Infinite chess

It has been found that even though the board is unbounded, there are ways in which a player can win the game in a finite number of moves.

However, the history of chess includes variants of the game played on boards of various sizes.

This chess-like game, which dates to the mid 16th century, was played on a 36×36 board (1296 squares).

[6][7][8][9][10] For infinite chess, it has been found that the mate-in-n problem is decidable; that is, given a natural number n and a player to move and the positions (such as on

) of a finite number of chess pieces that are uniformly mobile and with constant and linear freedom, there is an algorithm that will answer if there is a forced checkmate in at most n moves.

A simple infinite chess scheme (starting position). More complex schemes have the addition of various fairy chess pieces as well as the infinitely large board.
Taikyoku shōgi (36×36 squares), most likely starting position. The complete rules of this historical game are not conclusively known.