Five Up

Raumschach, which was invented before World War I, is a classic 3D chess variant. The 5x5x5 board is an ideal size, and the additions to the FIDE set of pieces are minimal, making the game easy to learn. However, Raumschach suffers from a couple of nontrivial problems. The unicorn (which in the original version moves only on 3D diagonals) is too weak to be a useful piece, and the king is too mobile, making checkmate difficult. In addition, the piece density is less than 1/3 (40 pieces in all on a 125-cell board), which is arguably less than ideal. Richard Goode's variant of Raumschach has better unicorns, which I have adopted (see below), but his king, being restricted to single-cell moves on the 3D diagonals, is too weak.

The changes below, which transform the game into a version I call Five Up, are intended to make Raumschach as playable as possible. I've kept the discussion short, on the assumption that most readers will already understand the basic dynamics of piece movement on a 3D board. Throughout, I have used the word "cell" in preference to "square," since the pieces' locations are in effect small cubes, not flat squares.

Each player begins the game of Five Up with the usual complement of chess pieces, plus two unicorns, two added pawns, and three pieces in reserve. The initial setup is shown in Figure 1. The basic rules of FIDE chess apply, and a stalemate is a draw.

Figure 1. The opening setup in Five Up. In the ASCII diagram, black pieces are shown as lower-case letters bracketed by asterisks. White pieces are capital letters. The A layer can be visualized as the top of the cube, the E layer the bottom, or vice-versa. The layers are positioned side by side in the ASCII diagram purely for ease in viewing or printing. Note that a slight asymmetry in the initial setup is required to put the bishops (and also the unicorns) on cells of opposite colors.

           = A =
   +---+---+---+---+---+   
 5 |*r*|*n*|*k*|*n*|*r*|   
   +---+---+---+---+---+   
 4 |*p*|*p*|*p*|*p*|*p*|   
   +---+---+---+---+---+   
 3 |   |   |   |   |   |   
   +---+---+---+---+---+   
 2 |   |   |   |   |   |   
   +---+---+---+---+---+   
 1 |   |   |   |   |   |   
   +---+---+---+---+---+   
     a   b   c   d   e

           = B =                    = D =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 |*b*|*u*|*q*|*b*|*u*|  5 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 |*p*|*p*|*p*|*p*|*p*|  4 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   |   |   |   |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 |   |   |   |   |   |  2 | P | P | P | P | P |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   |   |   |   |   |  1 | U | B | Q | U | B |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

           = C =                    = E =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 |   |   |   |   |   |  5 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 |   |   |   |   |   |  4 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   |   |   |   |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 |   |   |   |   |   |  2 | P | P | P | P | P |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   |   |   |   |   |  1 | R | N | K | N | R |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

In addition to the pieces shown in Figure 1, each player has three pieces that are not on the board at the beginning of the game, but are added during play. The additional pieces are a wizard (W), a guard (G), and a silver unicorn (S). These pieces are placed on the board in the following manner:

Whenever a player moves one of his or her non-pawn pieces for the first time, the wizard, guard, or silver unicorn may be placed, immediately after the move, on the cell just vacated. This placement is optional, and may occur at any time during the game, provided the non-pawn piece is being moved for the first time. The wizard, guard, and silver unicorn are themselves non-pawn pieces, so a player could, for instance, move a knight and place a wizard on the knight's home cell, then on his or her next turn move the wizard and place the silver unicorn on this cell, and later move the silver unicorn and place the guard on the same cell. It's probably a good idea to enter these three pieces into play early, as doing so in the middle game, in the heat of a skirmish elsewhere on the board, may prove inconvenient.

The rook moves along unobstructed orthogonals, including verticals, the bishop along unobstructed 2D (but not 3D) diagonals in any plane. The queen combines the moves of rook and bishop. (This makes the queen a bit weaker than the original Raumschach queen, which can also use the 3D diagonals.) The knight makes a normal knight's move within any vertical or horizontal plane, and can pass through other pieces.

The pawn moves one cell either vertically or horizontally, always proceeding toward the enemy's "home row" (the row on which the enemy king begins the game). The pawn captures by moving toward the enemy's home row diagonally. The diagonal move can be either in a horizontal or a vertical plane; this gives it, except when it's at the edge of the board, two possible non-capturing moves and five possible cells where it can capture, as shown in Figure 2. There is no initial double move, and thus no en passant. Pawns are promoted to any piece (except a king) on reaching the enemy's home row.

Figure 2. The white pawn shown here, which is advancing upward (toward the top layer) can make capturing moves to the cells marked 'x' and non-capturing moves to the cells marked 'o'.

 _ _ _ _ _
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
 _ _ _ _ _
|_|_|_|_|_|
|_|x|_|_|_|
|x|o|x|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
 _ _ _ _ _
|_|_|_|_|_|
|x|o|x|_|_|
|_|P|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
 _ _ _ _ _
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
 _ _ _ _ _
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|
|_|_|_|_|_|

The king can move a single cell in any of the six orthogonal directions, but not diagonally. In addition, it can capture (but not make a non-capturing move) by moving one cell along a 3D diagonal.

An optional rule: The king can castle at any point in the game, even if both king and rook have moved. In a castling move, the king and rook simply exchange positions. They must be on the same orthogonal (row, file, or column) and the cells between them must be empty. The king cannot castle through check or to get out of check.

