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        riddles >> medium >> White to Play and Win (III)
        
(Message started by: THUDandBLUNDER on Oct 2nd, 2003, 2:45am)
Title: White to Play and Win (III)
Post by THUDandBLUNDER on Oct 2nd, 2003, 2:45am
This is another standard chess puzzle.
Title: Re: White to Play and Win (III)
Post by Lightboxes on Oct 2nd, 2003, 10:13am
I believe I see the solution your looking for thud:
(hint and question for Thud)
::[hide]However, the interesting thing is...if black does what you want him to do and loses fairly quickly, then why wouldn't he not take the OTHER path (white using both N and B) and let white work harder for it?[/hide]::
Title: Re: White to Play and Win (III)
Post by THUDandBLUNDER on Oct 2nd, 2003, 11:04am

Quote:
then why wouldn't he not take the OTHER path

Yes, why not - but it is still a win for White.

(By the way, can you win with B+N+K v. K in 50 moves or less?)
Title: Re: White to Play and Win (III)
Post by Mike_V on Oct 2nd, 2003, 11:56am
I don't know if this can be answered, but is there a BNKvK mate in 50 moves from ANY initial setup? I mean, assuming best stratagies, I can imagine that the black king can, in some situations, delay the mate sufficiently.

modified
and can you prove it?
Title: Re: White to Play and Win (III)
Post by wowbagger on Oct 2nd, 2003, 1:15pm

on 10/02/03 at 11:56:29, Mike_V wrote:
I don't know if this can be answered, but is there a BNKvK mate in 50 moves from ANY initial setup?

Yes, there is. A decent computer program can accomplish this. It doesn't use brute force, though (as far as I know). Or maybe this depends on the definition of "brute force".


Quote:
modified
and can you prove it?

No, I can't. Wait, I can't myself, but my computer can win it, so I could check every possible initial setup. Yes, I can. ;D


on 10/02/03 at 11:04:47, THUDandBLUNDER wrote:
(By the way, can you win with B+N+K v. K in 50 moves or less?)

Though I'm probably not the one you asked:
I haven't tried yet and I'm not confident I would succeed, even though I know the basic plan. But I know someone who can do it.
This endgame hasn't occurred in my games (or those of players from my club) anyway. ::)
Title: Re: White to Play and Win (III)
Post by towr on Oct 2nd, 2003, 2:09pm

on 10/02/03 at 13:15:57, wowbagger wrote:
Yes, there is. A decent computer program can accomplish this. It doesn't use brute force, though (as far as I know). Or maybe this depends on the definition of "brute force".

There's only 64^4 possible states and at most 30 transitions going to and from each state. So I think it'd be possible to do it brute-force. (Though it's a bit more tricky than finding the shortest path in a graph, unless the lone king has a deathwish :P)
In any case the search tree won't get wider than 64^4 at any depth, and is at most 50 moves (100 half-moves) long.
(Still, there's much smarter ways to do it, and waiting a few second is better than waiting minutes or hours)
Title: Re: White to Play and Win (III)
Post by Lightboxes' Clone on Oct 2nd, 2003, 3:15pm
Is the 50 moves vaild only from the last capture?  You could always allow black to attemp to save his pawn and trap him closer to a corner.  Unless the king goes to the middle of the board but you could kill one of his pawns at the last possible second to position your men better first.
Title: Re: White to Play and Win (III)
Post by Mike_V on Oct 2nd, 2003, 3:23pm

on 10/02/03 at 13:15:57, wowbagger wrote:
but my computer can win it, so I could check every possible initial setup. Yes, I can.


I'm not convinced. Just cause the computer can win from any given setup, doesn't mean that it's always winnable. The lone king may not have played optimally.

I believe you'd have to do it is as towr mentioned. I'd write one myself, but I'm still a little foggy on what exactly you would search as you go through the tree.
Title: Re: White to Play and Win (III)
Post by Lightboxes on Oct 2nd, 2003, 3:33pm
Well, this is what I orginally was thinking:
::
[hide]Ba6 , Kc7
Kc5 , KxN
Kd6 , Ka8
Kc7 , P moves "up"
Bb7+
[/hide]::
Title: Re: White to Play and Win (III)
Post by THUDandBLUNDER on Oct 2nd, 2003, 8:51pm
Lightboxes, in your variation Black can [hide]avoid having his king trapped by playing 2)...d6+ [/hide]


Quote:
I'm not convinced. Just cause the computer can win from any given setup, doesn't mean that it's always winnable. The lone king may not have played optimally.  

Ken Thompson, who with Dennis Ritchie created C and Unix, also developed endgame tablebases (EGTBs).
These are able to play some endgames perfectly. So far, only 3, 4, 5, and 6-man tablebases have been completed. Most of these can be downloaded free from http://www.uib.no/people/pfvaf/chesslib/Nalimov.htm and used with a compatible chess program such as Fritz.

You may find the following page interesting: http://www.xs4all.nl/~timkr/chess/perfect.htm
Title: Re: White to Play and Win (III)
Post by Lightboxes on Oct 2nd, 2003, 9:22pm
yeah, I noticed that a few hours after my post.  I came back hoping someone had the answer so I could quit without having to quit  ;D
j/k
Title: Re: White to Play and Win (III)
Post by towr on Oct 2nd, 2003, 11:37pm

on 10/02/03 at 15:23:27, Mike_V wrote:
I believe you'd have to do it is as towr mentioned. I'd write one myself, but I'm still a little foggy on what exactly you would search as you go through the tree.
The easiest way conceptually, is to just make the whole tree, and then work backwards. At each level in the tree prune away the branches which are worst for the player who's turn it is at that level. (Or, alternatively do it only for one side, so you get a roadmap that will work even if the opponent plays suboptimally. But that's not necessary for a proof that it's winnable, for that there only needs to be an endnode left at the end)
Title: Re: White to Play and Win (III)
Post by wowbagger on Oct 5th, 2003, 10:25am

on 10/02/03 at 15:23:27, Mike_V wrote:
I'm not convinced. Just cause the computer can win from any given setup, doesn't mean that it's always winnable. The lone king may not have played optimally.

In principle, you're right. My wording probably was a bit too careless. However, as a reply to the question "can you prove it?", I meant with optimal play of the defending side.
As T&B mentioned, endgames with only a few pieces left are played optimally by computers because they just look up the position instead of using brute force to find a mate in 50.
Title: Re: White to Play and Win (III)
Post by Lightboxes on Oct 6th, 2003, 1:40am
Here's the other one me and my cousin solved together.
I'll give hints for this one:
Reading hints 2 and 3 severly limits the number of moves needed and is easily solved.  Try not to look at these two if you want to solve it mainly on your own.
hint #1[hide]This one can be easily accomplished if you logically think it out.  If one unit has to die...which one HAS to die in order to leave a possible checkmate and forced moves?[/hide]::
hint #2[hide]Where does the black king HAVE to be to have a check mate with only two white units (king and an "adult" piece)?[/hide]::
hint #3[hide]What two black units HAVE to be alive to allow black to get checkmated?[/hide]::


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