St Petersburg paradox

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A paradox of decision making first presented to the St Petersburg Academy in 1738 by the Swiss mathematician and physicist Daniel Bernoulli (1700–82). A coin is tossed; if it falls heads then the player is paid one rouble and the game ends. If it falls tails then it is tossed again, and this time if it falls heads the player is paid two roubles and the game ends. This process continues, with the payoff doubling each time, until heads comes up and the player wins something, and then it ends. How much should a player be willing to pay for the opportunity to play this game? According to the principles of probability theory, the player wins one rouble with probability 1/2, two roubles with probability 1/4, four roubles with probability 1/8, and so on, therefore the game's expected value is (1/2)(1) + (1/4)(2) + (1/8)(4) +  … , and this sum is infinite because each of its terms is equal to 1/2. But it would obviously be absurd to pay a large amount for the privilege of playing the game, because there is a high probability of losing everything, including a 50 per cent chance of losing it on the very first toss, and the game is fatally damaging to the principle of maximizing expected value. The discovery of the paradox led directly to Bernoulli's introduction of ‘moral worth’, which later came to be called utility (1). Also called the St Petersburg game. See also risk aversion. Compare Allais paradox, common ratio effect, Ellsberg paradox, modified Ellsberg paradox.

Subjects: Psychology.

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