Chess Variants/Hexagonal Chess

Hexagonal Chess is a term used to refer to a family of chess variants played on boards that are made up of hexagons instead of squares.

The earliest hexagonal chess variamts were developed in the mid-19th century, but the first notable member of this family is Gliński's hexagonal chess, invented in 1936 by Polish game designer Wladyslaw Gliński and launched in the United Kingdom in 1949. After its launch the variant proved the most popular of the hexagonal chess variants, gaining a notable following in Eastern Europe, especially Poland. At the height of its popularity the variant had over half a million players, and more than 130,000 sets were sold. Gliński also released a book on the rules of the variant, Rules of Hexagonal Chess, which was published in 1973.

Several other hexagonal chess variants were created over the latter half of the 20th century, mostly differing from Gliński's variant in the starting setup, the shape of the board and the movement of the pawns.

Before one can learn the rules of the hexagonal chess variants, one must learn how the hexagonal board's geometry affects piece movements.

As the name suggests, the hexagonal chess variants are all played on boards made up of regular hexagons instead of squares. The hexagonal board uses three space colours instead of two, so that no two hexes of the same colour touch each other, and there are three bishops instead of two so the bishops can cover the entire board. The hexagons can be arranged with corners pointing either vertically (as in de Vasa and Brusky's variants) or horizontally ( as in Gliński's, McCooey's and Shafran's variants).

Generally in board games, there are two broad axes of positioning and movement; the orthogonal axis and the diagonal axis.

The orthogonal axis is the axis that runs straight up, down, left and right. Squares are said to be orthogonally adjacent if they share an edge in common, and an orthogonal move transfers a piece over the edge of a square into the neighbouring square. Since each square has four neighbours, this translates into four orthogonal directions. On the diagram at left, crosses are used to visualise the orthogonal axis.

On the other hand, the diagonal axis runs in two orthogonal directions simultaneously. Squares are said to be diagonally adjacent if they share a single corner in common, and a diagonal move transfers a piece over the corner of a square into the square that is one up and to the left, or one up and to the right, or one down and to the left, or one down and to the right. On the square board the diagonal axis runs at a 45 degree offset to the orthogonal axis, as seen at right.

Now with a hexagonal board, each hex has six neighbours instead of four, which means there are six orthogonal directions instead of four. The diagonal axis still runs in between the orthogonal directions (30 degrees as opposed to 45), but since all of the hexes share at least one side in common the corner-sharing definiton for diagonal adjacency does not work with a hexagonal board. Instead, two hexes are said to be diagonally adjacent if their two closest corners can be connected using the shared side of the two hexes in between them. So in the diagram at right, hexes A and D are said to be diagonally adjacent because their two closest corners can be connected using the shared side of hexes B and C. Like with the orthogonal directions, the hexagonal board features six diagonal directions.

Because there are twelve directions total (six orthogonal, six diagonal), and the directions are all equally spaced apart from each other, they can be referenced using the directions of the numbers on the face of an analogue clock. With hex corners pointing horizontally, the orthogonal directions are the 12 o'clock, 2 o'clock, 4 o'clock, 6 o'clock, 8 o'clock and 10 o'clock directions, whilst the diagonal directions are the 1 o'clock, 3 o'clock, 5 o'clock, 7 o'clock, 9 o'clock and 11 o'clock directions. With hex corners pointing vertically the orthogonal and diagonal directions are reversed.

Gliński's hexagonal chess is played on a horizontal-aligned board of 91 hexes, arranged into the shape of a hexagon with edges six hexes long. The central hex is always medium tone. The board has eleven files that run vertically, notated with the letters a through l, sans j, and 11 ranks that run parallel to the bottom edges of the board, bending 60 degrees at the f-file. The first through sixth ranks have eleven hexes each, then the seventh rank has nine hexes, the eighth rank seven, the ninth rank five, the tenth rank three, and finally the eleventh rank only has a single hex, f11.

All of the normal chess pieces are used, with an extra pawn and bishop for both sides. The initial setup is at right. The pieces move as follows:

• The rook may move any number of hexes in a straight line orthogonally until it reaches an obstacle, such as another piece or the edge of the board.
• The bishop may move any number of hexes in a straight line diagonally until it reaches an obstacle.
• The queen combines the moves of the rook and the bishop.
• The king may move one hex in any orthogonal or diagonal direction, providing the destination hex is not under attack. There is no castling.
• The knight first moves two hexes orthogonally. It then turns one orthogonal direction clockwise or counterclockwise and mvoes one more hex. It may jump over any pieces in its path.
• The pawn moves one hex vertically forward, and captures one hex orthogonally forward at a 60-degree angle to the vertical, including capturing en passant. If the pawn has not yet been moved in the game it may move two hexes forward. If a pawn captures an enemy piece and lands on the starting hex of any friendly pawn it may still move two hexes forward. When the pawn reaches the top edge of the board from its starting position, it may promote as usual.

