H. G. Muller wrote on Fri, Jun 27, 2008 01:27 PM UTC:
On a more chessic note:
Why are you saying the Falcon does not have mating potential? I ran a tablebase for the Bison (a non-lame (1,3)+(2,3) compound leaper), and the KBiK ending on 8x8 is generally won (100.00% with wtm, 80% with btm including King captures, longest mate 27 moves). I think it should make no difference that the Falcon, unlike the Bison, is lame: to block any Falcon move, at least 2 obstacles are needed, and this is very unlikely to ever occur with only two other pieces (the Kings) on the board. In the mating sequence I looked at, the Bison is mainly shutting in the bare King from open space, the attacking King closing off another direction.
I also cannot imagine that expanding the board size from 8x8 to 10x8 would make any difference. Usually it is the narrowest dimension that counts. So I really think King+Falcon vs King is a totally won end-game on 10x8, although I could not exactly say in how many moves.