What interrupted-game problem did Pierre de Fermat and Blaise Pascal solve in their 1654 correspondence?

In their 1654 correspondence, Pierre de Fermat and Blaise Pascal addressed the "problem of points," which concerns the fair division of stakes in a game of chance that has been interrupted before completion.1

The problem was brought to their attention by the chevalier de Méré, a gambler who asked how to equitably distribute the total wager if two players, who have each contributed an equal amount, are forced to stop playing while one player is ahead of the other. For example, in a game where the first to reach three points wins, if player A has two points and player B has one, the stakes must be divided based on the probability of each player winning the remaining rounds.1

Fermat and Pascal arrived at the same numerical conclusion using different methods: Fermat calculated the probabilities of all possible future outcomes, while Pascal utilized the concept of "expectation" to determine the fair share for each player. This exchange is widely considered the foundation of the modern mathematics of chance.1