Editing Mathematical game

{{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)}}
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[[File:Clumsy wagon (IME-USP).webm|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 clear [[mathematics|mathematical]] parameters.<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}}</ref>{{Verify source|date=August 2021}}{{clarify|reason=What's a mathematical parameter?|date=February 2024}} 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]].{{Citation needed|date=August 2021}}

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.{{Citation needed|date=August 2021}}

Some mathematical games are of deep interest in the field of [[recreational mathematics]].<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>{{Verify source|date=August 2021}}

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 [[solved game|solution]].{{Citation needed|date=August 2021}}

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 game]]s are listed below:

=== Lattice board ===

* [[Angel problem|Angels and Devils]]
* [[Arimaa]]
* [[Checkers]] ([[English draughts]])
**[[Draughts#Invented variants|Checkers variants]]
* [[Chess]]
** [[Chess variants]]
* [[Chomp]]
* [[Domineering]]
* [[Dots and boxes]]
* [[Go (board game)|Go]]
** [[Go variants]]
*[[Gomoku]]
* [[Hex (board game)|Hex]]
* [[Hexapawn]]
* [[L game]]
*[[Reversi|Othello]]
*[[Pente]]
* [[Phutball|Philosopher's football]]
* [[Rhythmomachy]]
*[[Tak (game)|Tak]]
* [[Tic-tac-toe]]
** [[Tic-tac-toe variants]]

=== Non-lattice boards and other games ===

* [[Graph pebbling]]
* [[Hackenbush]]
* [[Chopsticks (hand game)]]
*[[Mancala]]
* [[Nim]]
* [[Sim (pencil game)|Sim]]
* [[Sprouts (game)|Sprouts]]
* [[Four fours]]
* [[Contract Bridge]]

=== Chance involved or imperfect information ===
* [[24 (puzzle)|24]]
* [[Prisoner's dilemma]] <!--- Double ---->

== See also ==
* [[Games of skill]]

== References ==
{{Reflist}}

{{Polyforms}}
{{Authority control}}

[[Category:Mathematical games| ]]