 The standard version of the St. Petersburg paradox is derived from the St. Petersburg game, which is played as follows: A fair coin is flipped until it comes up heads the first time. At that point the player wins \(\$2^n,\) where n is the number of times the coin was flipped. How much should one be willing to pay for playing this game? Decision theorists advise us to apply the principle of maximizing expected value. According to this principle, the value of an uncertain prospect is the sum total obtained by multiplying the value of each possible outcome with its probability and then adding up all the terms (see the entry on  normative theories of rational choice: expected utility).  In the St. Petersburg game the monetary values of the outcomes and their probabilities are easy to determine. If the coin lands heads on the first flip you win $2, if it lands heads on the second flip you win $4, and if this happens on the third flip you win $8, and so on. The probabilities of the outcomes are \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{1}{8}\),…. Therefore, the expected monetary value of the St. Petersburg game is