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H.G. Muller, This is not a bison question, but do you have a ubuntu version of Joker?, although it is apparently working under wine.
'On 2008-07-06 H. G. Muller concluded that King and Bison can force checkmate on boards as large as 12x12. ' That was actually even 14x14. King + Bison vs Kings is absolutely won on 14x14 and smaller, with white to move. (i.e. not a single draw position.) The Bison cannot be trapped in a corner; its large stride simply makes it leap out of trouble. In addition there are no corner stalemates (such as in KNK: k N . . . . ), because a Bison can alway check the square . . . . . next to it in 1 move. K . . . . . . . . . The longest mates (against perfect defense) are: BOARD MOVES (K,Bi,k) 16x16: 76 (a4,b7,b1) (but 90% of all wtm positions are draw) 14x14: 82 (a1,n14,c3) (100% won) 12x12: 55 (a1,L12,c3) ' 10x10: 40 (a1,j10,c3) ' 8x8: 27 (a2,b2,b4) '
On 2008-07-06 H. G. Muller concluded that King and Bison can force checkmate on boards as large as 12x12. I once thought about using Bisons, but later changed my mind. Back in February, 2000 Sergey Sirotkin used both Bisons and Camels in his 7x7 chess variant HERD.
The Bison definitely has mating potential on an 8x8 board. Denoting Bison by Y: I have built a tablebase for the KYK end-game, and it is 100% won for white to move. (With black to move there are of course positions where the bare King captures an undefended Bison on the first move, and these are then draw.) Longest mate against best defense takes 27 moves. I cannot build tablebases on other boards yet, but I adapted Joker80 so it would move Knights like Bisons. If I let it think a few min/move it does find mate in 20 or so in all psositions where the bare King is not too well centralized (and the white King is). As it is rather easy to drive the bare K out of he center with K+Y, this makes it likely that KYK is also won on 10x8. If I give the winning side a time-odds handicap of a factor 100, (40/60 vs 40/0:36) so it searches only 9-12 ply, where the defending King searches 22-28 ply, the bare King starting from w:Ke1,Yg1 b:Ke8 gets menouevred into mated-in-31 position quite rapidly (without the K+Y side knowing yet), after which it sees the mating net being tightened until the winning side finally gets a mate-in-12 within its horizon. I couldn't say anything about 12x12. Note that the Bison is equivalent to the patented Falcon in these games, as there is not enough material on the board to block the Falcon moves.
Bison moves h7-e6-g3-d4-c1-f2-c4 to force mate in six in this position: White King (b3), White Bison (h7), Black King (b1). The Black King has very little freedom - it must alternate between (b1) and an adjacent square. I could use an answer to the following question. In general, can the Bison force a lone King into a corner (and checkmate) on a 12x12 board? [EDIT] For a positive answer, check out some comments made in July 2008.
WHITE MATES IN SIX
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