H. G. Muller wrote on Tue, Jul 15, 2008 02:04 PM UTC:
The Buffalo is upward compatible with the Bison, and adds the Knight moves
to it. Although this does not endow it with more speed, it helps
tremendously in accelerating the checkmating of a bare King. The long
stride of the Bison makes for very awkward manouevring. The Bison mates
are very tedious, the average mate is only some 10 moves shorter than the
longest mate. On 14x14, of the 18.5M positions (with the white King in a
given quadrant), only some 100,000 have a DTM < 60. After that it
explodes, the most common DTM shared by 203,408 positions being 73.
Apparently there is a very easy initial phase, probably just walking the
winning King to the center, driving away the bare King from there with the
aid of the Bison. But after that, a very painstaking drive towards the
corner starts, in which the Bison can only barely prevent that the bare
King nescapes back into the open.
The extra Knight move of the Buffalo allows you to cutt off the bare King
much more efficiently:
8x8 10x10 12x12 14x14 16x16
Bison: (CZ) 27 40 55 82 -
Buffalo: (CNZ) 18 24 31 38 45
The remaing Camel/Knight/Zebra compound, the GNU or Wildebeest (NZ), has
no mating potential. There are only 2 irreducible checkmate positions, and
they cannot be enforced on any size board. Similar to KNNK, the bare King
would voluntarily have to step into a mated-in-1 position.
For the Griffon no computer is needed to give the proof. The system is
similar to the Rook, and works even in the corner of an infinite board.
(So certainly for boards of any size.) It is even easier, because the
Griffon immediately traps the bare King in a corner, without the latter
being able to attack it, like it could do for a Rook.
In fact, with the Griffon there is even a much faster method than with the Rook, as a Griffon can trap the bare King in a narrow corridor, its own King acting as a piston to push the bare King to the edge.
The Buffalo is upward compatible with the Bison, and adds the Knight moves to it. Although this does not endow it with more speed, it helps tremendously in accelerating the checkmating of a bare King. The long stride of the Bison makes for very awkward manouevring. The Bison mates are very tedious, the average mate is only some 10 moves shorter than the longest mate. On 14x14, of the 18.5M positions (with the white King in a given quadrant), only some 100,000 have a DTM < 60. After that it explodes, the most common DTM shared by 203,408 positions being 73. Apparently there is a very easy initial phase, probably just walking the winning King to the center, driving away the bare King from there with the aid of the Bison. But after that, a very painstaking drive towards the corner starts, in which the Bison can only barely prevent that the bare King nescapes back into the open. The extra Knight move of the Buffalo allows you to cutt off the bare King much more efficiently: 8x8 10x10 12x12 14x14 16x16 Bison: (CZ) 27 40 55 82 - Buffalo: (CNZ) 18 24 31 38 45 The remaing Camel/Knight/Zebra compound, the GNU or Wildebeest (NZ), has no mating potential. There are only 2 irreducible checkmate positions, and they cannot be enforced on any size board. Similar to KNNK, the bare King would voluntarily have to step into a mated-in-1 position. For the Griffon no computer is needed to give the proof. The system is similar to the Rook, and works even in the corner of an infinite board. (So certainly for boards of any size.) It is even easier, because the Griffon immediately traps the bare King in a corner, without the latter being able to attack it, like it could do for a Rook. In fact, with the Griffon there is even a much faster method than with the Rook, as a Griffon can trap the bare King in a narrow corridor, its own King acting as a piston to push the bare King to the edge.