The other day I was wasting time by playing Grandest Fleet, an ancient computer game which still ranks as one of the best such games ever. I marveled at how I was still able to enjoy it even after having played it thousands of times; for though it is clearly not so deep as Chess, at least when one gets tired of playing on one map one can choose a different map.
How sad it is, I thought, that in Chess we play always on the same map; and a bare nanosecond later I had conceived of Shifted Square Chess.
Actually, Shifted Square Chess is any form of Chess played on a Shifted Square Board. Well, almost any form of Chess. Cylindrical Chess does not work well with the Shifted Square.
8 . * . * . * . * 7 * . * . * . * . 6 . * . * . * . * 5 Z A A A A A A A A Z 4 Z A A A A A A A A Z 3 * . * . * . * . 2 . * . * . * . * 1 * . * . * . * . x a b c d e f g h zThe square can be removed from anywhere in the area marked A, and added anywhere in the area marked Z.
8 . * . * . * . * 7 * . * . * . * . 6 . * . * . * . * 5 . * . * . * . * . 4 . * . * @ * . * 3 * . * . * . * . 2 . * . * . * . * 1 * . * . * . * . x a b c d e f g h zThe square e4, marked with an @, is not a square at all. It is a hole in the board.
Therefore, a Pawn at x5 cannot advance except by capturing onto a6. This ruling follows the lead of F. V. Morley, whose book "My One Contribution to Chess" should be read by everybody.
The relevant text, on page 90, reads
After 1. e4 e6 2. d4 d5 3. Nc3 Nf6, the move e4-e5 is not legal, and Black equalizes.
On the other hand, a hole at e6 would surely oppress Black, and that is why the zone marked A is so restricted.
8 . * . * . * . * 7 * . * . * . * . 6 X B B B B B B B B X 5 Z A A A A A A A A Z 4 Z A A A A A A A A Z 3 X B B B B B B B B X 2 . * . * . * . * 1 * . * . * . * . x a b c d e f g h zTo create a Double Symmetrical Shifted Square Board, first take away one square from A or B, then replace it in X or Z, then take and replace symmetrically.
"Symmetrically" means that if e3 is taken away and replaced by z4, then d6 must be taken away and replaced by x5. The point is that the symmetry guarantees fairness and therefore allows a wider taking zone.
A full discussion of Tirebiter Shifted Square Chess, and of even stranger developments of the same idea, can be expected in the near future.