The Chess Variant Pages

Derick Peterson's Grand Hexachess

copyright 9/5/97

Board

The game is played on a base-7 hexagonal grid of 127 hexagons, each of which is painted one of 3 colors such that no two hexagons which share a side are of the same color, and all digaonals are of one color.

For aesthetic reasons, 2 of the 3 colors should match the colors of the pieces used, and the third should be chosen to be clearly different from them, though it should not clash.

My boards are desert yellow (matching my "White" wooden pieces), brown (matching my "Black" pieces, which are actually brown), and deep green (many hexagonal boards use red rather than green), giving it a somewhat military but earthy feel. I chose green for the color of the center hex for a feel of neutrality.

Castling

There is no castling rule, nor is there any need for one since the King and rooks are very mobile and quite well protected.

Ranks And Files

Ranks and files are composed of hexes in straight lines which share adjacent sides. The 7th (center) rank is the longest, having 13 files.

Definition Of A Diagonal

A diagonally adjacent hex is a hex which can be reached by first moving to one of the 6 adjacent hexes along a rank or file, then moving to one of the adjacent hexes along a 120-degree angle from the initial movement. This is analogous to the square board diagonal, where the turn is 90 degrees rather than 120 degrees.

The Pieces And Their Movement

Set-up

The following set-up is for White, and Black's pieces are the usual reflection of White's pieces.

All 11 pawns begin on the 5th rank, blocking all access of the enemy's sliding pieces as well as restraining your own sliding pieces until they are freed by pawn movements. All 11 pawns begin protected by the pieces which begin on the 3rd rank.

From left to right, the 3rd rank contains the following 9 pieces: Bishop, Knight, Rook, Queen, Bishop, War Machine, Rook, Knight, Bishop.

The King begins on the central square of the 7-hex 1st rank, with the Vizir directly to his right and the Duke directly to his left.

If the optional pieces are not used, then no pieces begin on the 1st rank, and the King is placed in the War Machine's position; this variant might be called Standard HexaChess, though I prefer Grand HexaChess since it is useful --not to mention more fun and interesting-- to have more mating power given the King's mobility and the large board. The relative proportions of jumpers and sliders is also more balanced in Grand HexaChess.

With Standard HexaChess, optionally, the board could be altered such that the 1st two ranks and the last two ranks are removed from play; this would give the King less mobility, for example. Finally, as with FIDE Chess it is also possible to play Pre-HexaChess, where pieces are placed on the board alternately by each player, or Screen HexaChess, where players secretly deploy their forces however they choose on their side of the seventh rank before movement begins.

Comparison With Other Hexagonal Chess Variants

Since inventing this game, I discovered that several hexagonal chess variants predate mine. However, it is my opinion that my rules make for a more interesting game which is closer in spirit to FIDE Chess.

In particular, the movement and capturing rules for the pawns in addition to the initial positions of the pieces seem to be a little strange in most other variants.

Comparing the movement of pieces in hexagonal variants to the movement of pieces in FIDE Chess, it is clear that the pieces should have 50% more mobility each since there are 12 directions on hexagonal grids vs. 8 directions on a square grid. This is one of the reasons that I allow pawns to move in 2 directions rather than the one direction allowed, for example, in Glinski's and McCooey's variants. Another good reason for this is that there are insufficient pawns to cover every file; thus it is useful to be able to shift pawns around somewhat.

My pawn captures, like McCooey's, are to adjacent diagonal hexes, but because of McCooey's rotated board when his pawns capture away from the center file they advance two steps closer to promotion. Glinski may have thought of this, and this is why his pawns capture to one of the two adjacent hexes which are one rook's step forward into one of the two adjacent files. However, the result is that when Glinksi's pawns capture toward the center file they make absolutely no progress toward promotion. Moreover, it is odd for that his pawns do not capture along a true diagonal. Also, the total number of hexes influenced by Glinksi's and McCooey's pawns is only 3, the same number influenced on a square grid; my pawns influence 4 hexes, reflecting the need for increased mobility on the hexagonal grid. I do not allow pawns to capture diagonally straight toward the enemy's back rank since this would not preserve the pawn's distance to promotion; this form of capture is allowed, however, in some other hexagonal chess variants which use pawn movements similar to mine.

As for the initial set-up of pieces, my set-up is unusually close to FIDE Chess since all pawns begin protected, and all bishops and rooks are blocked by their own pawns; this is not true for most other hexagonal chess variants.

Also, I use just enough pawns to totally block enemy attacks and block the movements of the pieces behind the pawns; I've seen variants which use twice as many pawns to achieve this purpose, but this seems unnecessary to me. It is not a simple task for White to grab the center hex in my variant since Black can amply defend it if he chooses; though it is not clear to me that the center hex has special significance, this property of fairness shows that White's first-move advantage is not too great. Along these lines, it is important in my set-up that pawns may not be advanced 2 hexes on their first move.

