Corresponding squares

Does anyone know how to use corresponding squares and can explain it?  I have not seen any useful explanation anywhere.  For example, the wikipedia page gives a bunch of examples with the square numbers already filled in, with no explanation of how to actually fill in the numbers.

How do you actually fill in the numbers?

Here is an example position where I believe corresponding squares could be used, but I don't know how.  The solution is very difficult without corresponding squares.

Thanks a bunch!

Hi Berder.  In this type of Endgame there is always a file where is necessary to win the opposition.  I know that because I am studying Dvoretsky's Endgame Manual.  It is no use to win the opposition on the e-file because black pawn is attacking e5 and you can not make it to that square.  So the opposition has to be won on the f-file instead.  This leads to 1.Kg2 and depending on where black goes then you gain opposition; 1...Kf6 2. Kf2 winning opposition to later on outflank.

Thanks for that insight.  That's interesting but it's not the whole problem because after white wins the opposition on the f file, he can't break through on the kingside.  He has to switch over to the queenside:

I think corresponding squares could be used to analyze this completely, start to finish.

Hi Berder.  I am not an expert that is for sure but I am learning quite a lot with Dvoretsky's book.  There might be some solution on the queenside as you mention, that I do not know.  White wins by outflanking on the f-file.  No need to go to queenside.  You gain opposition on f-file then black will be on zungswang (not sure the spelling) and black pawn is lost.  On your example,  1. Kg2 Kf6 the correct second move is 2.Kg3 not 2.Kf2.  Sorry about that suggestion of mine, my mistake.  Also keep in mind that black king can not leave his pawn, it must defend it.  Cheers.

My line was taken from the Nalimov databases so it is correct.  After 2. Kg3, it's a draw because of 2. ... Ke5 taking the c pawn.

Yes.  2.Kg3 it is a draw, you are right I am wrong.  I guess maybe the solution to 1..Kf6 must take the Kings to queenside.  Dvoretsky's analysis does 1..Kf7 with the result I told you about without going to queenside.  Maybe that is what is going on; one moves keeps you on kingside the other takes you to queenside, same result though, white wins, pretty cool.  Thanks for the post was nice to discuss.

that one is a famous position. The solution is Kg1! that is the only move that wins for white.

4 other move "loses" (in the sense that black can force the draw), 1 other move allow to repeat the position.

I've seen a position about corresponding square that was much, much more complicated than that one. I found it somewhere in the chess mentor and it blew my mind. If you're interested I can try to find it a post it.

In the one above, it's not hard for black to play: the way I understand it is that if the white K is on e4 you cannot have the opposition there (because the e6 square is taken away from you). But you can simply keeping him out if you have the opposition at the right moment. The way I learned is: the 5th rank if your strongest rank and it's there that you have to hold your blockade.

Tantale posted a few topics on this, mostly over my head, I'm afraid.

Here's one:

http://www.chess.com/forum/view/general/only-one-winning-move

And here is another.  Welcome to the frustrated club 

http://www.chess.com/forum/view/general/corresponding-squares-is-it-hard

JamesColeman

I don't have the slightest knowledge on the subject but, reading your post, I wonder whether would be possible learn something from the position, in the old-fashioned way, without making use of the theory of the corresponding squares.

Ive read several endgame books on the subject.

Corresponding squares are ones which the defender's king must be on when the attacker's king is on another. For example, in that diagram, Black's king would have to be on e7 when White's is on e4, to make sure it can get to both sides in time to prevent an outflanking. From that, you can figure out more squares that Black's king has to be on when White's king is on a particular square. And then, the attacker will win by going on the corresponding square to the one Black is on, forcing Black to move off that corresponding square. Basically, on the attacker's turn, the defender's king and attacker's king have to be on the same square to make the defence work.

If you want to know more about it, you should get Dvoretsky's Endgame Manual. It's a great book on endings.

I think the corresponding squares in your diagram are: e4 e7, f5 f7, g5 g7, h5 f7, f4 f6, g4 g6, h4 f6, d4 d7, d3 d8, h6 f6, h7 f7, etc.

Note that although Black uses the f7-square as a corresponding square to f5, h7, and h5, White cannot exploit that because he cannot get to one of those  squares from another of those squares in 1 move.\

Was that helpful?

JamesColeman
Would the following be reasonable?
1) It's quite natural that the ultimate upshot be staged on the queenside, since there the white king can cooperate with his extra pawn on c4 and, besides, the black king has less space to maneuvering.
2) The black king is commited to fight against his outflanking on the kingside, otherwise his pawn will be eventually lost.
3) In the course of such fight on the kingside, as can be learnt from berder's post of the solution, at the sixth move, when the white king is on f4, the black king must go to g6 to prevent the intrusion of the white king.
4) Now, if we come back to the starting position, and count the moves from f1 (where the white king is), needed to reach b4, we find 4. Also from that same starting position, the black king needs equally four moves to reach b6 (starting from e7) and, which is still better, grabbing the opposition.
5) From the situation created after the sixth moves, if we count the needed moves for the white king to reach b4, they will be still four moves but, now, to the black king come to b6 will be needed 5 moves. So, the diversion maneuvers of threatening outflank the black king on the kingside have gained, to white, one tempo. Now, when the white king reaches b4,  the black king will be just arriving at c7. Then, moving to a5, the white king grabs the diagonal opposition and the remaing is straight forward.
6) Finally, it seemed, at least to me, a nice problem but, if one is forced to make use of the theory of the corresponding squares, it may easily escape to our reach, which turns out to be simply one more loss to us, simple mortals.

Actually Berder, I'm pretty sure after 2.Kg3 Black wins, because he controls the key squares in front of the d-pawn.

What I mean is that, in the particular example, we could still face things not as a question of correspondence of squares, but as the usage of means to push away the opponent's king from the squares of invasion. It wouldn't be a question of being in the wrong place at the wrong moment, but of being pushed too far away to come back just in time.

Dvoretesky's Endgame Manual on this postition:

"Taking the distant opposition with Ke1? leads only to a draw. The opposition on the e-file is meaningless, Ke1 Ke8!... etc.

And if the White king leaves the e-file, his opponent will take the opposition forever, Kf2 Kf8!, etc.

In such situations there is usually a major line, where it is important to capture to opposition. And when the opposing king retreats from it, you must outflank it, etc." Here, thats the f-file.

So, Dvoretsky goes on to explain that Kg2 wins because White will eventually capture the opposition, e.g. Ke8 Kg4! Ke7 Kg5!

I agree with JamesColeman. It seems the corresponding squares can only be determined after calculating, at least in any position with at least a moderate amount of complexity. So if you have already gone through the calculations, trying to remember the corresponding squares would only serve as a distraction. At least OTB.

My guess is that the theory was developed as a useful tool to help analyze  adjourned games (in the days before computers and tablebases), as well as study problems. If a player or his second kept coming back to a particular pawn endgame in his analysis, it would be simpler to just record and then refer to the corresponding squares rather than a fifteen move variation and all its subvariations.