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Robin Smith

Joined: 08 Mar 2006
Posts: 2307
Location: Brownsville Texas USA

Post subject: Re: Is this positions drawn ??    Posted: Sat May 19, 2007 4:00 am

Uri Blass wrote:
smirobth wrote:
Uri Blass wrote:
Terry McCracken wrote:
 Tobias Lagemann wrote: Hi, the position is a typical fortress (and draw). Topalov and Mamedyrov know this, engines don't. Tobias

Indeed, it's a trivial draw.

Terry

I believe it is a draw but in order to prove that it is a draw you need to tell me a strategy for black were to put the king and rook against every possibility of squares for white king and queen.

Without it I cannot be sure that white cannot force black into a zugzwang and win the rook by a fork.

Uri

Hi Uri,
It seems pretty trivial to me:
1) The rook just stays on f6 while Black's king moves around the squares g8-h8-h7. If the queen is on the eight rank, so that king moves are impossible, the rook can leave f6 to any one of many squares (for example on f2 the rook and king cannot ever be forked, and if the queen is on the 8th rank it cannot also hit the f2 square) and then move back to f6 next turn. There would also be squares on the 6th rank for the rook, if White's king were to guard the f2 square. With so many good potential squares for the rook and king zugzwang will not ever become a factor.
2) Even if you remove Black's h-pawn (a change which can't possibly help Black in this case) tablebases prove the position is still a draw.

1)It is correct that the queen cannot hit the f2 square but queen e8 king e3 may force the rook to go f6-f1 assuming that black keep the rook at the f file.

After that white can make some checks.
It is correct that I do not see checks that lead to fork but it is not a proof that there are not checks that lead to fork in another line.

2)removing black's h pawn can give the rook the square h6 so I am not sure that it cannot help black.

I strongly believe that it is a draw but I am careful not to say that I saw a proof that it is a draw.

Hi Uri,

Here is a pretty simple algorithm for generating Black's moves that I think will make the draw 100.0% clear, and perhaps would satisfy you as a proof. I mentioned this same idea before, but perhaps if I make my explanation more rigorous it will help. Black can play the first move that meets a listed criterion:

1) If the queen can be captured, capture it.
2) If the king is in check, move out of check to any one of the squares g7, g8, h8.
3) If the rook is not on f6, move it to f6.
4) If the rook is already on f6 and it is possible to leave it there, shuffle the king around on squares g8-h8-h7.
5) If the queen is on the 8th rank so that king moves are not possible, move the rook to f2, unless f2 is guarded by White's king.
6) If king moves are impossible and f2 is guarded by White's king, move the rook to any of the 6th rank squares a6, b6, or c6 that is a) not controlled by White's queen, and b) cannot be attacked in a way that forks the rook and king. Note that a fork of the rook on a6 and king on h7 can only happen from d3, that a fork of a rook on b6 and king on h7 is not possible, and that a fork of a rook on c6 and king on h7 can only happen from e4. There is no square on the 8th rank from which the queen can move to both d3 and e4 (nor can the queen ever fork the king and rook if the rook is on b6) therefore at least one of the squares a6, b6 and c6 will always be safe if the queen is on the 8th rank and White's king is guarding f2. A queen on the 8th rank can only control 2 of these 3 squares, at least one will always be safe, and if the White king is guarding f2 it cannot also guard a6, b6 or c6 at the same time.

