The St. Petersburg Paradox
A coin-flipping game whose average winnings are infinite. How much of your own money would you actually pay to play?
1713 (posed by Nicolaus Bernoulli), 1738 (published by Daniel Bernoulli)19 min read
Viennese mathematics
Karl Menger
1902 – 1985
Member of the Vienna Circle and a founder of dimension theory, later professor at Illinois Institute of Technology. His 1934 paper on uncertainty in value theory delivered the sharpest blow to the St Petersburg literature: for any unbounded utility function whatsoever, a "super-St-Petersburg" game can be built whose expected utility is again infinite. Bounded utility is therefore not a convenience but a requirement.