Toroidal Chess

I'd heard about toroidal chess but thought such a game was rather silly because how could you practically play chess on a toroidal board. Even with magnetic pieces attached to a metallic toroidal board, playing comfortably would be almost impossible. It came as something of a revelation that this variant of chess could be played quite easily on a standard chess board.

Diagram 1

To see how, let's start with a cylinder chess which, as the name suggests, is played on a cylindrical board in which the left hand side of the board is joined to the right hand side. Here are some excerpts from what Wikipedia has this say about cylinder chess:

The game is played as if there is no edge on the side of the board. When a piece goes off the right edge of the board in cylinder chess, it reappears on the left edge; when a piece goes off the left edge, it reappears on the right edge (see Diagram 1) ... bishops are more valuable in this variant ... the game is sometimes played with changed rules for castling ... some cylinder chess problems allow moves that don't change the position (null moves). 

In Diagram 2 an example of such a problem is shown. The solution is to put Black in zugzwang by playing 1.Rh4-h4. Now, after any move by Black, White has a mate. The move 1.Rg4 doesn't work because of 1...Ka5 threatening to capture the rook on h6.

Diagram 2

It took me a while to understand what was happening in Diagram 2 but I eventually got it. Certainly it takes some getting used to. However, things getting far more difficult once the bottom of the board is joined to the top to create the torus. This also brings the White and Black back ranks up against each other, which necessitates a repositioning of the initial starting position of the pieces.

This revised starting position is shown in Diagram 3. Note that "in the starting setup, the rooks protect each other, while being threatened by the opponent's rooks. They are supported by the knights on the sides of the board, making their positions more defensible" . A reason for moving the Knight from its usual position is that if "the knight starts from its normal starting square, say g1 ... (then) moving through h1 to a1, it can then make the orthogonal move to a8, potentially taking a rook!" Further advice is to "watch out for diagonal attacks from pawns positioned on the side of the board" and to "note that the queens threaten the rooks at a1 and a8, making the rooks on that side of the board slightly less secure than the king's side rooks"(link).

Diagram 3

I should add that there is no castling and only pawns on the a, b, g, and h files can move two spaces on their first turn, and consequently, those are the only pawns that en passant can apply to. A piece cannot move eight spaces and wrap around to its starting position and be considered to have moved - all moves must change the board position. There seems to be a site where one can play toroidal chess on the Internet. I checked it out but there weren't any other online players at that time. There is another site where a wide variety of chess variants can be played, including Cylinder Chess and Fischer Random Chess but not apparently toroidal chess. The site seems to be quite active although I haven't tested it out.

I'm not all that keen to attempt to play either cylinder chess or toroidal chess. I find the conventional game demanding enough and there's something comforting about having all the action confined to the 64 checkered squares with rigid borders at the top and bottom, left and right. Once one or both of the borders are removed, the nature of the game seems to be fundamentally altered. It's interesting nonetheless and I was drawn to it via the mathematical problem of how many ways can two non-attacking amazons be placed on an n X n toroidal chess board. I wrote about this in a post to my mathematics blog titled The Mathematics of Chess.