Three-dimensional chess

thumb|[[Ferdinand Maack demonstrating his various Raumschach variants at the Hamburg Chess Exhibition]]

thumb|Raumschach (German for Space chess) set created by a hobbyist

thumb|The 8×8×3 layout is a common play space in several modern 3D chess variants.

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. 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 (three stacked boards), including a 3D Chess game published in 1967 by Dimensional Games, Inc, as well as Strato Chess (1973) by Dynamic Games, and Space Chess (1970) 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".

Early history

thumb|Kubikschach 8×8×8 gamespace

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 (1806–1853) demonstrating a game called Kubikschach (Cube chess) 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. 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, uses the whole of space. Thus, in chess, attacks from above and below must be made possible" (Anleitung zum Raumschach).

Ferdinand Maack promoted the game with demonstrations, articles, magazines and several books, such as Das Schachraumspiel: Dreidimensionales Schachspiel (1907), Spielregeln zum Raumschach (Rules of Space Chess), and Raumschach: Einführung in die Spielpraxis (1919). An article first appeared in a 1907 edition of the Frankfurter Zeitung, though the reception was initially mixed.

Variant move sets

Regarding the pawn, the key principle is that they move one step like a rook or capture one step like the bishop. However, Maack and the Hamburg space chess club played with four different move sets for the pawns. There seems to have been much discussion and testing around the movement of the pawn, as Maack writes in Raumschach: Einführung in die Spielpraxis that "from the very beginning, the greatest difficulties and the liveliest controversies among space-chess players have arisen in answering the two questions: How are the pawns to move? and how are the pieces to be set up at the beginning of the game?"

The four options outlined by Maack in Einführung in die Spielpraxis are as follows:

Maack also discusses various options for the movement of the knight, including allowing the knight to move as a unicorn and a 2D knight.

The four level game on 4x4x4 can be played with four different army configurations: 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 (one cannot force mate).

Because of this, Maack suggested that adding special rules could improve this situation. He recommended various possibilities: While articles appeared in Time, and The New Yorker in the 1950s, the game did not attract a wide following.

Alice chess – a game which uses two adjacent 8×8 boards; pieces move "through the looking glass" in between these boards
Cubic chess – a 6×6×6 variant with added Maack unicorns; pawns can move and capture one cell forward, either orthogonally, diagonally, or triagonally
Tamerlane Cubic Chess – another variant by Parton which adapts Tamerlane chess to a 3D board
Sphinx Chess – a game which uses a unique "four dimensional" playing field consisting of nine 4×4 grids arranged in a 3×3 pattern
Ecila Chess – named for "Alice" spelled backward, uses several cubic boards in various arrays; Parton called this game "six dimensional" chess

Parton also introduced several new 3D chess pieces. One of these was the narwhal, which can move as either the nook or the Maack unicorn. Others include the wyvern and the hippogriff. This depiction of a 3D chess, played by the heroes of the show, fueled the imagination of a generation of game designers and led to increasing interest in 3D chess. The design retained the 64 squares of a traditional chessboard, but distributed them onto separate platforms in a hierarchy of spatial levels, suggesting to audiences how chess adapted to a future predominated by space travel. Rules for the game were never invented within the series – in fact, the boards are sometimes not even aligned consistently from one scene to the next within a single episode.

Rules development

While the original prop was never created to a real game, Tri-D chess was included in the Star Trek Star Fleet Technical Manual by Franz Joseph, who created starting positions for the pieces and short rules which state: A free summary in English of the Standard Rules is contained on Charles Roth's website, including omissions and ambiguities regarding piece moves across the four Tri‑D gameboard 2×2 attack boards.

A complete set of tournament rules for Tri-Dimensional Chess written by Jens Meder is available on his website. Meder's rules are based on FIDE's rules more than Andrew Bartmess' Standard Rules, with some deviations too. A repository of Tournament Rules games can be found on the website of Michael Klein.

