Three-dimensional chess

Three-dimensional chess (or 3D chess) refers to a family of chess variants that replaces the two-dimensional board with a three-dimensional array of cells, usually stacked chessboards. There are numerous 3D chess board arrays depending on the design of the specific game. Unlike standard chess, where pieces move solely on a single plane, 3D chess requires players to navigate across multiple levels, introducing a vertical z-axis to the game. The expression "three-dimensional chess" is sometimes used as a colloquial metaphor to describe complex, dynamic systems with many competing entities and interests, including politics, diplomacy and warfare. To describe an individual as "playing three-dimensional chess" implies a higher-order understanding and mastery of the system beyond the comprehension of their peers or ordinary observers, who are implied to be playing "regular chess". The basic rules of most 3D chess variants generally preserve the movement logic of traditional pieces while extending their range into the third dimension. For example, in many variants, a rook can move vertically through the levels as if traveling along a column. Capturing and checkmate remain the primary objectives, but the number of available squares and the complexity of the "lines of sight" make the 3D game significantly more difficult than two-dimensional versions. Some variants also introduce new pieces that take advantage of the three-dimensional play space. Three-dimensional variants have existed since at least the late 19th century. One of the oldest and most enduring variants is Raumschach (German for "Space chess"), invented in 1907 by Ferdinand Maack, which uses five stacked 5×5 boards (though there were different board spaces designed). Maack's game is considered by chess variant enthusiasts to be the classic form of 3D chess. The game was played in clubs in Hamburg and London during the early 20th century. Numerous other variants of 3D chess have been...