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This page is written by the game's inventor, Alberto Monteiro.

4 x 4 x 8 Tri-dimensional Chess

written by Alberto Monteiro

Origins

This game was probably developed by my cousin Silvio Levy in 1980, with whom I played some games until we decided upon a minor change. Since then, I have played it with Carlos Seiblitz and with Oscar Luiz Vieira Ferreira.

However, the advance of the game is so slow, that in the c. 20 games I played, I never gave a checkmate to anyone; all the games either finished by being suspended, or by the opponent's resignation.

The Board

The Board is composed of four 4 x 8 chessboards placed one over the other. Silvio had build a nice 3-D set once, but we usually played in common boards, imagining the 3-D display.

The initial setup is: 


     a   b   c   d     e   f   g   h     i   j   k   l     m   n   o   p    
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 8 | r | n | n | r | | b | k | q | b | | b | c | c | b | | r | n | n | r | 8   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 7 | p | p | p | p | | p | p | p | p | | p | p | p | p | | p | p | p | p | 7   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 6 |   |   |   |   | |   |   |   |   | |   |   |   |   | |   |   |   |   | 6   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 5 |   |   |   |   | |   |   |   |   | |   |   |   |   | |   |   |   |   | 5   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 4 |   |   |   |   | |   |   |   |   | |   |   |   |   | |   |   |   |   | 4   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 3 |   |   |   |   | |   |   |   |   | |   |   |   |   | |   |   |   |   | 3   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 2 | P | P | P | P | | P | P | P | P | | P | P | P | P | | P | P | P | P | 2   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
 1 | R | N | N | R | | B | K | Q | B | | B | C | C | B | | R | N | N | R | 1   
   +---+---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+     
     a   b   c   d     e   f   g   h     i   j   k   l     m   n   o   p
C = Cardinal; all other pieces have the same name as Orthochess.

The game has rotational symmetry: if the King, Queen, and the King's Pawn are coplanar, so are the King, King's Knight and King's Pawn. In other words, the game would be exactly the same if, instead of the design, above, the columns were placed in the order (a,e,i,m), (b,f,j,n), (c,g,k,o), (d,h,l,p).

If we look from the White's side, the board would look like this: 

 
    +---+---+---+---+
    | R | N | N | R |
    +---+---+---+---+
    | B | C | C | B |
    +---+---+---+---+
    | B | K | Q | B |
    +---+---+---+---+
    | R | N | N | R |
    +---+---+---+---+

Movement

In the earlier version, all Orthochess pieces would move like Orthochess, with the generic interpretation of the plane of its movement. For example, a Knight at b1 might choose to move in the (a,b,c,d) x (1-8) plane, to a3, c3 or d2; or in the (b,f,j,n) x (1-8) plane, to f3 or j2; or in the (a,b,c,d) x (b,f,j,n) plane, to h1, i1 or k1.

The exceptions were the Cardinal. (In Raumschach, or 5x5x5 Variant, this piece is the Unicorn), that would move in the long diagonals (example: a1 - f2 - k3 - p4), and the King and Queen, that would also get long-diagonal movements.

But, since the Cardinal would only control 1/4 of the squares, we decided to change the movements of the Cardinal for those of the Bishop. In this way, each one of the four bishops would control 1/4 of the squares, so that they, together, would control the whole board (it might even be possible to checkmate with K + B + B + B + B vs K).

(Afterthought: it would be more correct to change the display, replacing the B[ishop] by U[nicorn], and the C[ardinal] by B[ishop]...)

Notice that this game has potential for increasing, with some natural pieces, like two 3D Knights (1,1,2) or (1,2,2) or a 3D Pawn (fcTfmW)

Strategies

It's very hard to give checkmate to the opposite King: a King in the center of the board can move to 26 different squares! Even if the King is cornered to a1 (or d1, m1, p1, a8, etc), there would still be 7 extra squares. A checkmate with K + R vs K is impossible.

So, the winning strategy is capture the other pieces, promote pawns to Queens, and, with massive material advantage, mate the King.

Since we are bound to 2D thinking, the Bishops become very powerful pieces, as soon as they are brought to the attack. The normal way of developing them is by fianchetto: b3 - B(e1)b2 - B(b2)l4, with pressure over g5 and b6; or by the central squares: j3 - B(e1)o3 or j3 - B(e1)j2 - B(j2)m3!. The Bishops are stronger when they are in the (a), (d), (m) or (p) columns, when they have maximum range.

The Knights are also very powerful (in an unbound board, each Knight would control 3! * 2 * 2 = 24 squares), and can be coordinated to assault the opponent's weak pawns. Since the limitations of the Board restrain the diagonal movements, the slowness of the Orthoknight is not inherited to 3D: the Knight is probably much stronger then the Cardinal, the Bishop and, maybe, the Rook.

Written by Alberto Monteiro.
WWW page created: June 30, 1997.