Author: Tim Foden
Date: 13:35:21 02/11/01
Go up one level in this thread
On February 11, 2001 at 10:39:26, Heiner Marxen wrote: >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. OK... you got me. =:O It could very well be possible to force the king onto a white square. >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. This seems to be the better method to follow for the proof. As Uri said in another post, the white king cannot get close enough to stop the black king moving to a black square after a check. >>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 I'm afriad I haven't been that organised with them. I just think about them as they come up in CCC or the Winboard Forum. One that I made up to test GLC's hash table and draw code was like this: [D]3k4/8/1p1p2p1/1PbP2P1/1p1p2p1/1P1P2P1/8/3K4 w Which is obviously a draw. It is also solvable by computers, but generally only after about a 30 ply search. Or this one, similar, but might be a bit more difficult for computers. [D]3k4/p1p1p1p1/P1P1P1P1/3Bb3/8/p1p1p1p1/P1P1P1P1/3K4 w Cheers, Tim.
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