Three-dimensional chess
Three-dimensional 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 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, invented in 1907 by Ferdinand Maack, which uses five stacked 5×5 boards. 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 invented since. David Pritchard's The Classified Encyclopedia of Chess Variants discusses some fifty 3D chess variations as well as a handful of higher-dimensional variants in Chapter 25. Chapter 11 also covers variants using multiple boards normally set side by side, which can also be considered to add an extra dimension to chess.
The modern cultural recognition of 3D chess is linked to the Star Trek franchise, which featured a "Tri-Dimensional Chess" set as a prop. The show provided no concrete rules, but fans and designers later codified various rule sets to make it playable. Subsequently, various Science fiction media have also featured some form of 3D chess as a prop or plot device, usually to indicate the intelligence of the players. The rising popularity of the concept also led to various commercial products using 8×8×3 layout, including a 3D Chess game published in 1967 by Dimensional Games, Inc, as well as Strato Chess by Dynamic Games, and Space Chess by Pacific Game Co. According to Pritchard, the variants which use a 8×8×3 layout or boards smaller than 8×8 are "less demanding on spatial vision, and hence more practical".
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".
Early history and large scale variants
Perhaps the first extension of chess into a three-dimensional space was accomplished by Alexandre-Théophile Vandermonde in 1771. Vandermonde is known for his unique chess problem, which was extension of the knight's tour into a 4×4×4 playing field.There are various reports of Baltic-German chess master Lionel Kieseritzky demonstrating a game called Kubikschach to the German master Adolf Anderssen at a London tournament. This game was also reported on in the Deutsche Schachzeitung. However, the exact rules and playing setup for Kubikschach are unknown. It is also unknown who exactly designed this game, though it is often assumed it was designed by Kieseritzky himself and various publications list him as the inventor.
Kubikschach influenced Ferdinand Maack in his development of Raumschach, and he discusses Kubikschach in his first Raumschach periodical. Kubikschach seems to have used an 8×8×8 board.
In 1918, the Russian mathematician Ervand Kogbetliantz also developed a form of 3D chess that used an 8×8×8 gamespace similar to Kubikschach. He increased the total number of chessmen to 64 for each player, adding even more complexity with new pieces like the fool, the hippogriff and the archbishop. Kogbetliantz published and promoted his ideas in the United States. Kogbetliantz published a Space Chess pamphlet in 1952, and promoted his game, now under the name Stereo Chess, at the New School for Social Research. While articles appeared in Time, and The New Yorker in the 1950s, the game did not attract a wide following. This is likely because Stereo chess was too complex for most people to learn and enjoy as a game.
According to David Pritchard, large scale formats similar to Kubikschach and Stereo chess are "the most popular 3‑D board amongst inventors, and at the same time the most mentally indigestible for the players."
Raumschach
The German mathematician Ferdinand Maack developed Raumschach in the early 1900s, patenting it with the German Imperial Patent Office in 1907. Maack contended that for chess to be more like modern war, attack should be possible from above and below, writing: "if the analogy to war is to be maintained, the third dimension is required. Modern strategy, with its steerable airships and submarines, utilizes the whole of space. Thus, in chess, attacks from above and below must be made possible".Maack's original formulation presented in 1907 was for an 8×8×8 board, as with Cubic chess. He labeled each plane with Greek letters. However, the long and difficult games that arose from the 8×8×8 space led Maack to experiment with numerous other smaller play spaces over the course of the following years. Maack eventually settled on a 5×5×5 playing field as the best. Other obvious differences between standard chess and Raumschach include two additional pawns per player, and a special piece called the unicorn. The unicorn has a special triagonal move which can shift one space in rank, file and level. In Spielregeln zum Raumschach, Maack explains the rules for the 5x5x5 game and also for a smaller game played on a 4x4x4 board without unicorns. This pamphlet also states that sets of the game were available at German toy stores.
Ferdinand Maack promoted the game with demonstrations, articles, magazines and several books, such as Das Schachraumspiel: Dreidimensionales Schachspiel, Spielregeln zum Raumschach '''', and Raumschach: Einführung in die Spielpraxis. An article first appeared in a 1907 edition of the Frankfurter Zeitung, though the reception was initially mixed. Maack gave the first public presentation of the game in the 1907 International Chess Tournament in Carlsbad. Maack also edited and published a journal on the game called Mitteilungen über Raumschach und wissenschaftliche Schachforschung.
file:Raumschach-on-Zillions.png|thumb|Raumschach on the Zillions of Games software
Maack later founded the Hamburg Raumschach Club in 1919, which remained active until WW2. Members included chess problemists like Hans Klüver and Willibald Roese. Raumschach achieved some limited popularity in England and Germany in the early 20th century, and is considered to be the classic form of 3D chess.
Raumschach was studied in detail by Thomas Rayner Dawson, an English chess problemist. He wrote a series of articles in The Chess Amateur on the game, and composed problems for it. Dawson also wrote a manuscript on Raumschach, which was picked up by Hans Gruber and Kjell Widlert, who published it in two parts under the title Raumschachfunken in 1993 and 1995. Alexey Troitsky is also known to have studied the game and its endgame problems.
While Raumschach is not a widespread game, it has been implemented in several modern computer programs, including the Windows software Zillions of Games. Numerous variants for Raumschach have also been designed by fans and some are also accessible in the Zillions program.
Board and starting positions
The Raumschach 3D board can be thought of as a cube sliced into five equal spaces across each of its three major coordinal planes. This sectioning yields a 5×5×5 game-space. The cubes alternate in color in all three dimensions.The horizontal levels were originally denoted by Greek letters in Maack's publications. Some English writings use capital letters A through E instead. Ranks and files of a level are denoted using standard chess algebraic notation.
As for the starting position, the armies are arrayed on four levels, two for each color. White starts on the α and β levels and Black starts on δ and ε.
Rules
White moves first. The game objective, as in standard chess, is checkmate. Rooks, bishops, and knights move as they do in chess in any given plane. The three dimensional movements are as follows:Game Rules & Endgames
Various commentators on 3D chess, including Maack himself and Ralph Betza, have noted that checkmating in 3D chess is more difficult, partly due to the king's increased mobility and the larger size of the play space. Maack himself writes that "it is significantly harder to checkmate a King in 3D space than on a 2D board." Betza writes that this issue would lead to many more draws. A king and a pawn vs a king is always a draw. Betza also argued that even king plus queen would be unlikely to mate a lone king.Because of this, Maack suggested that adding special rules could improve this situation. He recommended various possibilities:
- A Decoration rule: A piece that captures an enemy piece gains that piece's powers.
- A Recruitment rule: Captured pieces are not removed but are immediately added to your own army.
- Terrain Restriction: A bare King can be restricted from moving in the third dimension