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## Description

I had a thought about Chess on a Pillow, but decided to google it first to see if there is anyone who invented it already. Good for me I did. However, since this page deals with the board strictly in a mathematical concept, I'll write some thoughts about it as a game here.

The board is simply this, you move through the right and left edges like a cylindrical board, and like a circular board through the up and down edges.

The Knight (defined as a piece that moves one step orthogonally then one step diagonally or vice versa,) has a very very strange way of movement. Just see Figure 3 in the page to see the peculiarity of it. And I believe a King and Rook can mate a lone King on this board (because the Rook can control two files at once, unlike the cylindrical board.)

I would assume that it is impossible, or rather illegal, to move diagonally outward from a corner square. (The corner squares are e1,e8,d1,d5,a1,a8,h1,h8. Outward in this context means as south-west means to e1 in a normal board, or north-west to e8.)

The squares surrounding e1 (which is a corner square) are thus, west(w) is d1, n-w is d2, n is e2, n-e is f2, e is f1, s-e is c1, s is d1 (which is doubly adjacent,) and s-w doesn't exist. One could argue that d1 is also diagonally adjacent, but this would make the board too complicated and the bishop too powerful.

Naturally, there is no Castling; it is pointless.

My apologies for writing my own opinion where it is not supposed to be. Enjoy the paper.