A mathematical game is a multiplayer game whose rules, strategies, and outcomes can be studied and explained by mathematics. Examples of such games are Tic-tac-toe and Dots and Boxes, to name a couple. On the surface, a game need not seem mathematical or complicated to still be a mathematical game. For example, even though the rules of Mancala are straightforward, mathematicians analyze the game using combinatorial game theory.
Mathematical games differ from mathematical puzzles in that all mathematical puzzles require math to solve them whereas mathematical games may not require a knowledge of mathematics to play them or even to win them. Thus the actual mathematics of mathematical games may not be apparent to the average player.
Some mathematical games are topics of interest in recreational mathematics.
When studying the mathematics of games, the mathematical analysis of the game is more important than actually playing the game. To analyze a game mathematically, the mathematician studies the rules of the game in order to understand the inner-workings of the game, to determine winning strategies, and to possibly to determine if a game has a solution.
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".
Hexaflexagons, probability paradoxes, and the Tower of Hanoi; Martin Gardner's first book of mathematical puzzles and games.(Brief article)(Book review)
Dec 01, 2008; 9780521735254 Hexaflexagons, probability paradoxes, and the Tower of Hanoi; Martin Gardner's first book of mathematical puzzles...