Hexagonal chess


Hexagonal chess refers to a group of chess variants played on boards composed of hexagon. The best known is [|Gliński's variant], played on a symmetric 91-cell hexagonal board.
Since each hexagonal cell not on a board edge has six neighbor cells, there is increased mobility for pieces compared to a standard orthogonal chessboard. Three colours are typically used so that no two neighboring cells are the same colour, and a colour-restricted game piece such as the orthodox chess bishop usually comes in sets of three per player in order to maintain the game's balance.
Many different shapes and sizes of hexagon-based boards are used by variants. The nature of the game is also affected by the 30° orientation of the board's cells; the board can be horizontally or vertically oriented. The six-sidedness of the symmetric hexagon gameboard has also resulted in a number of three-player variants.
The first applications of chess on hexagonal boards probably occurred mid-19th century, but two early examples did not include checkmate as the winning objective. More chess-like games for hexagon-based boards started appearing regularly at the beginning of the 20th century. Hexagon-celled gameboards have grown in use for strategy games generally; for example, they are popularly used in modern wargaming.

Gliński's hexagonal chess

Gliński's hexagonal chess, invented by Władysław Gliński in 1936 and first launched in Britain in 1949, is "probably the most widely played of the hexagonal chess games". The game was popular in Eastern Europe, especially in Gliński's native Poland. At one point there were more than half a million players, and more than 130,000 board sets were sold. Gliński's book Rules of Hexagonal Chess was published in 1973.
The game is played on a vertically oriented regular hexagonal board with sides 6 cells long, which has 91 hex cells having three colours, with the middle cell usually mid-tone. The usual set of chess pieces is increased by one bishop and one pawn. The board has 11, marked by letters a–l, and 11 numbered . Ranks 1–6 each contain 11 cells, rank 7 has 9 cells, rank 8 has 7, and so on. Rank 11 contains exactly one cell: f11.
The diagrams show how each piece moves. As in orthodox chess, the knight can jump over other pieces，but unlike orthodox chess, two knights can mate a king and also a knight can triangulate. A player's three bishops, relegated to different colours, can never meet. The queen moves as rook plus bishop. There is no castling in [|Gliński's chess].
Pawns move straight forward and capture obliquely forward to an adjacent cell ; the pawn's capturing move direction is not diagonal like the bishop's move, as is the case in standard chess. All pawns can make a double step from their starting cells. If a pawn captures from its starting cell in such a way that it then occupies a starting cell of another pawn, it can still make a double move. For example, if the pawn on e4 were to capture a black piece on f5, the pawn retains the option to move to f7. The white pawn in the middle file cannot make a double step in the initial setup, since the target cell is occupied, but the double-step move could be made later when the cell is empty. En passant captures are also possible: for example, if the black pawn on c7 in the diagram moves to c5 in a single move, the white pawn on b5 can capture it: bxc6. Pawns promote on the last cell of a file; white pawns promote on the cells in the diagram marked with stars.
Stalemate is not a draw in Gliński's chess, but is still counted less than checkmate. In tournament games, the player who delivers stalemate earns point, and the stalemated player receives point.
A numeric notation exists. Every other detail is exactly as in ICCF numeric notation, except that there is no castling.

Timeline

Invented by Soviet geologist Isaak Grigorevich Shafran in 1939 and registered in 1956. It was demonstrated at the Worldwide Chess Exhibition in Leipzig in 1960.
The board is shaped as an irregular hexagon with nine and ten, comprising 70 cells as opposed to 91 in Gliński's board. The files are labelled a to i; the oblique ranks running diagonally from 10 to 4 o'clock are numbered 1 to 10. For example, the two kings start on e1 and e10; White's rooks start on a1 and i5, and Black's rooks start on a6 and i10. Each player calls the left-hand side of the board his "queen's flank" and the right-hand side his "bishops' flank"; note that they do not correlate.
All pieces except pawns and kings move and capture exactly as in Gliński's chess. In Shafran's chess, a pawn's first move can take it to the middle of the file. A pawn captures diagonally like a bishop, but one step away. When a pawn makes a multi-step move, it is subject to capture by en passant.
In the diagram, the black pawn on d8 has three possible moves, but none is safe: after 1... d7 it can be captured 2. exd7; after 1... d6 it can be captured 2. exd7 or 2. cxd6; after 1... d5 it can be captured en passant by either pawn.
Kings move as in Gliński's chess, except that castling is permitted in Shafran's chess. The usual restrictions apply. It can be long or short castling in either direction. The notation consists of Q- or B- followed by 0-0-0 or 0-0. In the diagram, the black king on h10 has castled long queenside and the black king on c8 has castled short bishopside. Castling does not typically increase the king's safety or make the rook more active, but it is present in the game nonetheless, for completeness.
Stalemate is a draw in Shafran's chess.

