Undenary Chess

Michael A. Rouse

Introduction

Undenary Chess is a large chess variant for two persons.

Board Layout

The board is made up of 121 alternating light and dark squares, with a light-colored square at each corner and the very center of the board. (See image below)

Board courtesy of Derek Nalls. Pieces from Alfaerie set by David Howe.

Rules and Pieces

22 Pawns. Each Pawn is a "complete" Pawn (sometimes called a Sergeant) with three possible moves: 1 square ahead straight or diagonally, with captures performed the same way. Upon reaching the back row of their opponent, a Pawn shall be promoted to a Queen, a Duke, or a Paladin (Archbishop), depending on the choice of the player.

6 Knights. Each Knight moves and captures in an L-shape, two moves forward and one move at 90 degrees, without regard to any intervening pieces, onto a square of a different color.

4 Bishops. Each Bishop moves along the diagonals of the square board along squares of the same color. They can only be blocked by a piece along the same color diagonal.

4 Rooks. Each Rook can move any distance along a row or column centered on its square, unless blocked by a piece.

3 Paladins (or Archbishops, also known as Cardinals). Combines the moves of a Knight and a Bishop.

2 Dukes (also known as Chancellors). Combines the moves of a Knight and Rook.

2 Queens. Combines the moves of a Bishop and Rook

1 King. A "super piece" that can move a single square in any direction, and can move as any other piece of the same color remaining on the board. At the beginning of the game, it combines the movement of Knight, Bishop, and Rook. After the final piece with a particular movement type is captured, that movement is lost to the King unless a Pawn is promoted with the necessary movement type. Capturing the King ends the game, hence no move that puts the player's King into check (danger of immediate capture) is legal, and any check by an opponent must be removed by the player's next move. In addition to "baring" his King (having no other pieces on the board to defend him), a player that cannot get out of check loses the game (is checkmated).

Initial Placement

The board is oriented so that a "flat" edge of eleven squares faces each opponent.

Back row (closest to player): Rook, Rook, Duke, Paladin, Queen, King, Queen, Paladin, Duke, Rook, Rook.

Second row: Knight, Knight, Knight, Bishop, Bishop, Paladin, Bishop, Bishop, Knight, Knight, Knight.

Third row: Eleven Pawns.

Fourth row. Eleven Pawns.

Gameplay

White and Black alternate moves, starting with White. A legal move is one in which a single movement and/or capture follows the rules for that piece.

A player is in "check" when an opponent's move directly threatens the player's King with capture. A player may not move so as to place his King in check, nor may he leave his King in check during his move. "Checkmate" occurs when a player places an opponent in check, and the opponent has no legal moves to get out of check. It is considered a win for the player, and worth a full point. In addition, a player may resign an untenable position, taking a loss.

Another method of winning is by "baring" the opponent's King -- removing every other piece of the same color from the board. This is to prevent long, tedious, memorized endgames of the type computers are famous for. A totally-destroyed army should count as much as a captured King, so it is worth a full point (the defeated King receives zero).

A stalemate occurs when the opponent is not in check, but every legal move would place him in check. It gives advantage to the player, or 3/4 point for the "winner" to 1/4 point for the "loser" of the stalemate.

Finally, if no logical progression of moves will yield a checkmate or a stalemate, or if an identical position occurs three times in a row, or if fifty moves occur without a capture or Pawn movement, the game shall be considered drawn, and half a point granted to each side.

Some thoughts behind Undenary Chess.

With so many chess variants out, it seems as if all the cool names have already been taken. "Undenary" means "pertaining to eleven," and the game is played on an 11x11 board, hence "Undenary Chess." It's a large chess variant that grew out of a hexagonal version I created called Hexmate. The games are quite similar - other than the difference between a square board and a hexagonal one, there are 6 fewer board positions and two fewer bishops in Undenary Chess than in Hexmate (a reasonable change because of the one fewer color), and one more pawn. Other than a few placement issues, the rules are as nearly identical as practical.

In Chess and most variants, it seems like the King is a doddering old man, depending on his amazon-like Queen and others to protect him. In Undenary Chess (as in Hexmate), the King has the strength of the Queen combined with the fortitude of a Knight, the power of a Duke and the blessings of a Bishop, and the bravery of a Paladin inside the defense of a castle. As long as the player has a piece with matching movement on the board, the King may attack or defend as a Knight, a Bishop, or a Rook, with all the strength of that legendary chess piece, the Giraffe (or Amazon). Unlike that overpowered piece, however, it cannot attack the enemy King directly (theoretically it can in the endgame, if it still has a movement type not shared by the enemy King, but such circumstances should be rare), and its movement options depend on the strength of its remaining forces. More than a few endgames will have the king as the vital piece in a checkmate of the opponent. Here are some thoughts behind the design.