I do not consider this a disadvantage since my guess is that the double pawn advance and en passant captures evolved in square chess to speed the opening and give the pawns a little more mobility since they begin so far apart; this is not necessary in HexaChess. Similarly, I have no castling rule since there is no need for one with the King's and Rook's mobility in HexaChess. Finally, my pawns begin equidistant from the enemy's pawns; again, this is not true of several variants including McCooey's.

Speculative Endgame Results

Since the movements of most of my pieces are identical to those of McCooey's and Glinkski's variants, I expect that McCooey's endgame database results also hold approximately for my variant. The only differences are that my board is one ring of hexes larger, my Duke may not be in his database, and my pawns move and capture differently than his (though he may not have included pawns in his endgame analyses anyway). McCooey also has results which include the Vizir and the War Machine, though I do not yet know what he has found.

Thus I predict that, as in McCooey's and Glinksi's variants:

King & 2 Knights can checkmate a lone King, though this is very difficult.
King & Rook beats King & Knight, with excellent play.
King & Rook beats King & Bishop
King & 2 Bishops cannot checkmate a lone King, except for some very rare positions.
King, Knight & Bishop cannot checkmate a lone King, except for some very rare positions.
King & Queen draws against King & Rook.
King & Rook can checkmate a lone King.

3-Player Hexachess

I have also come up with rules for a 3-player hexagonal chess variant which uses a base-9 hexagonal grid, though I have not yet played this game. Players pieces begin on alternating back ranks of the board in the order specified above for White in 2-player Standard HexaChess, and each player's 11 pawns begin on his 3rd rank. Pieces move as in 2-player HexaChess, but pawns only promote upon reaching one of the enemy's back ranks. Play proceeds clockwise, but there are some unique rules to limit the "petty diplomacy" problem of such a 3-player perfect information strategy game. Below, I will state these rules in general for an n-player chess variant since they can easily be adapted to improve other such games. For 3-Player HexaChess, n=3 and k=2 in what follows.

  1. Defending From Multiple Attackers: When one player is simultaneously threatened by k (1 < k < n) opponents, he is entitled to move up to k of his pieces during his turn subject to the following restrictions.
    1. No piece may be moved more than once.
    2. He may not capture more than one piece belonging to any one opponent.
    3. He may not threaten or capture any more than one new piece belonging to any one opponent unless all but one of his attacks on that opponent simultaneously attack pieces of other opponents.
    4. Unless he can simultaneously check or checkmate all of his k attackers, he may not use more than one of his moves to enforce checkmate on any one player even if the checkmating piece simultaneously attacks another opponent's piece.
    5. None of his moves can expose his king to check even if his next move in the same turn could parry the check.
  2. Fair Exchange Of Pieces Per Round: When any k players exchange pieces in the course of one "round" of moves, those n-k players not involved in the exchange are obliged to remove pieces of equal or greater value than the weakest piece involved in the exchange subject to the following restrictions.
    1. No player is obliged to remove his king or any piece which exposes his king to check.
    2. Here a "round" is defined to be a series of n players' turns, beginning with one player's capture of an opponent's piece.
    3. The players forced to remove their own pieces may choose which piece or pieces to remove, and these pieces are not removed until their turn following the round of exchange.
    4. Any player forced to remove pieces may choose to exchange a powerful piece for any of his captured pieces whose powers are a proper subset of the piece which is being exchanged. For example, a live queen can be exchanged for a captured rook or bishop but not a knight or pawn. The weaker exchanged piece must, of course, be placed on the square vacated by the more powerful hostage; note that this determines the color of a bishop taking the place of the queen, for example, and it poses no new threats to his opponents.
  3. Checkmate And Capture Of A King:
    1. A player is not out of the game until his King is actually captured.
    2. When his King is captured, his pieces remain on the board as immovable obstacles for the remaining players to navigate. If all players agree in advance, these pieces may be captured to remove them from the board; otherwise, these obstacles cannot be captured nor removed.
    3. When a player's King remains on the board, but he is in checkmate, he loses his turn until the checking piece withdraws. However, while in a checkmate freeze, except for his King that player's pieces are immune to attack from all other players.

4-Player Team Hexachess

Finally, I have come up with a sensible board design for a 4-player hexagonal chess variant, though it's difficult to describe the shape in words. It uses a subset of the hexes of a base-10 hexagonal grid. The pieces move as in my 2- and 3-player variants, but now two players are allied against the other 2 players, and the game is won by the team who first checkmates one of the players of the opposing team.


Written by Derick Peterson. Diagrams by Hans Bodlaender. HTML conversion by David Howe.
WWW page created: February 10, 1998.