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In probability theory and decision theory the St. Petersburg paradox describes a particular lottery game (sometimes called St. Petersburg Lottery) that leads to a random variable with infinite expected value, i.e. infinite expected payoff, but would nevertheless be considered to be worth only a very small amount of money. The St. Petersburg paradox is a classical situation where a naïve decision theory (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take. The paradox can be resolved when the decision model is refined via the notion of marginal utility or by taking into account the finite resources of the participants.

The paradox is named from Daniel Bernoulli's presentation of the problem and his solution, published in 1738 in the Commentaries of the Imperial Academy of Science of Saint Petersburg (Bernoulli 1738). However, the problem was invented by Daniel's cousin Nicolas Bernoulli who first stated it in a letter to Rémond de Montmort from 9th of September 1713.

Daniel was the first to solve the problem by showing that even though the expected payoff of the game is infinite, the expected log-payoff (i.e., the expected utility of playing the game) is finite.

Those whom the Gods wish to destroy They first make mad. -- Euripides
by Migeru (migeru at eurotrib dot com) on Fri Oct 20th, 2006 at 10:16:53 AM EST
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