CHESS CUBED
by L. Lynn Smith

There have been several versions of 4x4x4 chess proposed.  This is my product
of decades of development and my personal favorite.

The game consist of:

1 4x4x4 playing field
1 set of chess pieces(32 pieces)

Pieces are initially arrayed on the upper[D] and lower[A] levels of the playing field.

White pieces are thus:

 4 [B][N][N][B]
 3 [P][P][P][P]
 2 [P][P][P][P]  level D
 1 [R][Q][K][R]
    a  b  c  d

B = Bishop	K = King	N = Knight
P = Pawn	R = Rook	Q = Queen

Black pieces are thus

 4 [R][Q][K][R]
 3 [P][P][P][P]
 2 [P][P][P][P]  level A
 1 [B][N][N][B]
    a  b  c  d

 -Movement of the pieces-

Due to the compression of the field, there is a compression of the mobility
of the Queen, Rook, Bishop and Knight.  This is basically accomplished by
restricting pieces to only changing one level during a move.  And there are 
several possible forms which can accomplish this.

Let's start with the most simple:

PAWN steps one orthogonal without capturing toward the opponent's starting level
	and steps one diagonal with capturing toward the opponent's starting
	level.  They freely promote upon reaching any cell of the opponent's
	starting level.

KNIGHT steps triagonal.

BISHOP steps diagonal.

ROOK steps orthogonal.

Queen steps orthogonal, diagonal and triagonal. 

King steps orthogonal and diagonal.

The denial of the King the triagonal step serves two purposes.  One, differentiating
it from the Queen.  Two, increasing the opportunity of check with the triagonal step
of this simple Knight.

Castling can be accomplished by moving an unmoved King and an unmoved Rook. The King 
cannot be under attack, nor any cell which it must translate. The Rook is allowed to
move onto an attacked cell.  The King takes the original position of the Rook and the 
Rook will change one level orthogonal.  Any cell between the pieces must be vacant and 
the destination of the Rook must be vacant.  It is only necessary to relocated the 
Queen if the player castles Queen's side.  King's side can be castled on the first turn.

The object is to checkmate the opponent's King.  You may notice that the King can be 
mated with only a Queen.  Go ahead and try.


 -Variants-

Players can adjust piece movements, increasing their power.  Though the changing of 
only one level restriction will be maintained.

LEAPING KNIGHT steps triagonal, or leaps one orthogonal on its level then one diagonal
	to either the same or the next level.

Example:

 4 [x][ ][x][ ]
 3 [ ][ ][ ][x]
 2 [ ][N][ ][ ]  start level
 1 [ ][ ][ ][x]
    a  b  c  d

 4 [ ][x][ ][ ]
 3 [x][ ][x][ ]
 2 [ ][ ][ ][x]  adjacent levels
 1 [x][ ][x][ ]
    a  b  c  d

SLIDING ROYALTY allow the Bishop, Rook and Queen to slide upon their level.

Thus the Bishop:

 4 [ ][ ][ ][x]
 3 [x][ ][x][ ]
 2 [ ][B][ ][ ]  start level
 1 [x][ ][x][ ]
    a  b  c  d

 4 [ ][ ][ ][ ]
 3 [ ][x][ ][ ]
 2 [x][ ][x][ ]  adjacent levels
 1 [ ][x][ ][ ]
    a  b  c  d

And the Rook:

 4 [ ][x][ ][ ]
 3 [ ][x][ ][ ]
 2 [x][R][x][x]  start level
 1 [ ][x][ ][ ]
    a  b  c  d

 4 [ ][ ][ ][ ]
 3 [ ][ ][ ][ ]
 2 [ ][x][ ][ ]  adjacent levels
 1 [ ][ ][ ][ ]
    a  b  c  d

The Queen combines the movement of these, along with the triagonal step.

With this form of movement, the King could easily be allowed the triagonal step.


VICIOUS PAWN steps one orthogonal without capturing on the same or next level
	and steps one diagonal with capture on the same or next level.

Example:

 4 [ ][ ][ ][ ]
 3 [c][m][c][ ]
 2 [m][P][m][ ]  start level
 1 [c][m][c][ ]
    a  b  c  d

 4 [ ][ ][ ][ ]
 3 [ ][c][ ][ ]
 2 [c][m][c][ ]  adjacent level toward opponent starting level
 1 [ ][c][ ][ ]
    a  b  c  d

c = capture	m = non-capture move

With this form of movement, the player is not obligated to immediately
promote upon reaching the far level.

Some might allow the triagonal step with capture, but this can result in 
very powerful Pawns which will dominate the game.  Resulting in games which 
may be only battles for promotion.

 -Author's Afterward-

This form of Chessplay within the 4x4x4 playing field has been the product
of many games between friends and relatives.  It even spurred an attempt
to translate the game of Checkers into the field, but this remains under
development.

When the Zillions-of-Games program became available, this was one of the
first implementations that I wrote.  I then began a series of tests to
determine the effectiveness of the various rules, allowing the program
to run through hundreds of games at various settings.

I was surprised that the games actually appeared to be quite balanced, with
each player having an equal opportunity of achieving the win.  In fact,
draws were quite rare.  Most games average around 50 turns.

And castling being often not advantageous in most 3D Chess, I expected the Zillions
program to rarely opt for this move.  With the most simple movement rules, this was
exactly the case.  But surprisingly with the more power movement rules, this option
was often exercised.  Particularly the King's side castling.

Do I think that Zillions is the final arbitrator for this form of Chessplay
within the 4x4x4 field?  Nope.  That is the purview of its players.

And do I think this is the best form of Chessplay within the 4x4x4 field?  Hopefully, 
a some may find this game enjoyable.  Both comprehensible and challenging.

If you have the Zillions program, check out their website for a copy of this implementation.