Cylindrical chessboard

Cylinder chess (or cylindrical chess) is a chess variant. The game is played as if the board were a cylinder, with the left side of the board joined to the right side. Cylinder chess is one of six chess variants described by the Arabic historian Ali al-Masudi in 947.[1][lower-alpha 1]

The cylindrical board is used in some chess problems.

Rules and gameplay

abcdefgh
8
b8 black cross
d8 black cross
a7 black cross
e7 black cross
f6 black cross
h6 black cross
g5 black cross
a4 black circle
f4 black cross
g4 black circle
h4 black cross
a3 black cross
b3 black circle
e3 black cross
f3 black circle
b2 black cross
d2 black cross
h2 black knight
b1 black circle
c1 white bishop
f1 black circle
8
77
66
55
44
33
22
11
abcdefgh
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.

The game is played as if the left and right sides of the board are connected. When a piece goes off one edge of the board, it reappears from the other edge.[2] For example, 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 move to h4 by going from c1 to a3, and then going up and left from a3 to h4; if White has a pawn on a5, Black has a pawn on h7 and Black plays 1...h7–h5, White can capture the black pawn en passant with 2.axh6; and so on.

Castling can be handled in one of three ways:

  • Castling is allowed, but not with a rook over the board edge. This maintains the options for castling available in standard chess.
  • Castling is not allowed. Proponents of this convention argue that the purpose of castling is nullified due to all files being equally dangerous on a cylindrical board.
  • In addition to normal castling, castling with a rook over the board edge is also allowed. This is done by moving the king two squares toward the rook and moving the rook to the square that the king passed over (in the same manner as usual).

Some cylinder chess problems allow null moves, or moves such that every piece stays in the same place, as long as any piece performing such a move travels a nonzero distance by crossing over the edge of the board.[3] However, most actual games of cylinder chess disallow null moves.

Strategy

abcdefgh
8
a8 black rook
b8 black knight
c8 black bishop
d8 black queen
e8 black king
f8 black bishop
g8 black knight
h8 black rook
a7 black pawn
b7 black pawn
c7 black pawn
d7 black pawn
e7 black cross
f7 black pawn
g7 black pawn
h7 black pawn
f6 black cross
e5 black pawn
g5 black cross
h4 black cross
a3 black cross
b3 white pawn
a2 white pawn
b2 black cross
c2 white pawn
d2 white pawn
e2 white pawn
f2 white pawn
g2 white pawn
h2 white pawn
a1 white rook
b1 white knight
c1 white bishop
d1 white queen
e1 white king
f1 white bishop
g1 white knight
h1 white rook
8
77
66
55
44
33
22
11
abcdefgh
Position after 1.b3 e5: The diagram shows the weakness of the move 1...e5 by Black, as the c1-bishop has been allowed access to the edge of the board by way of the movement of the b3-pawn. This principle applies to an easy check on a player's king by an enemy bishop in the same manner.

In cylinder chess, the traditional hierarchy of piece strengths is changed, with bishops being significantly stronger than knights. The knight and rook do not gain much more power from the cylindrical board, but bishops and especially queens become stronger. The center squares are unimportant to control, and moving a pawn to the center in the opening is very weakening because it opens the player's center to attacks by the opponent's bishops, which have been allowed faster access to the flank squares.

Cylinder chess also has different endgames than standard chess. For example, unlike in standard chess, a king and rook cannot force checkmate against a lone king on the cylindrical board.

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

Symbol
Piecepawnknightbishoprookqueen
Value13+144511

In chess problems

abcdefgh
8
c6 black pawn
h6 white rook
b5 black king
c5 black pawn
h4 white rook
a3 white king
8
77
66
55
44
33
22
11
abcdefgh
White to play and mate in two

The diagram shows a cylinder chess problem that allows null moves. The move 1.Rg4, threatening 2.Rg5#, fails due to 1...Ka5. The solution is to put Black in zugzwang by playing 1.Rh4, moving the rook on h4 to its own square; then, after either 1...Ka5 or 1...c4, 2.R4h5# is mate.

Toroidal chessboard
abcdefgh
8
a8 black rook
c8 black bishop
f8 black bishop
h8 black rook
a7 black pawn
b7 black pawn
g7 black pawn
h7 black pawn
a6 black knight
c6 black pawn
d6 black queen
e6 black king
f6 black pawn
h6 black knight
d5 black pawn
e5 black pawn
d4 white pawn
e4 white pawn
a3 white knight
c3 white pawn
d3 white queen
e3 white king
f3 white pawn
h3 white knight
a2 white pawn
b2 white pawn
g2 white pawn
h2 white pawn
a1 white rook
c1 white bishop
f1 white bishop
h1 white rook
8
77
66
55
44
33
22
11
abcdefgh
Toroidal chess starting position

In horizontal cylinder chess, the first and last ranks of the chessboard are connected. In toroidal chess, the board has the form of a torus. A toroidal board can be formed by connecting the first and last ranks of the cylindrical board.

Horizontal cylinder chess and toroidal chess, unlike cylinder chess, cannot use the starting position of standard chess; otherwise, both kings will begin the game in checkmate. The adjacent diagram shows the starting position for toroidal chess on a standard board. In the starting setup, the rooks protect each other while being threatened by the opponent's rooks. They are supported by the knights on the sides of the board, making their positions more defensible.

On the toroidal board, checkmate is impossible with king and queen versus king,[5] but it is possible with king and two rooks versus king.

Notes

  1. Other described variants include astrological chess and circular chess.

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. "Cylinder Chess".
  5. Е.Я. Гик, Шахматы и математика, Наука, Москва, 1983 (in Russian)
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