Dream Chess 46

The general principle is that any square board of side x can have its squares reduced by removing from opposite corners a square block of side y, for any integer y less than x/2. This formation can also be seen of two overlapping square boards of side x-y - supersquares within the board as a whole - with the overlap a square array of side x-2y. It can quickly be proved that these definitions give the same number of squares: 2(x-y)²-(x-2y)² = 2(x²+y²-2xy)-(x²+4y²-4xy) = (2-1)x²+(2-4)y²+(4-4)xy = x²-2y². The case of x=8, y=3 gives 46 squares. I include the number 46 to distinguish from potential variants with different values of x and y - which as far as I can see give a different number of squares for each combination from x=6 (with half-size armies) to x=12 (probably with Pass-variant-style enlarged ones). However, x=13, y=5 gives 119 squares - the same as x=11, y=1.

An asymmetry between the two Bishop bindings made me ponder what to do to Bishops to unbind them. I considered but rejected the Yang Qi King swap, as using it in a variant not based on Yang Qi seemed too presumptuous. I also rejected an additional move along a single "forward" orthogonal, as the orientation does not suit such a definition of forward. Problems of defining "forward" also inspired me to replace the Pawn with something more versatile. My final decisions are covered as individual pieces.

Setup

Pieces

	The King, Queen, and Knight are the standard FIDE pieces.
	The Chatelaine is a Rook that can also make a single step along any diagonal, and the Primate is a Bishop that can also make a single step along any orthogonal. I have often used these pieces, mostly as promotees in Shogi-based variants. They can of course be represented by the physical Rooks and Bishops of a FIDE set.
	The Steward is an expansion of the Pawn to all eight radial directions. It can capture one step along any diagonal, or move without capturing one step along any orthogonal. My own first use of it is in Irwell. They can of course be represented by the physical Pawns of a FIDE set.

Rules

There is no initial double-step move, En Passant, or Castling.

A Steward reaching either far edge of the enemy supersquare may optionally be promoted to a stronger piece captured by the enemy. If there is no such piece available, or the player judges it advantageous to leave the Steward unpromoted, it continues as a Steward, which it can because it is not forward-only.

Check, Checkmate, and Stalemate are as usual.

Last revised by H. G. Muller.