A mathematical game is a

game A game is a structured type 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 video games) or art ...

whose rules, strategies, and outcomes are defined by clear

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

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

tic-tac-toe Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who ta ...

and

dots and boxes Dots and boxes is a pencil-and-paper game for two players (sometimes more). It was first published in the 19th century by French mathematician Édouard Lucas, who called it . It has gone by many other names, including dots and dashes, game of do ...

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

Mancala Mancala ( ''manqalah'') is a family of two-player Turns, rounds and time-keeping systems in games, turn-based Strategy game, strategy board games played with small stones, beans, marbles or seeds and rows of holes or pits in the earth, a board ...

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. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

. 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 * Solu ...

. Additionally, mathematical games can aid children in grasping fundamental concepts such as addition, subtraction, multiplication, and division, enhancing their arithmetic skills in an engaging manner.

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 An abstract strategy game is a type of strategy game that has minimal or no narrative theme, an outcome determined only by player choice (with minimal or no randomness), and in which each player has perfect information about the game. For example ...

s are listed below:

Lattice board

* Angels and Devils *

Arimaa Arimaa () is a two-player strategy board game that was designed to be playable with a standard chess set and difficult for computers while still being easy to learn and fun to play for humans. It was invented between 1997 and 2002 by Omar Syed, ...

Checkers Checkers (American English), also known as draughts (; English in the Commonwealth of Nations, Commonwealth English), is a group of Abstract strategy game, strategy board games for two players which involve forward movements of uniform game ...

(

English draughts 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. The pieces m ...

) ** Checkers variants *

Chess Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...

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 co ...

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 Domineering (also called Stop-Gate or Crosscram) is a mathematical game that can be played on any collection of squares on a sheet of graph paper. For example, it can be played on a 6×6 square, a rectangle, an entirely irregular polyomino, or ...

Dots and boxes Dots and boxes is a pencil-and-paper game for two players (sometimes more). It was first published in the 19th century by French mathematician Édouard Lucas, who called it . It has gone by many other names, including dots and dashes, game of do ...

* Go **

Go variants There are many variations of the simple rules of Go (board game), 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 yea ...

Gomoku ''Gomoku'', also called ''five in a row'', is an Abstract strategy game, abstract strategy board game. It is traditionally played with Go (game), Go pieces (black and white stones) on a 15×15 Go board while in the past a 19×19 board was standa ...

Hex Hex usually refers to: * A curse or supposed real and potentially supernaturally realized malicious wish * Hexadecimal, a base-16 number system often used in computer nomenclature Hex, HEX, or The Hex may also refer to: Magic * Hex sign, a b ...

Hexapawn Hexapawn is a deterministic two-player game invented by Martin Gardner. It is played on a rectangular board of variable size, for example on a 3×3 board or on a regular chessboard. On a board of size ''n''×''m'', each player begins with ''m'' p ...

L game The L game is a simple abstract strategy board game invented by Edward de Bono. It was introduced in his book ''The Five-Day Course in Thinking'' (1967). Description The L game is a two-player game played on a board of 4×4 squares. Each player ...

Othello ''The Tragedy of Othello, the Moor of Venice'', often shortened to ''Othello'' (), is a tragedy written by William Shakespeare around 1603. Set in Venice and Cyprus, the play depicts the Moorish military commander Othello as he is manipulat ...

Pente Pente is an Abstract strategy game, abstract strategy board game for two or more players, created in 1977 by Gary Gabrel. A member of the M,n,k-game, m,n,k game family, Pente stands out for its Custodian capture, custodial capture mechanic, which ...

Philosopher's football Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's '' Winning Ways for your Mathematical Plays''. Rules Phutball is played on the in ...

Rhythmomachy Rithmomachia (also known as rithmomachy, arithmomachia, rythmomachy, rhythmomachy, the philosophers' game, and other variants) is an early European mathematical board game. Its earliest known description dates from the eleventh century. The nam ...

* Tak *

Tic-tac-toe Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who ta ...

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 Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, r ...

Hackenbush Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of line segments connected to one another by their endpoints and to a "ground" line. Other versions of the game use differently co ...

Chopsticks (hand game) Chopsticks (sometimes called Splits, Calculator, or just Sticks) is a hand game for two or more players, in which players extend a number of fingers from each hand and transfer those scores by taking turns tapping one hand against another. Chop ...

Nim Nim is a mathematical combinatorial game in which two players take turns removing (or "nimming") objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all ...

* Sim * Sprouts *

Four fours Four fours is a mathematical puzzle, the goal of which is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four. No other digit is allowed. Most versi ...

Contract Bridge Contract bridge, or simply bridge, is a trick-taking game, trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two Team game, competing partnerships, with partners sitting opposite each othe ...

Chance involved or imperfect information

* 24 *

Prisoner's dilemma The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while def ...

References

{{Authority control

List of games

Lattice board

Non-lattice boards and other games

Chance involved or imperfect information

See also

References