- This article is about using mathematics to study the inner-workings of multiplayer games which, on the surface, may not appear mathematical at all. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and A multiplayer game is a Game which is played by several players. If you were looking for games that directly involve mathematics in their play, see mathematical puzzle. This article is about puzzles that require mathematics in order to solve them
- Mathematical Games was a column written by Martin Gardner that appeared in the Scientific American. Martin Gardner (b October 21, 1914, Tulsa Oklahoma) is a popular American mathematics and science writer specializing in Recreational mathematics Martin Gardner (b October 21, 1914, Tulsa Oklahoma) is a popular American mathematics and science writer specializing in Recreational mathematics Scientific American is a Popular science magazine, published (first weekly and later monthly since August 28, 1845, making it Information on his column and other recreational mathematics publications can be found in the recreational mathematics article. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games.
A mathematical game is a multiplayer game whose rules, strategies, and outcomes can be studied and explained by mathematics. A multiplayer game is a Game which is played by several players. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Examples of such games are Tic-tac-toe and Dots and Boxes, to name a couple. Dots and Boxes (also known as Boxes, Squares, Paddocks, Square-it, Dots and Dashes, Dots, Smart Dots, or simply On the surface, a game need not seem mathematical or complicated to still be a mathematical game. For example, even though the rules of Mancala are straightforward, mathematicians analyze the game using combinatorial game theory. Mancala is a family of board games played around the world sometimes called " Sowing " games or "count-and-capture" games which describes the This article is on the theory of combinatorial games For the theory that includes games of chance and games of imperfect knowledge see Game theory
Mathematical games differ from mathematical puzzles in that all mathematical puzzles require math to solve them whereas mathematical games may not require a knowledge of mathematics to play them or even to win them. This article is about puzzles that require mathematics in order to solve them Thus the actual mathematics of mathematical games may not be apparent to the average player.
Some mathematical games are topics of interest in recreational mathematics. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games.
When studying the mathematics of games, the mathematical analysis of the game is more important than actually playing the game. To analyze a game mathematically, the mathematician studies the rules of the game in order to understand the inner-workings of the game, to determine winning strategies, and to possibly to determine if a game has a solution. A two player Game can be " solved " on several levels; Ultra-weak In the weakest sense solving a game means proving whether the first player will win
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Applications and Relations
- Mathematicians use statistical analysis to study card games in order to understand and improve play techniques. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. A card game is any Game using Playing cards either traditional or game-specific
- Game theory has wide social and military applications for tactical and strategic planning. Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering,
- Determinacy is the study of when a player has a guaranteed winning strategy for an infinitely long game, and has important consequences in set theory and descriptive set theory. In Mathematical logic, descriptive set theory is the study of certain classes of " Well-behaved " subsets of the Real line and other
- Conway's combinatorial game theory and surreal numbers cover those games that do not involve chance and are played in turns. John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups This article is on the theory of combinatorial games For the theory that includes games of chance and games of imperfect knowledge see Game theory In Mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers Such games are often called abstract strategy games. An abstract strategy game is a board or card game with Perfect information, no chance and (usually two players or teams
People
Specific mathematical games and puzzles
Abstract Strategy Games (No chance involved)
Sometimes it is not immediately obvious that a particular game involves chance. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games. Often a card game is described as "pure strategy" and such, but a game with any sort of random shuffling or face-down dealing of cards should not be considered to be "no chance".
Lattice board
- Angels and Devils
- Chess
- Chomp
- Dewdney's Voters
- Domineering
- Dots and boxes
- Go
- Hex
- Hexafex
- Hexapawn
- L game
- Philosopher's football
- Rhythmomachy
Non-lattice boards and other games
Chance involved or imperfect information
See also
External links
The angel problem is a question in Game theory proposed by John Horton Conway. Chess is a recreational and competitive Game played between two players. A chess variant is a Game derived from related to or similar to Chess in at least one respect Chomp is a 2-player game played on a rectangular "chocolate bar" made up of smaller square blocks (rectangular cells Domineering (also called Stop-Gate or Crosscram) is a Mathematical game played on a sheet of Graph paper, with any set of designs traced out Dots and Boxes (also known as Boxes, Squares, Paddocks, Square-it, Dots and Dashes, Dots, Smart Dots, or simply There are many variations on the basic game of Go. Some are ancient digressions whilst other are modern deviations Hex is a Board game played on a hexagonal grid, theoretically of any size and several possible shapes but traditionally as an 11x11 rhombus Hexapawn is a deterministic two-player Game invented by Martin Gardner. The L game is a simple strategic game invented by Edward De Bono. Phutball (short for philosopher's football) is a two-player Board game described in Elwyn Berlekamp, John Horton Conway, and Richard Rithmomachy (or Rithmomachia, also Arithmomachia, Rythmomachy, Rhythmomachy, or sundry other variants sometimes known as The Philosophers' Graph pebbling is a mathematical Game and area of interest played on a graph with pebbles on the vertices. Hackenbush is a two-player Mathematical game which may be played on any configuration of colored Line segments connected to one another by their endpoints and to the Chopsticks (also called Magic Fingers) is a commonly played two player traditional Japanese children's hand game. Nim is a two-player mathematical Game of strategy in which players take turns removing objects from distinct heaps The game of Sim is played by two players Red and Blue on a board consisting of six dots ('vertices' Sprouts is a Pencil-and-paper game with interesting mathematical properties The 24 Game is a Mathematical game in which the object is to find a way to manipulate four Integers so that the end result is 24 The Prisoner's Dilemma constitutes a problem in Game theory. It was originally framed by Merrill Flood and Melvin Dresher A two player Game can be " solved " on several levels; Ultra-weak In the weakest sense solving a game means proving whether the first player will win A game of skill is a Game where the outcome is determined mainly by mental and/or physical Skill, rather than by pure chance.Dictionary
mathematical game
-noun
- (mathematics) Any game featuring arithmetic or other branches of mathematics; a branch of recreational mathematics
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