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Bison. Makes (1-3)-jump or (2-3)-jump.[All Comments] [Add Comment or Rating]

H. G. Muller wrote on Wed, Jul 9, 2008 08:09 AM UTC:

'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)       '