The unicorn moves like a 3D version of the knight. Its move, which may be a bit hard to grasp at first, can best be visualized as a knight's move in any plane followed by a one-cell sideways move perpendicular to that plane (see Figure 3). Like the knight, the unicorn can pass through other pieces. Like the bishop, a given unicorn is restricted to cells of one color, and can reach only half of the cells on the board. Thus, while it can reach as many cells as the knight when starting from the center of the board, the unicorn is somewhat weaker than the knight.

Figure 3. The unicorn, shown here on Cc3, moves like a 3D version of the knight, allowing it to reach any of the cells marked 'o'.

           = A =
   +---+---+---+---+---+   
 5 |   |   |   |   |   |   
   +---+---+---+---+---+   
 4 |   | o |   | o |   |   
   +---+---+---+---+---+   
 3 |   |   |   |   |   |   
   +---+---+---+---+---+   
 2 |   | o |   | o |   |   
   +---+---+---+---+---+   
 1 |   |   |   |   |   |   
   +---+---+---+---+---+   
     a   b   c   d   e

           = B =                    = D =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 |   | o |   | o |   |  5 |   | o |   | o |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 | o |   |   |   | o |  4 | o |   |   |   | o |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   |   |   |   |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 | o |   |   |   | o |  2 | o |   |   |   | o |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   | o |   | o |   |  1 |   | o |   | o |   |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

           = C =                    = E =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 |   |   |   |   |   |  5 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 |   |   |   |   |   |  4 |   | o |   | o |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   | U |   |   |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 |   |   |   |   |   |  2 |   | o |   | o |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   |   |   |   |   |  1 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

The silver unicorn moves like a unicorn, but it can also move any number of cells along unobstructed 3D (but not 2D) diagonals.

The guard moves one cell in any direction, including orthogonals and both 2D and 3D diagonals. From an interior cell, it can reach 26 other cells, which makes it a powerful piece in spite of its limited range.

The wizard moves any number of unobstructed cells along 2D or 3D diagonals, as shown in Figure 4. Unlike the bishops but like the silver unicorn, the wizard can reach any cell on the board, because the 3D diagonal movement allows it to switch from black cells to white ones.

Figure 4. The wizard on Bb2 can reach any of the cells marked 'x' by moving along 2D or 3D diagonals.

           = A =
   +---+---+---+---+---+   
 5 |   |   |   |   |   |   
   +---+---+---+---+---+   
 4 |   |   |   |   |   |   
   +---+---+---+---+---+   
 3 |   |   | x | x | x |   
   +---+---+---+---+---+   
 2 |   |   | x |   | x |   
   +---+---+---+---+---+   
 1 |   |   | x | x | x |   
   +---+---+---+---+---+   
     a   b   c   d   e

           = B =                    = D =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 | x |   |   |   |   |  5 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 |   | x |   |   |   |  4 |   | x |   | x |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   | x |   | x |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 |   |   |   | W |   |  2 |   | x |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   |   | x |   | x |  1 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

           = C =                    = E =
   +---+---+---+---+---+    +---+---+---+---+---+
 5 |   |   |   |   |   |  5 | x |   |   | x |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 4 |   |   |   |   |   |  4 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 3 |   |   | x | x | x |  3 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 2 |   |   | x |   | x |  2 | x |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
 1 |   |   | x | x | x |  1 |   |   |   |   |   |
   +---+---+---+---+---+    +---+---+---+---+---+
     a   b   c   d   e        a   b   c   d   e

Board Geometry: A Footnote

There's no particular reason to restrict a 3D playing area to a Euclidean 3D space. One of the interesting things one can do with the Five Up board is warp it so that its sides join one another. The simplest way of doing this, and one that should make for good game play, joins the a and e faces in a simple four-dimensional hypercylinder. This is an exact higher-dimensional analog of the board in Cylindrical Chess. A rook, for instance, that leaves the playing area by traveling leftward from Cb1 through Ca1 reenters at Ce1. This is not a very interesting trajectory for a rook, but it gets more interesting when the cylindrical move is made by a knight or unicorn. Here, for instance, are the possible moves of a knight starting on Ca3 on a hypercylindrical board:

 _ _ _ _ _
|_|_|_|_|_|
|x|_|_|_|_|
|_|x|_|_|x|
|x|_|_|_|_|
|_|_|_|_|_|
 _ _ _ _ _ 
|x|_|_|_|_|
|_|_|_|_|_|
|_|_|x|x|_|
|_|_|_|_|_|
|x|_|_|_|_|
 _ _ _ _ _
|_|x|_|_|x|
|_|_|x|x|_|
|N|_|_|_|_|
|_|_|x|x|_|
|_|x|_|_|x|
 _ _ _ _ _
|x|_|_|_|_|
|_|_|_|_|_|
|_|_|x|x|_|
|_|_|_|_|_|
|x|_|_|_|_|
 _ _ _ _ _
|_|_|_|_|_|
|x|_|_|_|_|
|_|x|_|_|x|
|x|_|_|_|_|
|_|_|_|_|_|

We could go further, linking the A and E layers and the 1 and 5 faces to form a hypertorus. This is a fascinating four-dimensional object -- unlike a 3D torus, it has two holes. It has no edges: All 125 cells are equally "in the center of the board." There is probably no practical way to play chess on such a board, however, because it's not possible to get the opposing armies far enough apart at the beginning of the game to prevent their attacking one another.

If you'd care to play a game of Five Up by email, please feel free to wander over to the Contributors page, where the author's email address is located.

An updated version of this variant can be found at: Jim Aikin's Chess Variants (Link.)