Cylinder chess

Cylinder chess (or cylindrical chess) is a chess variant with an unusual board. The game is played as if the board were a cylinder, with the left side of the board joined to the right side. According to Bill Wall, in 947 in a history of chess in India and Persia, the Arabic historian Ali al-Masudi described six different variants of chess, including astrological chess, circular chess and cylinder chess.[1]

Cylindrical chessboard
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The diagram shows possible moves of a bishop on c1 and a knight on h2 on a cylindrical board. The bishop cannot move through the board's upper and lower sides.

Cylindrical board is also used in chess problems.

Rules and gameplay
Cylinder chess with the null move
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Mate in 2

The game is played as if there is no edge on the side of the board. When a piece goes off the right edge of the board in cylinder chess, it reappears on the left edge; when a piece goes off the left edge, it reappears on the right edge.[2]

It is legal to move a rook from a3 to h3, even if there is a piece on b3, since the rook can move left from a3. A bishop on c1 can go to h4, by moving from c1 to a3, and then going up and left from a3 to h4. Moves that do not change the position, like 1.Ra3–a3 (assuming the 3rd rank is empty), are usually not allowed, but sometimes they are in some problems. It is allowed to capture en passant over the board edge. For example, if White has a pawn on a5, Black on h7 and Black plays 1...h7–h5, White can capture it: 2.axh6.

Bishops are more valuable in this variant. And, unlike in standard chess, a king and rook cannot enforce checkmate against a lone king on the cylindrical board.

The game is sometimes played with changed rules for castling:

  • Castling is not allowed. Proponents of this convention argue that the purpose of castling is nullified by all files being equivalent, as they are on a cylinder.
  • In addition to normal castling, castling with the wrong rook (over the board edge) is also allowed. When castling in this way on the kingside, the king moves from e1 to g1 and the rook on a1 moves to f1. On the queenside, the king moves to c1 and the rook on h1 moves to d1.

Some cylinder chess problems allow moves that don't change the position (null moves).[3] The diagram shows an example of such a problem. The solution is to put Black in zugzwang by playing 1.Rh4–h4. Now, after any move by Black, White has a mate. The move 1.Rg4 doesn't work because of 1...Ka5 threatening to capture the rook on h6.

Strategy
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The diagram shows the vulnerability of the move e5 by Black, when the bishop has been allowed access to the edge of the board by way of the knight's pawn. This applies to an easy check on the kings by the bishop in the same manner.

In Cylinder chess, the traditional hierarchy of queen, rook, knight/bishop, pawn, is changed, with bishops stronger than knights. The knight and rook do not gain much more power from the cylindrical board, but bishops and especially queens gain strength. Also, the traditional important center squares, and the common moves of pawn e4, d4, e5, d5, become very vulnerable moves in Cylinder chess, because it opens the player's center to attacks by the bishops which have been allowed access to the side squares.

Piece values according to H. G. Muller are as follows:[4]

Symbol
Piecepawnknightbishoprookqueen
Value1​3 1⁄44511

Horizontal Cylinder chess and Toroidal chess
Toroidal chessboard
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Torus chess starting position

In Horizontal Cylinder chess, first and last rank are connected. In Toroidal chess the board has the form of a torus. One can get a toroidal board by connecting the first and last ranks of the cylindrical board. On the toroidal board, king and queen can't checkmate a lone king,[5] but two rooks and a king can.

See the Torus Chess link below for a toroidal variant that can be played, with an explanation of moves and strategy. The adjacent diagram shows the starting position for play on a standard board, using toroidal geometry.

References
  1. Earliest chess books and references by Bill Wall.
  2. D.B. Pritchard (1994). The Encyclopedia of Chess Variants (p. 79). ISBN 0-9524142-0-1.
  3. From A. W. Mongredien, Bulletin de la FFE, No. 19, 1926
  4. http://hgm.nubati.net/rules/Cylinder.html
  5. Е.Я. Гик, Шахматы и математика, Наука, Москва, 1983 (in Russian)
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