Mathematical game
From Wikipedia, the free encyclopedia
- This article is about using mathematics to study the inner-workings of multiplayer games which, on the surface, may not appear mathematical at all. If you were looking for games that directly involve mathematics in their play, see mathematical puzzle.
- Mathematical Games was a column written by Martin Gardner that appeared in the Scientific American. Information on his column and other recreational mathematics publications can be found in the recreational mathematics article.
A mathematical game is a multiplayer game whose rules, strategies, and outcomes can be studied and explained by mathematics. Examples of such games are Tic-tac-toe and Dots and Boxes, to name a couple. 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.
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. 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.
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.
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[edit] Applications and Relations
- Mathematicians use statistical analysis to study card games in order to understand and improve play techniques.
- Game theory has wide social and military applications for tactical and strategic planning.
- 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.
- Conway's combinatorial game theory and surreal numbers cover those games that do not involve chance and are played in turns. Such games are often called abstract strategy games.
[edit] People
[edit] Specific mathematical games and puzzles
[edit] Abstract Strategy Games (No chance involved)
Sometimes it is not immediately obvious that a particular game involves chance. 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".
[edit] Lattice board
- Angels and Devils
- Chess
- Chomp
- Dewdney's Voters
- Domineering
- Dots and boxes
- Go
- Hex
- Hexafex
- Hexapawn
- L game
- Philosopher's football
- Rhythmomachy
