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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