Author: J. Wesley Cleveland
Date: 14:38:46 06/11/01
Go up one level in this thread
On June 10, 2001 at 05:11:51, Joachim Heuser wrote: >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. I took a quick look at kbbkn.tbs and found just over 51% draws. Assuming almost half the positions have two bishops of the same color, the winning percentage is about 95%. The other 5% may be accounted for by white having to lose or trade a bishop, so maybe it is always won if black can't quickly convert.
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