This blew my mind. Very fun to play, if you like chess variants.
For the non-math geeks, toroidal chess means chess played on a torus, which is math speak for the shape of a donut. A torus is a flat surface that is connected on all four sides. Imagine a chess board (7x7 actually, in
this implementation), then bring the two opposite edges together to form a cylinder. Then bring the two ends of the cylinder together to form the torus (donut shape).
One very famous game is played on a torus: Asteroids. Remember this? When your ship flies off the left side you appear on the right, and off the bottom, to the top. So now in toroidal chess, you have a queen that can fly around pieces in the center of the board by going in the opposite direction, across the edges, which are actually meaningless. There are no edges in toroidal chess.
The pieces move almost the same as in normal chess, except for the pawns. With no edges, there is no pawn promotion, of course. And with no edges there is also no strict idea of direction either. So pawns can move 1 square immediately adjacent to it in any "direction", and capture to any square diagonally adjacent to it.
Visualizing this is somewhat difficult. You have two options to choose from: the fundamental domain and the tiling option. Tiling makes it look like there is more material on the board than there really is. It's just an option to make the different directions of attack more noticeable.
The fundamental domain. Note that the white queen and bishop both attack each of black's pawns.
Tiled, clearly seeing the many ways white can attack black.
Tiled, seeing the many ways black can attack white.
Imagine a king that you have to checkmate, but without a corner to do it in. Imagine a king that you must defend from every angle, not just one or two. This is is toroidal chess. We have 9 pieces: a king, a queen, two rooks, two pawns, two knights and a bishop. I haven't figured out why two bishops weren't included, perhaps because nine pieces fit nicely together. But why 2 knights? I'd rather substitute a knight for the other color bishop.
What is apparent is that you need more material to checkmate a king in toroidal chess. I haven't worked out the exact minimum. But king+queen vs king is not enough. I can imagine KQNvK working, but how do you force such a mating position? I checkmated the computer using a Queen and a rook in a game I just played:
Checkmate!
