A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters.[verification needed] 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.
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.
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.
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:
- Angels and Devils
- Checkers (English draughts)
- Dots and boxes
- L game
- Philosopher's football
Non-lattice boards and other games
Chance involved or imperfect information
- "game". planetmath.org. Retrieved 2021-08-11.
- "Games, theory of - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2021-08-11.
- Sumpter, Lovisa (January 2015). "Recreational Mathematics – Only For Fun?". Journal of Humanistic Mathematics. 5 (1): 121–138. doi:10.5642/jhummath.201501.07. Retrieved 11 August 2021.