Author: Heiner Marxen
Date: 07:39:26 02/11/01
Go up one level in this thread
On February 11, 2001 at 08:33:11, Tim Foden wrote: >On February 11, 2001 at 00:29:23, Uri Blass wrote: > >>On February 10, 2001 at 16:26:39, Pete Galati wrote: >> >>>This is another position that crashes Crafty, so I assume that the Chessbase >>>interfaces probably won't like it either. >> >>The chessbase interface have different rules then crafty. >> >>It does not like positions when >>max(number of white bishops-2,0)+max(number of white knights-2,0)+max(number of >>white rooks-2,0)+max(number of white queens-1,0)+number of white pawns>8 >> >>It also does not like cases when it is truth for black and does not like >>positions with more or less than one king for one of the sides >>It does not like positions when the side to move threats check >>or positions when there are pawns in the 1st or 8th rank. >> >>There is no problem with other positions including this position that is >>illegal: >> >>[D]B1Bk4/1B6/B1B5/3B4/4B3/5B2/6B1/4K2B w - - 0 1 >> >>It is interesting to know how much time do your program need to see the draw(if >>your program does not accept the position then you may remove one bishop from >>the board). > >I think most (if not all) programs will have a very hard time solving this >position. GreenLight did the same as Crafty in Pete's reply, but I was not at >all surprised. > >>Can chest prove that there is no mate when the number of moves is not important? > >I don't think so, but I'm not sure. Normally not. Sometimes this (no mote) is obvious, and coded as "there is no mate in 63". >>I have no problem to prove it. >>Uri > >I agree. Neither do I. So the questions are: > >1. What exactly do we do when we solve it? >2. How can we get a computer to do the same? > >In answer to (1.), my proof was: >In order to checkmate a king, you must be able to check him. Only the bishops >can check the black king. The bishops are all on the white squares, so the king >can always avoid check by not moving onto any white square, or be stalemated. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ You have not yet proven this. The obvious part is: If there is a dark square legally reachable, there is no mate in the next move. Also: if there is no square at all reachable, there is no mate next, since it is stalemate. But what, if the king is forced to enter a light square by zugzwang? And such positions _can_ appear with this setup (in the corner). I just want to point out, that such a proof is not trivial to construct. Whe we humans think of such a proof more often than not the proof is not complete (although the result is mostly correct). >Therefore the position is draw. > >There are also other ways to prove this I think. e.g. You could prove that if >the king is in check, he will always be able to get out of it. > >For (2.) though, I haven't a clue! (Yet ;-) > >I think this is an interesting area really, as I have been giving thought to >quite a few of these - easy for humans/hard for computers - positions. > >Cheers, Tim. Together with commentary what makes them so easy/hard that would make a great reading for me. I find this very interesting, too. I would like to teach Chest to recognize some sorts of "this side cannot loose" proofs. Heiner
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