St. Petersburg paradox

Portrait of Nicolas Bernoulli (1723)

The St. Petersburg paradox or St. Petersburg lottery[1] is a paradox involving the game of flipping a coin where the expected payoff of the lottery game is infinite but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naïve decision criterion that takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take. Several resolutions to the paradox have been proposed, including the impossible amount of money a casino would need to continue the game indefinitely.

The problem was invented by Nicolas Bernoulli,[2] who stated it in a letter to Pierre Raymond de Montmort on September 9, 1713.[3][4] However, the paradox takes its name from its analysis by Nicolas' cousin Daniel Bernoulli, one-time resident of Saint Petersburg, who in 1738 published his thoughts about the problem in the Commentaries of the Imperial Academy of Science of Saint Petersburg.[5]

  1. ^ Weiss, Michael D. (1987). Conceptual foundations of risk theory. U.S. Dept. of Agriculture, Economic Research Service. p. 36.
  2. ^ Plous, Scott (January 1, 1993). "Chapter 7". The psychology of decision-making. McGraw-Hill Education. ISBN 978-0070504776.
  3. ^ Eves, Howard (1990). An Introduction To The History of Mathematics (6th ed.). Brooks/Cole – Thomson Learning. p. 427.
  4. ^ de Montmort, Pierre Remond (1713). Essay d'analyse sur les jeux de hazard [Essays on the analysis of games of chance] (Reprinted in 2006) (in French) (Second ed.). Providence, Rhode Island: American Mathematical Society. ISBN 978-0-8218-3781-8. Translated by Pulskamp, Richard J (January 1, 2013). "Correspondence of Nicolas Bernoulli concerning the St. Petersburg Game" (PDF). Archived from the original (PDF) on April 14, 2021. Retrieved July 22, 2010.
  5. ^ Bernoulli, Daniel; originally published in 1738 ("Specimen Theorize Naval de Mensura Sortis", "Commentarii Academiae Scientiarum Imperialis Petropolitanae"); translated by Dr. Louise Sommer (January 1954). "Exposition of a New Theory on the Measurement of Risk". Econometrica. 22 (1): 22–36. doi:10.2307/1909829. JSTOR 1909829. Retrieved May 30, 2006.{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)