The paths d1-b2-a4-b6-d7 and d1-f2-g4-f6-d7 indicate that a Half-Rose on d1 can, so to speak, 'double-check' a King on d7. I will follow Duke in defining the Half-Rose to be a circular nightrider making from one to four leaps. On a 12x12 board this piece seems to be worth as much as a Rook, perhaps a little more than a Nightrider. [EDIT 2007] Rose Chess XII has these three pieces, with the Half-Rose definitely looking stronger than the other two.
Seven years ago I looked at the combination of Knight and (3,3) leaper, decided that it was too strange, and went on to invent the Quarter-Rose. Replacing the Queens in the standard game with this two-step leaper can lead to: 1. d1-c3 c7-c5, 2. c3-b5 mate! Black's foolish move left both c7 and d6 empty, which means that the mate cannot be blocked. Clearly this can be a dangerous piece on an 8x8 board. Looks like King, Knight, and Quarter-Rose can force mate against a lone King.
The paths d1-b2-a4-b6-d7 and d1-f2-g4-f6-d7 indicate that a Half-Rose on d1 can, so to speak, 'double-check' a King on d7. I will follow Duke in defining the Half-Rose to be a circular nightrider making from one to four leaps. On a 12x12 board this piece seems to be worth as much as a Rook, perhaps a little more than a Nightrider. [EDIT 2007] Rose Chess XII has these three pieces, with the Half-Rose definitely looking stronger than the other two.
Seven years ago I looked at the combination of Knight and (3,3) leaper, decided that it was too strange, and went on to invent the Quarter-Rose. Replacing the Queens in the standard game with this two-step leaper can lead to: 1. d1-c3 c7-c5, 2. c3-b5 mate! Black's foolish move left both c7 and d6 empty, which means that the mate cannot be blocked. Clearly this can be a dangerous piece on an 8x8 board. Looks like King, Knight, and Quarter-Rose can force mate against a lone King.