Daniel Bernoulli and the St. Petersburg ParadoxLATEX file:StPetersburgParadox— Daniel A. Graham, June 19, 2005Suppose you are offered the chance to play the following game. A fair coin will be tossed until a headappears. If a head occurs for the first time on thenth toss then you will be paid 2ndollars. How muchwould you be willing to pay to play this game?TheSt. Petersburg Paradoxis that although the expected value of the payoff is infinite, 21(1/2)1+22(1/2)2+ · · · =1+1+ · · · = ∞, no one seems to be willing to pay anything approaching this sum toplay this game.
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