Horse lottery

A horse lottery is the two-stage act introduced by Francis Anscombe and Robert Aumann in their 1963 decision-theoretic framework. In the first stage, a state of the world is realized — whether a horse wins a race, whether it rains, whether a market crashes. In the second stage, an objective lottery — with probabilities generated by a physical random device like a roulette wheel — determines the final payoff. The term 'horse lottery' derives from the canonical example: a bet on a horse race where the winning horse determines which roulette-wheel gamble the bettor receives. The structure allows the separation of subjective probability (over horse-race outcomes) from utility (over roulette payoffs), a separation that the Anscombe-Aumann representation theorem proves is both mathematically clean and behaviorally meaningful.