Solution
St. Petersburg Paradox
Show the problem again
A casino flips a fair coin until heads appears. If heads appears on flip n, you win $2^n. What is the expected value of this game in dollars?
Worked solution
The expected value is infinite. The probability of winning $2^n is (1/2)^n, so the contribution of each outcome to the expected value is exactly $1. Summing infinitely many $1 contributions gives an infinite expected value. Yet most people would pay very little to play, illustrating that expected monetary value alone does not capture rational decision-making.
Source: Posed by Nicolas Bernoulli (1713); the utility resolution is due to Daniel Bernoulli (1738). Statement written for AxiomIQ.