"The Gibbon of Math History". Who Invented the St. Petersburg Paradox? Khinchin's resolution

Abstract

A sentence from Carl Boyer's A History of Mathematics can be interpreted so that the full brothers Nicolaus II (02/06/1695 - 07/31/1726) and Daniel Bernoulli (02/08/1700 - 03/17/1782) are the authors of the St. Petersburg paradox. The paradox was formulated by their cousin Nicolaus I Bernoulli (10/21/1687 - 11/29/1759). The author did not find evidences that Nicolaus II and Daniel Bernoulli discussed the paradox. The key articles on the topic and its history from Karl Menger and Paul Samuelson, and recent papers presenting the time resolution miss Alexandr Khinchin's resolution of the paradox in his paper "On Petersburg game." Matematicheskii sbornik, Volume 32, No 2, 1925, pp. 330 - 341. The C++ program khinchin.cpp simulates conditions of two Khinchin's theorems and confirms his results providing concrete empirical dependencies of the frequencies corresponding to geometric and arithmetic mean payments on the number of Petersburg games.