The [[Pascal Problem]], also known as the [[Problem of Points]], is a classical problem in probability theory. It 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. The problem is to determine how the prize should be divided if the game is interrupted before either player has won the required number of rounds. The Pascal Problem was first solved by [[Blaise Pascal]] and [[Pierre de Fermat]] in the 17th century. They used a recursive approach, considering all possible continuations of the game and counting how many of them would lead to each player winning. The Pascal Problem has important applications in gambling, insurance, and other areas. It is also a fundamental problem in probability theory, and its solution has helped to lay the foundations of the field. Here is an example of the Pascal Problem: Two players are playing a game to 10 points. They contribute equally to a prize pot of $100. If the game is interrupted when the score is 7-5, how should the prize be divided? Using the recursive approach, we can consider all possible continuations of the game. There are two possible ways for the game to end: - Player 1 wins the next two points and wins the game. - Player 2 wins the next two points and ties the game. In the first case, Player 1 would win the entire prize of $100. In the second case, the prize would be divided equally, with each player getting $50. Therefore, the fair way to divide the prize when the score is 7-5 is to give Player 1 7/12 of the prize and Player 2 5/12 of the prize. The Pascal Problem can be generalized to games with any number of players and any number of points. The solution is always the same: the prize should be divided in proportion to the number of points each player still needs to win in order to achieve overall victory. ## Some possible applications in the Cryptocurrency world In [[Ordinals|Ordinal Theory]], there is a notion of [[satpoint]], which can be used as a unit or a point system for the [[Problem of Points]]. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Pascal Problem") sort title, authors, modified ```