A mathematical game is a

game A game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (suc ...

whose rules, strategies, and outcomes are defined by clear

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

parameters. Often, such games have simple rules and match procedures, such as

Tic-tac-toe Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...

and Dots and Boxes. Generally, mathematical games need not be conceptually intricate to involve deeper computational underpinnings. For example, even though the rules of

Mancala The mancala games are a family of two-player turn-based strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other playing surface. The objective is usually to capture all or some ...

are relatively basic, the game can be rigorously analyzed through the lens of

combinatorial game theory Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the player ...

. Mathematical games differ sharply from

mathematical puzzles Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that sati ...

in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or mathematical aspects. Some mathematical games are of deep interest in the field of

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

. When studying a game's core mathematics, arithmetic theory is generally of higher utility than actively playing or observing the game itself. To analyze a game numerically, it is particularly useful to study the rules of the game insofar as they can yield equations or relevant formulas. This is frequently done to determine winning strategies or to distinguish if the game has a

solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...

List of games

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". Several

abstract strategy game Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect informatio ...

s are listed below:

Lattice board

* Angels and Devils * Arimaa *

Checkers Checkers (American English), also known as draughts (; British English), is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers ...

(

English draughts English draughts (British English) or checkers ( American English), also called straight checkers or simply draughts, is a form of the strategy board game checkers (or draughts). It is played on an 8×8 checkerboard with 12 pieces per side. ...

) ** Checkers variants *

Chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...

Chess variants A chess variant is a game related to, derived from, or inspired by chess. Such variants can differ from chess in many different ways. "International" or "Western" chess itself is one of a family of games which have related origins and could be c ...

Chomp Chomp is a two-player strategy game played on a rectangular grid made up of smaller square cells, which can be thought of as the blocks of a chocolate bar. The players take it in turns to choose one block and "eat it" (remove from the board), to ...

* Domineering * Dots and boxes * Go **

Go variants There are many variations of the simple rules of Go. Some are ancient digressions, while other are modern deviations. They are often side events at tournaments, for example, the U.S. Go Congress holds a "Crazy Go" event every year. National va ...

Gomoku ''Gomoku'', also called ''Five in a Row'', is an abstract strategy board game. It is traditionally played with Go pieces (black and white stones) on a Go board. It is played using a 15×15 board while in the past a 19×19 board was standard. Be ...

* Hex * Hexapawn * L game *

Othello ''Othello'' (full title: ''The Tragedy of Othello, the Moor of Venice'') is a tragedy written by William Shakespeare, probably in 1603, set in the contemporary Ottoman–Venetian War (1570–1573) fought for the control of the Island of Cyp ...

Pente Pente is an abstract strategy board game for two or more players, created in 1977 by Gary Gabrel. A member of the m,n,k game family, Pente stands out for its custodial capture mechanic, which allows players to "sandwich" pairs of stones and cap ...

* Philosopher's football * Rhythmomachy * Tak *

Tic-tac-toe variants Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an ''m''×''n'' board until one of them gets ''k'' in a row. Harary's generalized tic-tac-toe is an even broader generalization. The game can also be genera ...

Non-lattice boards and other games

* Graph pebbling *

Hackenbush Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of colored line segments connected to one another by their endpoints and to a "ground" line. Gameplay The game starts with the ...

* Chopsticks (Hand game) *

* Nim * Sim * Sprouts * Four Fours

Chance involved or imperfect information

* 24 *

Prisoner's dilemma The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("def ...

References

{{Polyforms

List of games

Lattice board

Non-lattice boards and other games

Chance involved or imperfect information

See also

References