QED
_________________
- Robin Smith
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
Subject Author Date/Time
M ANSARI Fri May 18, 2007 8:15 pm
Tobias Lagemann Fri May 18, 2007 8:53 pm
Terry McCracken Fri May 18, 2007 9:01 pm
Uri Blass Fri May 18, 2007 9:17 pm
Robin Smith Fri May 18, 2007 9:35 pm
Alex Brown Fri May 18, 2007 9:47 pm
Uri Blass Fri May 18, 2007 10:29 pm
Torstein Wed May 23, 2007 12:33 pm
Paulo Soares Fri May 18, 2007 10:18 pm
nuff Fri May 18, 2007 10:27 pm
Paulo Soares Fri May 18, 2007 10:34 pm
Uri Blass Fri May 18, 2007 10:39 pm
Terry McCracken Fri May 18, 2007 10:53 pm
Dann Corbit Sat May 19, 2007 12:27 am
Terry McCracken Sat May 19, 2007 4:57 am
Dann Corbit Sat May 19, 2007 6:13 am
Terry McCracken Sat May 19, 2007 4:14 pm
George Tsavdaris Sat May 19, 2007 4:52 pm
Terry McCracken Sat May 19, 2007 6:15 pm
George Tsavdaris Sat May 19, 2007 6:20 pm
Terry McCracken Sat May 19, 2007 7:43 pm
Uri Blass Sat May 19, 2007 6:31 pm
Terry McCracken Sat May 19, 2007 7:39 pm
Alessandro Scotti Sat May 19, 2007 9:10 pm
Terry McCracken Sun May 20, 2007 3:27 am
Dann Corbit Wed May 23, 2007 4:17 am
M ANSARI Wed May 23, 2007 6:53 am
George Tsavdaris Wed May 23, 2007 4:19 pm
Dann Corbit Wed May 23, 2007 6:19 pm
Uri Blass Fri May 18, 2007 10:36 pm
nuff Fri May 18, 2007 10:41 pm
Uri Blass Fri May 18, 2007 11:50 pm
Graham Banks Fri May 18, 2007 11:59 pm
Uri Blass Sat May 19, 2007 12:03 am
Graham Banks Sat May 19, 2007 12:13 am
Re: Is this positions drawn ?? Robin Smith Sat May 19, 2007 4:00 am
Uri Blass Sat May 19, 2007 6:14 am
Terry McCracken Sat May 19, 2007 4:17 pm
Uri Blass Sat May 19, 2007 5:13 pm
Terry McCracken Sat May 19, 2007 6:09 pm
Dann Corbit Mon May 21, 2007 9:51 pm
Robin Smith Tue May 22, 2007 3:15 am
Dann Corbit Tue May 22, 2007 4:02 am
Terry McCracken Tue May 22, 2007 4:20 am
Robin Smith Tue May 22, 2007 10:24 pm
Terry McCracken Tue May 22, 2007 4:29 am
Dann Corbit Wed May 23, 2007 11:42 pm
J. Prata Thu May 24, 2007 12:19 am
Dann Corbit Thu May 24, 2007 12:42 am
Robin Smith Thu May 24, 2007 1:20 am
Terry McCracken Thu May 24, 2007 2:29 am
Robin Smith Thu May 24, 2007 3:21 am
Terry McCracken Thu May 24, 2007 4:29 am
Uri Blass Thu May 24, 2007 7:20 am
Terry McCracken Thu May 24, 2007 2:25 am
glorfindel Fri May 25, 2007 1:38 am
Terry McCracken Fri May 25, 2007 2:11 am
glorfindel Fri May 25, 2007 3:04 pm
Terry McCracken Fri May 25, 2007 5:04 pm
Robin Smith Fri May 25, 2007 2:35 am
glorfindel Fri May 25, 2007 3:25 pm
Richard Sutherland Fri May 25, 2007 3:50 pm
Terry McCracken Fri May 25, 2007 4:09 pm
Robin Smith Fri May 25, 2007 4:50 pm
Terry McCracken Fri May 25, 2007 5:05 pm
Dann Corbit Fri May 25, 2007 2:23 am
Terry McCracken Tue May 22, 2007 4:19 am
Dann Corbit Wed May 23, 2007 10:56 pm
Paulo Soares Fri May 18, 2007 10:15 pm
Uri Blass Fri May 18, 2007 10:26 pm
Paulo Soares Fri May 18, 2007 10:58 pm
Uri Blass Sat May 19, 2007 12:01 am
Paulo Soares Sat May 19, 2007 12:24 am
Daniel Mehrmann Wed May 23, 2007 11:40 pm

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