Problem of points
problem about a game of chance with 2 players who agree in advance that the 1st player to have won N rounds will collect a prize; if the game is interrupted before either player has won N rounds, how should one divide the prize?
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
The problem concerns a game of chance with two players who have equal chances of winning each round. The players contribute equally to a prize pot, and agree in advance that the first player to have won a certain number of rounds will collect the entire prize. Now suppose that the game is interrupted by external circumstances before either player has achieved victory. How does one then divide the pot fairly? It is tacitly understood that the division should depend somehow on the number of rounds won by each player, such that a player who is close to winning will get a larger part of the pot. But the problem is not merely one of calculation; it also involves deciding what a "fair" division actually is.
History
Early solutions
Luca Pacioli considered such a problem in his 1494 textbook Summa de arithmetica, geometrica, proportioni et proportionalità. His method was to divide the stakes in proportion to the number of rounds won by each player, and the number of rounds needed to win did not enter his calculations at all.
This brief starts where responsible research should: with the source description of “Problem of points” as problem about a game of chance with 2 players who agree in advance that the 1st player to have won N rounds will collect a prize; if the game is interrupted before either player has won N rounds, how should one divide the prize. Everything that follows is an evidence route, not borrowed authority.
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The subject matters to the people & ideas register because the source frames it as problem about a game of chance with 2 players who agree in advance that the 1st player to have won N rounds will collect a prize; if the game is interrupted before either player has won N rounds, how should one divide the prize. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Chronology provides the most reliable spine for this subject; interpretation should follow only after identities and dates are secure. The source revision retrieved here is dated May 26, 2026. The linked authority identifier is Q623680. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1494.
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This entry incorporates text from “Problem of points” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.