- 03 Apr '08 22:45Corresponding squares is the most difficult thing I've ever studied about chess. Mined squares is a part of it. The best and only book I've found dedicated to it is THE FINAL COUNTDOWN by Willem Hajenius & Herman Van Riemsdijk. I can not pretend to understand it yet.

The best way I can explain it is that our basic understanding of opposition is like Euclidean geometry where everything works on squares, rectangles, triangles, and straight lines. However, pawn structure can distort this relationship creating a curviture of space on the chessboard, more like non-Euclidean geometry where straight lines no longer exist and relatinships become very complex.

I've never used corresponding squares in one of my games; I'm sure I've had the opportunity, but it's kind of like learning a new word. You think you've never heard it before then you hear it a dozen times before the day is gone. - 04 Apr '08 00:19 / 1 edit

Sorry if I'm missing something completely obvious, but what can white play after 1. ...Kb4 to stop Kc3 winning the pawn?*Originally posted by Kepler***Not so sure that was a joke. He is correct, the side on move loses!**

Edit: Eh, nevermind. Black wins the pawn, but not the game. - 04 Apr '08 19:50 / 2 editsI was unfamiliar with the term "mined squares", but was familiar with the concept. I think the term is derived from "land mine", where you want your opponent to step onto the "mined square" before you do. Here's the position discussed in the blog (I'll undoubtedly need a few edits to get the FEN right):

after the correct 1... Kb4, if White follows suit with 2. Kf5, then Black wins with 2... Kc3 3. Ke5 (stepping on the mined square first) Kc4 etc.

Correct play is therefore 1... Kb4 2. Kf3 Kc3 3. Ke2 Kxd4 4. Kd2 and drawn. Note that if Black plays the tricky 3...Kc4, White should respond with 4. Kd1, as 4. Kd2 loses to 4... Kxd4. I suppose by that definition, that d2 and d4 are also "mined squares". - 04 Apr '08 20:38

So i understand mined squares they're simple. Triangulation and Corresponding squares is a bit more difficult, I don't understand how to find which squares are targets using this technique. I'm only able to find them by thinking through variations, is their a technique to discover which squares are going to be "mined" in more complex situations than 1/2 pawns?*Originally posted by petrovitch***Corresponding squares is the most difficult thing I've ever studied about chess. Mined squares is a part of it. The best and only book I've found dedicated to it is THE FINAL COUNTDOWN by Willem Hajenius & Herman Van Riemsdijk. I can not pretend to understand it yet.**

The best way I can explain it is that our basic understanding of opposition is li ...[text shortened]... think you've never heard it before then you hear it a dozen times before the day is gone.

Seems like the difficult part is in fact discovery, not usage. - 04 Apr '08 21:10

There is some discussion at*Originally posted by Adorea***So i understand mined squares they're simple. Triangulation and Corresponding squares is a bit more difficult, I don't understand how to find which squares are targets using this technique. I'm only able to find them by thinking through variations, is their a technique to discover which squares are going to be "mined" in more complex situations than 1/2 pawns?**

Seems like the difficult part is in fact discovery, not usage.

http://www.chessvideos.tv/forum/viewtopic.php?f=16&t=1458

Search for Corresponding Squares. The authors of THE FINAL COUNTDOWN really show you how to mathematically prove the solution to triangulation.

It's so hard that I've avoided it for the past few months. I just need time to think about it more. I've never played it in a game; thgibbs told me about a game he played on rhp using corresponding squares, but that was when the server lost the moves so I never got to see the game. - 04 Apr '08 21:18

if u want some good examples of corresponding squares, or puzzles for triangulation let me know, i've got a couple good ones. The K+2p vs K+1p puzzles are pretty simple, and the example earlier in this thread is frighteningly simple. The part where it becomes difficult is in multi pawn endings where both kings are "inside the square" with multiple corresponding squares in different corners of the "square" making calculation of movement from 1/2/3's difficult, because movement across the "square" becomes a poisonous problem.*Originally posted by petrovitch***There is some discussion at**

http://www.chessvideos.tv/forum/viewtopic.php?f=16&t=1458

Search for Corresponding Squares. The authors of THE FINAL COUNTDOWN really show you how to mathematically prove the solution to triangulation.

It's so hard that I've avoided it for the past few months. I just need time to think about it more. I've never p ...[text shortened]... ding squares, but that was when the server lost the moves so I never got to see the game.

thanks for the link...on my way now! - 04 Apr '08 21:19

Is it really that hard to understand? I was thinking of hunting for a copy of The Final Countdown, but now I'm not sure I even want to bother with the concept. If you can't understand it, what chance do I have?*Originally posted by petrovitch***There is some discussion at**

http://www.chessvideos.tv/forum/viewtopic.php?f=16&t=1458

Search for Corresponding Squares. The authors of THE FINAL COUNTDOWN really show you how to mathematically prove the solution to triangulation.

It's so hard that I've avoided it for the past few months. I just need time to think about it more. I've never p ...[text shortened]... ding squares, but that was when the server lost the moves so I never got to see the game. - 04 Apr '08 21:37

its not as bad as your thinking. The mathematical proof can be hard to follow should you be interested there, however for simple problems its rather easy. If you understand key squares in endgames then this isn't to big of a jump. The part thats breaking my skull is in the multiple pawn islands.*Originally posted by Mad Rook***Is it really that hard to understand? I was thinking of hunting for a copy of The Final Countdown, but now I'm not sure I even want to bother with the concept. If you can't understand it, what chance do I have?**

This and the bishop+knight mate are two of the deepest "simple" positional problems for me.

then you add a rook and it all goes to hell.