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You have permission to print and copy these pages for classroom use. This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Petersburg lottery is a paradox related to probability and decision theory in economics. A casino offers a game of chance for a single player in which a fair coin is tossed at each stage.
The initial stake starts at 2 dollars and is doubled every time heads appears. The first time tails appears, the game ends and the player wins whatever is in the pot. Assuming the game can continue as long as the coin toss results in heads and in particular that the casino has unlimited resources, this sum grows without bound and so the expected win for repeated play is an infinite amount of money. Considering nothing but the expected value of the net change in one’s monetary wealth, one should therefore play the game at any price if offered the opportunity. Several approaches have been proposed for solving the paradox.
The classical resolution of the paradox involved the explicit introduction of a utility function, an expected utility hypothesis, and the presumption of diminishing marginal utility of money. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount. It is a function of the gambler’s total wealth w, and the concept of diminishing marginal utility of money is built into it. Let c be the cost charged to enter the game. He demonstrated in a letter to Nicolas Bernoulli that a square root function describing the diminishing marginal benefit of gains can resolve the problem.