Three-dimensional chess (or 3D chess) refers to any of various chess variants that use multiple boards at different levels, allowing the chess pieces to move in three physical dimensions. Three-dimensional variants have existed since the late 19th century, one of the oldest being Raumschach (German for "Space chess"), invented in 1907 by Dr. Ferdinand Maack and considered the classic 3D game. Maack founded a Raumschach club in Hamburg in 1919, which remained active until World War II.
Chapter 25 of Pritchard's The Classified Encyclopedia of Chess Variants discusses games using boards with three or more dimensions and contains some 50 such variations. Chapter 11 covers variants using multiple boards normally set side by side: "Such games can also be considered as examples of three-dimensional chess"—Beasley.
The inventor contended that for chess to be more like modern warfare, attack should be possible not only from a two-dimensional plane but also from above (air) and below (underwater). Maack's original formulation was for an 8×8×8 board, but after experimenting with smaller boards eventually settled on 5×5×5 as best. Other obvious differences from standard chess include two additional pawns per player, and a special piece (two per player) named unicorn.
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 (125-cube) gamespace. The cubes (usually represented by squares and often called cells) alternate in color in all three dimensions.
The horizontal levels are denoted by capital letters A through E. Ranks and files of a level are denoted using algebraic notation. White starts on the A and B levels and Black starts on E and D. (So, the kings begin on cells Ac1 and Ec5.)
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. A rook, for example, moves through the six faces of a cube in any rank, file, or column. A bishop moves through the twelve edges of a cube. A knight makes a (0,1,2) leap (the same effect as one step as a rook followed by one step as a bishop in the same outward direction) enabling it to control 24 different cells from the board's center. A unicorn moves in a manner special to a 3D space (i.e. triagonal movement) through the corners of a cube, any number of steps in a straight line.[note 1] The queen combines the moves of a rook, bishop, and unicorn.[note 2] The king moves the same as the queen but one step at a time. As in chess, a pawn moves and captures forward toward the promotion rank (rank E5 for White, rank A1 for Black). This includes moving one step directly upward (for White) or downward (for Black), and capturing one step diagonally upward (White) or diagonally downward (Black), through a front or side cube edge. There is no pawn initial two-step advance, no en passant, and no castling in Raumschach.
Star Trek Tri-Dimensional Chess
Probably the most familiar 3D[note 3] chess variant to the general public in the middle 20th and early 21st centuries is the game of Tri-Dimensional Chess (or Tri-D Chess), which can be seen in many Star Trek TV episodes and movies, starting with the original series (TOS) and proceeding in updated forms throughout the subsequent movies and spinoff series.[note 4] The game can be seen being played in the latest Star Trek videogame, as well as in the TV series The Big Bang Theory.
The original Star Trek prop was crafted using boards from 3D Checkers and 3D Tic-Tac-Toe sets available in stores at the time (games also seen in TOS episodes) and adding futuristic-looking chess pieces. 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.
The complete Standard Rules for the game were originally developed in 1976 by Andrew Bartmess (with encouragement from Joseph) and were subsequently expanded by him into a commercially available booklet. A Creative Commons-licensed manual by Marco Bresciani gives a translation in Italian of the latest version of Bartmess's Standard Rules, and is available through the Star Trek Italian Club (for members only). 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's Standard Rules, with some deviations too. A repository of Tournament Rules games can be found on the website of Michael Klein.
Plans for constructing a Tri-D chessboard can be found on The Chess Variant Pages, as well as in Bartmess's Tri-D Chess Rules and in Bresciani's manual. Details for building a travel-size board are included on Meder's website.
There is software for playing Tri-D Chess; Parmen is a Windows application written by Doug Keenan and available free on his website.
Millennium 3D Chess
Millennium 3D Chess, created by William L. D'Agostino in 2001, employs three stacked 8×8 boards. The inventor describes his objective as "extending the traditional chess game into a multilevel environment without distorting the basic game."
In popular culture
- Leonard and Sheldon can be seen playing Tri-D chess in the beginning of Episode 11 in Season 1 of The Big Bang Theory. Sheldon and Penny also play in The Hofstadter Insufficiency.
- A three-dimensional chess variant may be seen in the Blake's 7 fourth season episode, "Games".
- A 3D chess set is used as a recurring prop in the lounge of the SHADO Moonbase in the British TV series UFO .
