The St. Petersburg Paradox and Expected Utility

In 1713, Nicholas Bernoulli posed a lottery: flip a coin until tails. You win 2ⁿ ducats where n is number of heads before first tail. Expected winnings = Σ (1/2ⁿ)·2ⁿ = infinite. Yet no one would pay more than a modest amount to play. Daniel Bernoulli resolved it by introducing utility: the marginal value of money decreases. The logarithmic utility function makes expected utility finite. This paradox birthed behavioural economics and the concept of risk aversion. It shows that infinite expected value doesn’t imply infinite desirability.