{{Short description|Game defined by mathematical parameters}} {{about|the mathematical analysis of games|games that involve mathematics|mathematical puzzle|the Martin Gardner column "Mathematical Games"|Mathematical Games (column)}} {{more citations needed|date=August 2021}} thumb|The wagon must travel a path that is given by a mathematical function.
A '''mathematical game''' is a game whose rules, strategies, and outcomes are ''defined by precise mathematical rules, strategies, and measurable outcomes''<ref>{{Cite news |title=Game theory {{!}} Definition, Facts, & Examples {{!}} Britannica |url=https://www.britannica.com/science/game-theory |archive-url=http://web.archive.org/web/20260228031606/https://www.britannica.com/science/game-theory |archive-date=2026-02-28 |access-date=2026-03-05 |work=Encyclopedia Britannica |language=en}}</ref>.<ref>{{Cite web|title=Games, theory of - Encyclopedia of Mathematics|url=https://encyclopediaofmath.org/wiki/Games,_theory_of|access-date=2021-08-11|website=encyclopediaofmath.org|archive-date=2020-07-16|archive-url=https://web.archive.org/web/20200716050809/https://encyclopediaofmath.org/wiki/Games,_theory_of|url-status=dead}}</ref>{{Verify source|date=August 2021}} Often, such games have simple rules and match procedures, such as tic-tac-toe 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 are relatively basic, the game can be rigorously analyzed through the lens of combinatorial game theory.<ref>{{Cite web |title=Combinatorial Game Theory |url=https://ics.uci.edu/~eppstein/cgt/ |access-date=2026-03-05 |website=ics.uci.edu}}</ref>
Mathematical games differ sharply from mathematical puzzles 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.<ref>{{Cite web |title=Mathematical puzzles {{!}} Mathematics {{!}} Research Starters {{!}} EBSCO Research |url=https://www.ebsco.com/ |access-date=2026-03-05 |website=EBSCO |language=en}}</ref>
Some mathematical games are of deep interest in the field of recreational mathematics<ref>{{Cite web |title=Mathematical games |url=https://mathshistory.st-andrews.ac.uk/HistTopics/Mathematical_games/ |access-date=2026-03-05 |website=Maths History |language=en}}</ref>.<ref>{{Cite journal|last=Sumpter|first=Lovisa|date=January 2015|title=Recreational Mathematics – Only For Fun?|url=https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1232&context=jhm|journal=Journal of Humanistic Mathematics|volume=5|issue=1|pages=121–138|doi=10.5642/jhummath.201501.07|s2cid=16590762 |access-date=11 August 2021|doi-access=free}}</ref>
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.<ref>{{Cite news |title=Game theory {{!}} Definition, Facts, & Examples {{!}} Britannica |url=https://www.britannica.com/science/game-theory |archive-url=http://web.archive.org/web/20260228031606/https://www.britannica.com/science/game-theory |archive-date=2026-02-28 |access-date=2026-03-05 |work=Encyclopedia Britannica |language=en}}</ref><ref>{{Cite web |title=Game Theory {{!}} World of Mathematics |url=https://mathigon.org/world/Game_Theory |access-date=2026-03-05 |website=Mathigon |language=en}}</ref>
Additionally, mathematical games can aid children in grasping fundamental concepts such as addition, subtraction, multiplication,<ref name="Easy Multiplication">{{cite web | title=Easy Multiplication | website=Play123| date=7 September 2023| url=https://www.play123.com/game/easy-multiplication }}</ref> 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 games are listed below:
=== Lattice board ===
* Angels and Devils * Arimaa * Checkers (English draughts) **Checkers variants * Chess ** Chess variants * Chomp * Dodgem * Domineering * Dots and boxes * Go ** Go variants *Gomoku * Hex * Hexapawn * L game *Othello *Pente * Philosopher's football * Rhythmomachy *Tak * Tic-tac-toe ** Tic-tac-toe variants
=== Non-lattice boards and other games ===
* Graph pebbling * Hackenbush * Chopsticks (hand game) *Mancala * Nim * Sim * Sprouts * Four fours * Contract Bridge
=== Chance involved or imperfect information === * 24 * Prisoner's dilemma <!--- Double ---->
== See also == * Games of skill
== References == {{Reflist}}
{{Polyforms}} {{Authority control}}
Category:Mathematical games