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OK, I have a new idea for a piece: A piece that does not move 90 or 45 degrees, like all the simple sliders in Chess, but a piece that can move 22.5 degrees.

This is akin to a Knightrider, but unlike a knightrider, it doesn’t hop over any squares.

A picture is worth a thousand words:

. . 1 . . . 2 . .
. . . 1 . 2 . . .
8 . . 1 . 2 . . 3
. 8 8 . 1 . 3 3 .
. . . 7 # 3 . . .
. 7 7 . 5 . 4 4 .
7 . . 6 . 5 . . 4
. . . 6 . 5 . . .
. . 6 . . . 5 . .

Or on the edge of a board:

1 . . . . . . . 2
. 1 . . . . . 2 .
. 1 . . . . . 2 .
. . 1 . . . 2 . .
. . 1 . . . 2 . .
. . . 1 . 2 . . .
8 . . 1 . 2 . . 3
. 8 8 . 1 . 3 3 .
. . . 8 # 3 . . .

This piece is in the same general class as the crooked rook, crooked bishop, rose, and other sliders that change direction as they slide: The piece goes out one square orthogonally, then turns 45 degrees to the left or right, goes out one square diagonally, then turns 45 degrees back to go outwards orthogonally again, goes one square, turns diagonally the same direction, etc.

Another way of looking at this piece is that it’s a “bent queen”, instead of going from its origin 0 degrees, 45 degrees, 90 degrees, etc., this piece goes from its origin 22.5 degrees, 67.5 degrees, 112.5 degrees, etc. Since Chess is quantized to its squares, the move is a little more awkward-looking on the grid.

There are, of course, a lot of ways of making other pieces based on this idea. There is the same piece starting with a diagonal instead of an orthogonal move, there can be versions of this piece whose rotation from the queen’s move is not 22.5 degrees, but some other rotation. We can have a “Betza Crab” version of this piece, etc. There are the forms of this piece that are “Bent rooks” or “Bent bishops” which are not left-right symmetrical. There is the possibility of combining this piece with other leapers and sliders. And so on.