early-modern · 1623 to 1662

Blaise Pascal: The founder of expected value

To settle a gambler's dispute about how to split the stakes of an unfinished game, Pascal and a correspondent invented the mathematics of probability, and with it the first decision made by expected value.

Facts reviewed 2026-07-11.

Blaise Pascal was a French mathematician, physicist, and philosopher who did foundational work before his death at thirty-nine. Among many contributions, he built one of the first mechanical calculators and made lasting advances in geometry and the study of pressure. But his most consequential work began with a gambler's question.

A nobleman asked Pascal how to fairly divide the stakes of a game of chance that had to be abandoned before it finished. Pascal took the problem to the mathematician Pierre de Fermat, and their exchange of letters in 1654 laid the foundations of probability theory.

The problem of points, how to split a pot when a game ends early, cannot be solved by looking at the current score alone. Pascal and Fermat saw that the fair division depends on each player's probability of eventually winning from the current position. That reframing, valuing a situation by its expected future outcome rather than its present state, is the birth of expected-value reasoning.