De Vasa's hexagonal chess

Invented by Helge E. de Vasa in 1953 and first published in Joseph Boyer's Nouveaux Jeux d'Echecs Non-orthodoxes. The rhombus-shaped board comprises 81 cells with initial setup as shown, in the revised form of the game. Rules for piece movement are the same as Gliński's variant, except for the pawns. Castling is permitted, and kings start on opposite wings of the board.
Players may castle either or . The king slides two cells when castling short; three cells when castling long. Other standard chess castling rules and restrictions apply.

Pawn's move

Pawns start on the players' third. A pawn moves forward to an adjacent cell, or, two cells forward in the same direction. A pawn captures diagonally forward to the sides.

Brusky's hexagonal chess

Invented by Yakov Brusky in 1966. The game features an irregular hexagon board comprising 84 cells. Piece movement rules are the same as Gliński's chess, except for the pawns, of which there are ten instead of Gliński's nine. Other differences from Gliński's: castling is permitted; kings start on opposite wings of the board; and draws are worth half a point.
Players may castle either or . The king slides two cells when castling short; three cells when castling long. Normal castling rules and restrictions apply.
As in algebraic notation, each cell is identified by a letter+number combination. are horizontal and identified by numbers 1–8. are straight and 30° oblique to the vertical, identified by letters a–l. Moves can be recorded in long algebraic notation to avoid confusion, for example: 1. d2-f4 rather than.

Pawn's move

A pawn moves forward to an adjacent cell, or, two cells forward in the same direction. If an enemy man blocks a pawn from moving in one of its two forward move directions, then that pawn is automatically blocked from moving in the other direction as well. But if the blocking man is a friendly piece the effect is not the same—the pawn is still free to move in the unblocked direction.
A pawn captures diagonally forward, to a cell of the same colour on which the pawn stands. But only a pawn on its initial cell may capture straight forward; once a pawn has moved, it may capture only to the sides. En passant captures are permitted in Brusky's chess.

Endgame studies

These endgame studies apply to Brusky's hexagonal variant:

McCooey's hexagonal chess

In 1978–79 Dave McCooey and Richard Honeycutt developed another variation of hexagonal chess very similar to Gliński's, having four differences: the starting array ; the pawn's capturing move; pawns on the f-file are not permitted an initial double step; and stalemate is counted as a draw.

Pawn's move

This diagram shows the pawn's move in McCooey's variant. The capturing move corresponds to a bishop's move: e.g. if the black pawn on e8 advances to e6, the white pawn on d5 may capture it en passant.
In the starting position, the f-file pawns may not advance two steps like the other pawns. The are also not defended in the opening array, and in fact smothered mate would result if it were captured by a knight, although this possibility would rarely occur in practical play.

Endgame studies

These endgame studies apply to both Gliński's and McCooey's variants:
Starchess is a hexagonal variant invented by Hungarian chess teacher László Polgár. The board is a horizontally oriented regular hexagram, consisting of 37 numbered cells. Due to the small board, games typically finish quicker than in standard chess.
Each player has five pawns, a king, knight, bishop, rook, and queen. The white pawns start at cells 5, 12, 18, 23, and 29; the black pawns at 9, 15, 20, 26, and 33. At the beginning of the game, the players place their other pieces alternately on the cells behind their pawns. As a consequence, there are ²=14400 possible setups.
Pawns move one step vertically forward and capture one step orthogonally left-forward or right-forward, and have an initial double-step option ; there is no en passant. The promotion zone for white pawns consists of Black's back rank, and for black pawns, White's back rank. A pawn that has lost its initial double-step option by making a capture is called a "limping pawn"; a pawn that ended up on cells 2, 3, 35, or 36 is called a "dead pawn"; a pawn on cells 1 or 37 is called a "mummy".
The king moves one step in any orthogonal direction; there is no castling. The knight jumps, two steps in any orthogonal direction, followed by one step in a different direction. The rook can move any number of steps, but only vertically; the bishop can move any number of steps, but not vertically. The queen combines the moves of the rook and the bishop, and thus can move any number of steps in any orthogonal direction.

Other hexagonal variants