Author: Robert Hyatt
Date: 14:23:56 06/09/01
Go up one level in this thread
On June 09, 2001 at 14:38:04, Joachim Heuser wrote: >On June 09, 2001 at 11:32:09, Robert Hyatt wrote: > >>On June 09, 2001 at 04:37:32, Joachim Heuser wrote: >> >>>On June 08, 2001 at 22:11:56, Jim Monaghan wrote: >>> > >>>I am quite sure that nearly every position from KBBKN is won for the two >>>bishops. >> >>Sorry, but you are quite wrong. Go to my ftp site, cd to the TB/tbs >>directory, and download kbbkn*tbs and take a look. More draws than >>wins. >> > >What i meant was: from nearly every position, where the two bishops are on >different colours and the knight cannot capture one of those bishops in the next >move, the two bishops can force mate or winning the knight, though this may take >more than 50 moves. >I set up some rather ugly positions with the two bishops not working together >and it took ~40-50 moves (according to cb-tablebases) to capture the knight. > >In the book german book from Kishon: "Schachcomputer" (1993), the author claims >that the machine "Alice" analysed this endgame to be always won (he doesn't >state when this analysis took place). There was a position, too, which should >take longest to capture the knight (66 moves): >K7/8/7B/8/8/5k2/6n1/7B w - - 0 1 >wKa8,Bh1,h6/bKf3,Ng2 > >I wasn't able to create a drawn position which matches the pattern mentioned >above. I haven't tried this, but the simple way to estimate how many wins vs draws there are in KBB vs KN is a Monte Carlo approach. Generate quite a few random positions with bishops on opposite colors, and probe to see if it is won or drawn. A few thousand should give an accurate percentage of what percentage is drawn vs won...
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