Infinite chess
Infinite chess is any of several variations of the game chess played on an unbounded chessboard. Versions of infinite chess have been introduced independently by multiple players, chess theorists, and mathematicians, both as a playable game and as a model for theoretical study. 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.
Classical (FIDE) chess is played on an 8×8 board (64 squares). However, the history of chess includes variants of the game played on boards of various sizes. A predecessor game called Courier chess was played on a slightly larger 12×8 board (96 squares) in the 12th century, and continued to be played for at least six hundred years. Japanese chess (shogi) has been played historically on boards of various sizes; the largest is Taikyoku shōgi ("ultimate chess"). This chess-like game, which dates to the mid 16th century, was played on a 36×36 board (1296 squares). Each player starts with 402 pieces of 209 different types, and a well-played game would require several days of play, possibly requiring each player to make over a thousand moves.
Chess player Jianying Ji was one of many to propose infinite chess. In 2000, he suggested a setup with the chess pieces in the same relative positions as in classical chess. Numerous other chess players, chess theorists, and mathematicians who study game theory have conceived of variations of infinite chess, often with different objectives in mind. Chess players sometimes use the scheme simply to alter the strategy; since chess pieces, and in particular the king, cannot be trapped in corners on an infinite board, new patterns are required to form a checkmate. Theorists conceive of infinite chess variations to expand the theory of chess in general, or as a model to study other mathematical, economic, or game-playing strategies.
For infinite chess, mathematical investigations have shown that in a general endgame, one player can force a win in a finite number of moves. More specifically, it has been found that infinite chess is decidable; that is, given a position (such as , and assuming pawns do not promote) of a finite number of chess pieces which are uniformly mobile and with constant and linear freedom, and (for example) White to move, there is an algorithm that will answer if White can win or force a draw, against any defense by Black.
...
Wikipedia