My first principle was simplicity -- making certain that rules for placement, movement, and capturing were simple, and that complexity arose out of depth of strategy and not exceptions to overly-complicated rules.

My second principle was symmetry -- left and right sides of the board are mirror images, as is the setup of both opponents.

My third principle was there had to be some development of short-range pieces before long-range "power" pieces could be thrown willy-nilly across the board, and no massive trade of pieces could take place until at least some setup had taken place. This meant putting the strongest long-range pieces along the back row, and the Bishops in the next-to-last row, both blocked by other pieces. They can still be moved out fairly quickly, but the opponent can protect his forces just as quickly.

My fourth principle was to provide plenty of opportunities for tactical excitement. One of the most exciting moves in chess is the Queen-King fork. In Undenary Chess, you can still have the Knight perform the Queen-King fork, but in addition you can have the Bishop perform a Duke-King fork, and the Rook perform a Paladin-King fork (although in each case the forking piece must have another piece protecting it, because of the King's power). Every piece, even the three most powerful pieces on the board (other than the King), can have another, weaker piece "sneak up" on it, which is why the King is the *only* Knight-Bishop-Rook "super piece."

My fifth principle was to provide some semblance of parity between the various classes. Using values associated with normal chess, a Queen is worth about nine Pawns, a Duke about the same, a Paladin about seven, a Rook about five, a Bishop about three, and a Knight about three. Figuring out the number of points tied up in various pieces, two Queens are about eighteen points, two Dukes about the same, three Paladins are about twenty-one points, four Rooks about twenty points, four Bishops about twelve points, and six Knights about eighteen points. By having two rows of Pawns in front, we have a total of twenty-two points in Pawns. Since the King is a singular piece and losing it means losing the game, its value is effectively infinite.

My sixth principle was, as mentioned earlier, to make the King the strongest and the most vital piece on the board. There is a dichotomy between wanting to use the most powerful piece, and trying to protect him, especially since losing him spells the end of the game. You couldn't simply hide him in a corner of the board and expect to win -- a more active King would destroy your army, and kill the pieces whose survival your King depends on for movement. Yet relying too heavily on the King means that you put him (and the game itself) in greater danger. I think that having one powerful piece on the board at all times (one who's strength is dependent on his other forces) would make each part of the game exciting, even a Pawn's race.

Random musings about the game:

To temper its mobility of the King in the endgame without ruining the part that worked, I came up with the following idea: The King has an inherent movement of one square in any direction, plus it can move like any other piece of the same color still remaining on the board. In addition to restricting its mobility in the endgame, this has an added benefit in strategy: the final piece with a specific movement type (the last Bishop, for example) might suddenly become more valuable than a strong piece you have plenty of (perhaps you have two Rooks, or even a couple of Dukes). In addition, Pawn promotion becomes even less "turn pawn into Queen unless the moon is blue" and more "choose a piece that adds movement and balances your options."

Another change (albeit a less drastic one) is with Pawn movement. Keeping the standard method of "move forward and capture diagonally" with different-sized jumps at the beginning and en passant moves would have violated my rule for simplicity. Instead, all Pawns can move one square straight ahead or on the diagonal, and capture the same way. This increases the strength of the Pawn and makes it impossible to simply block their movement with another piece. Some people may be bothered by the shear number of Pawns, but two rows were necessary to keep the more powerful pieces restrained until the "terrain" of the board formed. Most games will probably have an initial Pawn bloodbath, followed by sniping individual pieces and jockying for position, and ending with a final, brutal assault on the King. It should be a bit more dynamic and entertaining to watch (if more complicated to play) than standard chess.

Undenary Chess Variations

For those who feel the current version has limited options and strategy and want more of a challenge, there is "Undenary Choice" which uses the same board, pieces, and movement as Undenary Chess. Even the Pawns are kept in the same position. The difference is that, after a suitably random method of determining who moves first, players alternate first in placing major pieces, then in playing the game.

Each player is given eleven pieces to place -- one King, one Queen, one Duke, one Paladin, two Rooks, two Bishops, and three Knights. More than eleven pieces are actually set upon the board, of course, but because of rules of symmetry, only eleven options are needed. The placement restrictions are simple: all pieces have to be mirrored left and right (if I place a Knight in the bottom left corner, a Knight is automatically placed in the bottom right corner) and all pieces must be mirrored across the board (which means that, using the preceding example, a Knight placed in the far left and far right corners). The King and one Paladin can only be placed on the two center squares available, while the two Bishops must be placed on different colors. Other than these restrictions, the pieces may be placed anywhere. To make the games more fair, the first person to begin placing piece is the second person to move.

To be honest, I haven't tried Undenary Choice or its hexagonal variant -- even with the default board it is quite difficult. If these games were to be studied for centuries with the same intensity as chess, I could see where a variation (the Fischer Random Chess of large chess variants) might be necessary. This version would allow an even wider range of possibilities while keeping purely random elements to a minimum.