Britannica Sources used in this answer

How did Pierre de Fermat solve the interrupted-game problem?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

French philosopher Blaise Pascal — Blaise Pascal Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet–Histoire de Paris, Paris. Pascal laid the foundation for probability theory.

In the context of the correspondence between Pierre de Fermat and Blaise Pascal regarding the "interrupted-game problem," Fermat solved the issue by calculating the chances or probabilities of each player winning the remaining rounds.1

To solve the problem, Fermat identified a set of symmetrical cases based on the assumption that two more games would be sufficient to determine a winner. He analyzed the four equally likely outcomes for those two games: AA, AB, BA, and BB. By observing that only one of these four sequences results in a victory for player B, he determined that the odds for player A were 3:1. Consequently, he concluded that the stakes should be divided in a 3:1 ratio, awarding 48 pistoles to player A and 16 pistoles to player B in a game where each had originally wagered 32 pistoles.1