Author: Joachim Heuser
Date: 02:11:51 06/10/01
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On June 09, 2001 at 17:23:56, Robert Hyatt wrote: >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... Hmm, well, i'll go for it in my next vacation ;-) I looked at the kbbkn.tbs file - i cannot explain the contradiction between the rate draws/wins and my statement above. With approx. 60% draws due to "wrong" bishops it's still only a 6:5 win/draw-rate. I tried to reach a drawn position from a won position by choosing bad moves for the bishops. I came down to approx. 75 moves mating distance. In this region i looked for white moves only to draw - every move lost or traded one bishop. I'm at a loss. Isn't there a program by Nalimov which creates statistics about each tablebase-file? Joachim
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