- Four-dimensional chess is played in Arkady and Boris Strugatsky's 1961 science fiction collection Noon: 22nd Century.
- The game is parodied in episodes of Futurama.
- In the computer game Unreal 2, Aida, one of the main heroes, is called an international 3D chess-master. A board is present in her quarters, identical in appearance to a Star Trek board.
- In the Recess episode "Big Brother Chad", Vince's big brother Chad beats himself in 3D chess.
- The Doctor tells Jo Grant that he is used to playing 3D chess after she beats him at checkers.
- In a 2013 Audi commercial, Leonard Nimoy and Zachary Quinto are seen playing 3D Chess on their iPads.
- Alice Chess[note 5]—two adjacent 8×8 boards
- Cubic Chess—a 6×6×6 variant
- Parallel Worlds Chess—a 8×8×3 variant with two armies per player
- Dragonchess—three stacked 8×12 boards, a fantasy variant
- Space Shogi—a 9×9×9 shogi variant
- Thus each unicorn can reach a total of 30 cells of the Raumschach gamespace; each player's pair, 60.
- Thus giving the queen a total of 26 different directions to move (6 faces plus 12 edges plus 8 corners).
- An ongoing discussion is whether Star Trek Chess is really three-dimensional or not, as its structure is something in between 2D and 3D. But since a third coordinate is needed to describe the position of the pieces, it is known by many as "3D Chess".[dubious ]
- There is some discussion whether this game should be called "Tri-Dimensional Chess" as in the Star Trek Star Fleet Technical Manual or "Three-Dimensional Chess" as in The Star Trek Encyclopedia and as on Memory Alpha.
- "Alice Chess, a well-considered variant, may also be classified as a 3-D game." (Pritchard 1994:305). "In a sense, it is a three-dimensional game, since the board can be thought of as measuring 8×8×2 (in squares)." (Schmittberger 1992:197).
- Pritchard (2007), p. 229
- Pritchard (2007), p. 93
- Pritchard (2007), p. 226
- Franz Joseph (1975), p. T0:03:98:3x
- Okuda (1994), p. 342
- Okuda (1997), p.509
- Bartmess, Andrew (2005). The Federation Standard Tri-D Chess Rules, Revision 5.0, 8 pp.
- Pritchard (2007), p.227
- Pritchard, D. B. (2007). The Classified Encyclopedia of Chess Variants. John Beasley. ISBN 978-0-9555168-0-1.
- Pritchard, D. B. (1994). The Encyclopedia of Chess Variants. Games & Puzzles Publications. ISBN 0-9524142-0-1.
- Schnaubelt, Franz Joseph (1975). Star Trek Star Fleet Technical Manual. Ballantine Books. ISBN 0-345-34074-4.
- Okuda, Denise; Okuda, Michael; Mirek, Debbie (1997). The Star Trek Encyclopedia. Pocket Books. ISBN 0-671-53607-9.
- Schmittberger, R. Wayne (1992). "3D Chess Sets". New Rules for Classic Games. John Wiley & Sons Inc. pp. 103–07. ISBN 978-0471536215.
- Hooper, David; Whyld, Kenneth (1987). "Three-dimensional chess". The Oxford Companion to Chess. Oxford University Press. pp. 351–52. ISBN 0-19-281986-0.
- "Three Dimensional" (index) The Chess Variant Pages
- "Raumschach" by Bruce Balden and Hans Bodlaender, The Chess Variant Pages
- "3-D Chess FAQ File" by David Moeser, The Chess Variant Pages
- Raumschach at BoardGameGeek
- Pathguy.com a simple Raumschach program by Ed Friedlander
Star Trek Tri-D
- "3D Chess from Star Trek" by Hans Bodlaender, The Chess Variant Pages
- Tridimensional Chess Rules Andrew Bartmess's commercial site; history of Standard Rules
- Star Trek 3-D Chess Rules Charles Roth's site; free summary of Standard Rules
- 3D-chess site of Jens Meder Tri-D Chess Tournament Rules, boards, and more
- 3DChess Michael Klein's site; Tournament Rules game library and more
- PARMEN Doug Keenan's site; free Tri-D Chess for Windows, supports Standard and Tournament rulesets
- Three-dimensional chess at Memory Alpha (a Star Trek wiki)
- 3-D Chess at BoardGameGeek
- Tri-D Chess Tracker Tri-Dimensional Chess Tracker; Web-based Perl Program