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It has been almost three centuries since the first version of the so-called St. Petersburg Paradox has reached the academic environment through the work of Daniel Bernoulli. However, the relevance of this subject still reverberates in new scientific papers in many knowledge fields (especially, but not exclusively, in Economics and Statistics). A game with a simple rule in which the mathematical expectation of the player’s gains is unexpectedly infinite but hardly someone would be willing to pay any asked entrance fee to play it. In this work we pursued at first to present a critical analysis on the historical development of the proposed “solutions” to the paradox. After that, we showed an application of the paradox to a mathematical model, that is still in use today, to obtain a fair price of a stock share. At last we reviewed some results given by the modern probability theory through the convergence in probability.

A lei fraca de Feller para jogos de São Petersburgo