The Chess Variant Pages

Check out Marseillais Chess, our featured variant for February, 2024.

This page is written by both of the game's inventors, Ernst Saperow and Anatoly Khalfine.

Toroidal Byzantine Chess


Toroidal Byzantine Chess is a new chess variant derived from the Byzantine Chess (a historic version popular in late Constantinople).
The chess variant which came in Europe from the Arabic countries was Shatranj.
It differs  from the modern chess only by the functions of pieces.
In Byzantium of 1000 A.D. it was played on a circular board instead of a standard square 8x8.
This variant called as Byzantine Chess  is now reconstructed in the form of Circular Chess.

The Torus Chess  and Chess in a Toroidal Board  may serve a hint for playing Byzantine Chess on the torus shaped board.
As soon the edges of the circular board are joined a torus is constructed.
(The rules remain the same, only the geometry is changed).

Thus, the new variant is obtained and the name Toroidal Byzantine Chess  expresses its idea.

Perhaps, the Byzantine Chess on the toroidal board has been experienced in Constantinople,
recently (1999-2001) it was considered by several mathematicians (among whom the present authors).

On account of exotic geometry this variant belongs better to the scope of mathematics rather than sport or game.
But for playing for joy it is suited well. 


The initial setup is the same as in Byzantine Chess.
It is also convenient to imagine the circular board in the rectangular development  which is used for the Java  and Zillions-of-Games  computer programs playing Byzantine Chess and Toroidal Byzantine Chess. 

Rules and Pieces

Although the pieces obey the Byzantine Chess rules,  the toroidal geometry sets additional details.
Usually, the transition from the suqare board to the circular and toroidal board provides additional mobility to the pieces.
The table of pieces values shows this process.

The nominal strength of Bishops and Rooks does not depend on the changes of geometry.
But a Rook on the toroidal board has circular motion either over the long 16-cell circle (as on the circular board) or over the short 4-cell circle:



The essential changes concern the Knights and Queens.
There are no edges on the toroidal board and both figures feel themselves quite well everywhere, while on the circular board their abilities are restricted at the edges.

On the torus shaped board all 6 squares are always available for the Knight



and the Queen has all 4 squares


Playing Tips

The toroidal geometry increases the activity of the major pieces (Rooks and Knights) providing additional opportunities for tactics.

Perhaps, the most exotic is the Rook rotation along and across and
the Pawns phalanx with no edges at all (now the a-h pawns have two neighbors). .

Computer Play

If you have Zillions of Games installed on your computer, you can play this game

Sample Game

Let us ilustrate the role of toroidal geometry on a the particular example.
On the following diagram

Black has material advantage (the Knight for 2 Pawns) but position of his King is dangerous.

1. e6xh7++ (capturing across the glued edges) Ke8-f7 (the only move)
2. Rd1-e7+ Kf7-g6 (2. ...  Kf7 x f6  changes nothing)
3. Rh1-e1   Bh6  (3. ... g5 x f4  is followed by 4. Re1-e6+)
4. Rg7+   Kxf6 (the only move)
5. Rg7-e7  g5xf4 (this prevents 6. Re1-e6#)
6. Re1-e6+  Kf6-g5
7. Re7-g7+  Kg5-h4 (the only move)
8. Re6-e4# (the Rook strikes from e4 on h4 since the edges are glued)


To contact the authors (Anatoly Khalfine and Ernst Saperow), please email the authors at the email address you obtain by following this link.
Written by Anatoly Khalfine and Ernst Saperow 
WWW page created: January 28, 2002. Modified: November 13, 2002.