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.
The problemofpoints, also called the problemof division of the stakes, is a classical problem in probability theory. One of the famous problems that...
pair ofpointsproblem or closest pair problem is a problemof computational geometry: given n {\displaystyle n} points in metric space, find a pair of points...
trolley problem is a series of thought experiments in ethics, psychology and artificial intelligence involving stylized ethical dilemmas of whether to...
travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances...
the amount of dispersion. As a mathematician, Huygens developed the theory of evolutes and wrote on games of chance and the problemofpoints in Van Rekeningh...
indeed every set of 30 points in general position contains an empty hexagon. The problemof finding sets of n points minimizing the number of convex quadrilaterals...
problems stated in terms ofpoints only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously...
the problemof computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although...
expected value originated in the middle of the 17th century from the study of the so-called problemofpoints, which seeks to divide the stakes in a fair...
In mathematics, the Gauss circle problem is the problemof determining how many integer lattice points there are in a circle centered at the origin and...
geometry, the problemof dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created...
two triangle centers, the Ajima–Malfatti pointsof a triangle. The problemof maximizing the total area of three circles in a triangle is never solved...
The problemof evil is the philosophical question of how to reconcile the existence of evil and suffering with an omnipotent, omnibenevolent, and omniscient...
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items...
problem in mathematics: What is the asymptotic growth rate of the area of the smallest triangle determined by three out of n {\displaystyle n} points...
The Fourteen Points was a statement of principles for peace that was to be used for peace negotiations in order to end World War I. The principles were...
Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are...
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal...
Apollonius' problem can also be formulated as the problemof locating one or more points such that the differences of its distances to three given points equal...
In the philosophy of mind, the hard problemof consciousness is to explain why and how humans and other organisms have qualia, phenomenal consciousness...
problem from any customer. D4: Determine and Verify Root Causes and Escape Points: Identify all applicable causes that could explain why the problem has...
after 03:14:07 UTC on 19 January 2038. The problem exists in systems which measure Unix time – the number of seconds elapsed since the Unix epoch (00:00:00...
problem in mathematics: For how many points is it always possible to projectively transform the points into convex position? (more unsolved problems in...
to accompany during a trip. One problem was the so-called problemofpoints, a classic problem already then (treated by Luca Pacioli as early as 1494, and...
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