Board details

Plans for constructing a Tri‑D chessboard can be found on The Chess Variant Pages, as well as in Bartmess' Tri‑D Chess Rules. Details for building a travel-size board are included on Meder's website.

Software

There is software for playing Tri‑D Chess. Parmen (possibly named after a lead character in the episode "Plato's Stepchildren") is a Windows application written by Doug Keenan and available free on his website. A free Android version of Tri‑D Chess is offered by AwfSoft.

8×8×3 variants

thumb|Parallel worlds chess using a standard 8×8×3 space

The appearance of Tri-Dimensional chess in Star Trek led to a "renaissance" in 3D chess in the late 20th century, especially in the United States, as the popular television show fueled the imaginations of game designers for decades afterwards.

One of the first such variants was designed by Wally Hageman in the early 1960s. The pieces used were those of a regular FIDE chess army, with the movements of Raumschach, except the bishop, which moved as Kogbetliantz’ Archbishop. The game was popular enough to be featured in US media.

Other similar commercial games using the 8×8×3 board followed, capitalizing on the new craze. They include Space chess (1970) by the Pacific Game Company (with rules developed by US chess champion Larry Evans), Strato Chess (1973) by John Hansen Hageman's arrangement Company, Chess Cubed by Classic Games Company, and "Chess in the Third Dimension" by Skor Mor. Another Schmittberger variant using the same play space is Parallel worlds chess. The main difference in this variant is that it employs two armies per player.

In 2001, William L. D'Agostino developed another set of rules for 3D chess using a 8×8×3 play space. The rules for Millennium 3D chess are intended to keep the game as close as possible to classic FIDE chess while extending it to a 3D space.

Other 3D chess variants

Various other three-dimensional chess variants have been invented, including:

Total Chess (Charles Beatty, 1945) – which uses four standard 8x8 chessboards stacked.
Tedco Three-Dimensional Chess – a 4×4×4 playing field variant designed by Texas Educational Devices Co (established by Texas Instruments) in 1966.
3D XYZ chess (also called Exchequer) – another variant on the 4×4×4 playing field, designed by Rick Hewson.
Flying chess – two adjacent 8×8 boards
Isometric Chess – a game by Isometric Chess International (John Oden, 1977) which uses a field in a pyramid shape, with four tiers that begins with a 8×8 base and has a 2×2 center
3D Xiang Qi – a 3D version of xiangqi by Larry L. Smith which uses a 5×4 space
Space shogi – a large 9×9×9 shogi variant. Ralph Betza also had numerous other ideas for 3D chess variants

In fiction

As well as in Star Trek, multi-dimensional chess games are featured in various fictional works, usually in a futuristic or science fiction setting. Isaac Asimov's works include one of the earliest mentions of the game in fiction. His short-story A Perfect Fit describes a 3D chess game consisting of eight boards stacked on top of each other. Other examples include Asimov's Pebble in the Sky, Tristana (1970) by Luis Buñuel, Nova, Blake's 7, UFO, Starman Jones, Unreal 2, the Legion of Super-Heroes franchise, Doctor Who, The Big Bang Theory, and The Lego Movie. The concept is parodied in Futurama as "tridimensional Scrabble".

Notes

References

Primary sources

Dawnson, T.R. (1947) Caissa's Fairy Tales, Stroud News Publishing Co.
Dawnson, T.R. "Space Chess" (article), in Fabel, Karl; Kemp, C.E. Chess Unlimited
Maack, F. (1908) Anleitung zum Raumschach: Dreidimensionales Schachspiel
Maack, F. (1913) Spielregeln zum Raumschach (Rules of Space Chess)
Maack, F. (1919) Raumschach: Einführung in die Spielpraxis (Space chess: Introduction to the Game's Praxis)

Bibliography

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External links

;Raumschach:

– a simple program (in Java)

;Star Trek Tri‑D:

– commercial site; history of Standard Rules
– free summary of Standard Rules
– Tri‑D Chess Tournament Rules, boards, and more
– Tournament Rules game library and more

– Tri-Dimensional Chess Tracker; web-based Perl program