m,n,k-game
Sign in to savethumb|Example of a completed 11,10,5-game An '''m,n,k-game' is an abstract board game in which two players take turns in placing a stone of their color on an m-by-n board, the winner being the player who first gets k stones of their own color in a row, horizontally, vertically, or diagonally. Thus, tic-tac-toe is the 3,3,3-game and free-style gomoku is the 15,15,5-game. An m,n,k-game is also called a 'k-in-a-row' game on an m-by-n'' board.
~5 min read
Encyclopedic overview
7 sectionsContents
- Strategy stealing argument
- Applying results to different board sizes
- General results
- Specific results
- Multidimensional variant
- See also
- References
thumb|Example of a completed 11,10,5-game An '''m,n,k-game' is an abstract board game in which two players take turns in placing a stone of their color on an m-by-n board, the winner being the player who first gets k stones of their own color in a row, horizontally, vertically, or diagonally. Thus, tic-tac-toe is the 3,3,3-game and free-style gomoku is the 15,15,5-game. An m,n,k-game is also called a 'k-in-a-row' game on an m-by-n board.
The m,n,k-games are mainly of mathematical interest. One seeks to find the game-theoretic value, the result of the game with perfect play. This is known as solving the game.
Excerpted from Wikipedia’s “m,n,k-game” article, available under the CC BY-SA 4.0 licence.