of computer simulations within the framework suggested by Feller’s approach. The simulation results allow for an empirical evaluation of his coherent resolution.