In Gliński's hexagonal chess stalemate is a partial win for the player delivering the stalemate - under tournament rules the stalemating player earns ³/₄ of a point and the stalemated player earns ¹/₄ of a point.

In 1978-79, Dave McCooey and Richard Honeycutt developed their own hexagonal chess variant. According to McCooey himself:

A friend and I developed a hex-chess variation in 1978-79. Our goal was to create the closest hexagonal equivalent to the real game of chess as possible. I have since seen a few other hex-chess variants, including some that predate ours (e.g. Gliński's), but none are as "equivalent" to real chess as ours is.

McCooey's hexagonal chess plays mostly the same as Gliński's variant, with four differences:

• The intial setup (shown at tight) is different - it is more compact and uses seven pawns per player as opposed to nine.
• The pawns on the f-file are not permitted their initial two-step move.
• Stalemate is a draw like in standard chess, with each player receiving half a point.
• The pawns capture differently - moving one hex diagonally forward.

Shafran's hexagonal chess was invented by Soviet geologist Isaak Grigorevich Shafran in 1939 and registered in 1956. It would later be demonstrated at the Worldwide Chess Exhibition in Leipzig, Germany in 1960. Shafran's hexagonal chess is played on an irregular hexagonal board of 70 hexes. The board has nine files that run vertically and are lettered a through i, and ten ranks that run from the 10 o'clock to the 4 o'clock direction across the board, numbered 1 through 10. So for example the white king starts on hex e1, and the black queenside rook starts on i10.

The normal set of pieces is used, with an extra pawn and bishop for each player. The initial setup is shown at right. Each player calls the left side of the board the "queen's flank" and the right side the "bishop's flank". Note that these do not correlate - White's queen's flank is Black's bishop's flank, and vice versa.

All pieces move exactly the same as in Gliński's variant, with the exception of the pawns. On their first move the pawns are allowed to move to the centre of the file they start on - the d-, e- and f-pawns may move three hexes forward, the b-, c-, g-, and h-pawns may move two hexes forward, and the a- and i-pawns may only move one hex forward. They capture as in McCooey's variant.

Unlike Gliński and McCooey's variants, the player is allowed to castle in either direction if they want to, provided all of the usual conditions are met. A player can either castle short, moving the king two hexes towards the rook, or long, moving the king three hexes towards the rook. The rook is then moved to the other side of the king.

Like with McCooey's variant stalemate is considered a draw.

De Vasa's hexagonal chess was invented by one Helge E. de Vasa in 1953 and publish in a French chess book, Joseph Boyer's Nouveaux Jeux d'Echecs Non-orthodoxes, the following year. De Vasa's hexagonal chess is played on a rhombus-shaped board made up of 81 hexes, and unlike Gliński, McCooey and Shafran's variants the hexagons have their corners aligned vertically instead of horizontally. The board has nine files that run from the 11 o'clock to 5 o'clock directions lettered a through i, and nine ranks that run horizontally numbered 1 through 9.

The standard set of pieces is used plus an extra pawn and bishop for both sides, and the pieces all move the same as in Gliński's except for the pawns:

• The pawns move one hex forward at a time, to either of the two hexes adjcanet to the hex it is currently on.
• On its first move only a pawn may move two hexes forward.
• Pawns capture one hex diagonally at a 60 degree angle to the vertical.

Castling is allowed and works exactly the same as in Shafran's variant.

This variant wa sinvented by Yakov Brusky in 1966, and is played on an irregular hexagonal board of 84 hexes. Ranks and files work like in De Vasa's variant, with the files letter a through l and the ranks numbered 1 through 8.

The standard set of pieces is used plus two extra pawns and an extra bishop for both sides. All pieces move the same as in De Vasa's variant, but two additonal rules exist concerning the pawns:

• If a pawn has not yet moved in the game, then it is allowed to capture vertically forward in addition to its usual movement options.
• If a pawn is blocked by an enemy piece from moving in one direction, it is also blocked from moving in the other direction. This restrition does not apply if the pawn is blocked by a friendly piece.

Castling is allowed and works the same and in Shafran and De Vasa's variants.