A gamble with infinite expected value is one that almost nobody will pay much to play.
Nicolas Bernoulli posed it in 1713 and Daniel Bernoulli answered it in 1738. A coin is tossed until it falls heads, and the prize doubles with every tail, so the expected payout is unbounded. Almost nobody will stake more than a modest sum. Bernoulli's resolution was the diminishing marginal utility of money, the first statement of a principle that now runs through economics; bounded utility and the finite wealth of the house account for the rest.
In practice
- A pitch promising an enormous payoff at a tiny probability raises less money than a modest one with a plausible return, which is not irrational.
- A lottery sells much the same number of tickets whether the rolling jackpot is large or enormous.
- Standing
- Resolved rather than open, and historically important as the origin of utility theory. Compare the Allais and Ellsberg paradoxes.
- Further reading
- Wikipedia
- Subject
- Decision-making & Reasoning
- Essay
- Paradoxes that broke theories, and sayings that outlived them