Piececlopedia: Crooked Queen

Historical notes

On a 4x16 board, as in traditional Circular Chess or as in Race Chess, the Bishop seems awkward because its move is so shortened by the board.

In fact, the normal Bishop is a useful piece, but how much more pleasing it would seem to be to use instead the Crooked Bishop.

The Queen then should be a combination of Rook plus Crooked Bishop, and I shall name this piece the Crooked Queen.

Movement

The following diagram shows the movement of a Crooked Queen on an 8 x 8 board. The blue circles or +'s indicate squares moved to by Crooked Bishop moves only, the yellow circles or x's indicate squares moved to only by Rook moves, and the green circles or *'s indicate squares moved to by both kinds of moves.

  +---+---+---+---+---+---+---+---+
  |   |:::| + |:x:| + |:::|   |:::|
  +---+---+---+---+---+---+---+---+
  |:::|   |:::| * |:::|   |:::|   |
  +---+---+---+---+---+---+---+---+
  | + |:::| + |:x:| + |:::| + |:::|
  +---+---+---+---+---+---+---+---+
  |:x:| * |:x:|RzB|:x:| * |:x:| * |
  +---+---+---+---+---+---+---+---+
  | + |:::| + |:x:| + |:::| + |:::|
  +---+---+---+---+---+---+---+---+
  |:::|   |:::| * |:::|   |:::|   |
  +---+---+---+---+---+---+---+---+
  |   |:::| + |:x:| + |:::|   |:::|
  +---+---+---+---+---+---+---+---+
  |:::|   |:::| * |:::|   |:::|   |
  +---+---+---+---+---+---+---+---+

Value of the Crooked Queen

The Crooked Bishop is worth approximately the same as a Rook, but because so many of the destination squares are duplicated the Crooked Queen is not nearly worth two Rooks.

The Crooked Bishop by itself was too difficult for my mathematical skills to calculate a theoretical mobility value, so of course in due humility I decline to attempt it for the Crooked Queen; however, I will suggest a rule of thumb value: on the 8x8 board, the Crooked Queen is probably worth roughly as much as the normal Q.

On the 4x16 board, the Crooked Q is worth more than the normal Queen, I think. The narrowness of the board cuts off some of the zFF's mobility, but the Bishop suffers worse than the Crooked Bishop. RzFF may be worth RNN on the 4x16 board....

Power and Weakness of the Crooked Queen

A White RzFF at e5 and Pe2 give mate to a Black Ke3.

On the other hand, a Qe4 can threaten mate at h7 while also threatening capture on a8.

The power of the crooked Q is more concentrated, which has its advantages; but the dispersed power of the normal Q has its own advantages.

On a 4x16 board, the strength of the normal Q is cancelled.

Summary

The Crooked Queen will be mentioned in an article I intend to write soon, on the subject of 2x2x16 Race Chess. This piececyclopaedian article lays the groundwork for it.

This is an item in the Piececlopedia: an overview of different (fairy) chess pieces.

Written by Ralph Betza.

WWW page created: December 30th, 2002.

For author and/or inventor information on this item see: this item's information page.
Created on: December 30, 2002. Last modified on: December 30, 2002.