Saturday, July 14, 2007

A matter of technique

Most endings are for 95% practical and for 5% theoretical.
For the practical part of the endgame it suffices to acquire the general ideas by studying how the masters did it. You have to have a database with how a position will look like after you make a decision. Take for instance the following diagram:

diagram 1

Black to move.
White has just played Rb5.

If you haven't seen this kind of positions before, it is very tempting to play the logical move Ra8 in order to prevent white from taking on a5 and getting an outside passer. Only when you have seen the masters play this you will know that black will probably be killed in bed if he does so.
Black defends the weakness a5, white starts to push his kingside in order to create a second weakness. Whites rook will play a role in attacking both weaknesses, while blacks rook defends only one.

So black must play active and bring his rook behind the a-pawn. To a1 or a2 for instance. In that way he defends against the outside passer while he still can assist in an attack on the kingside.

Al these idea's how to play practical endgames cannot be found by yourself. Within a lifetime, that is. So you have to study the mastergames for that. You will not find this in an endgame book, unless in Secrets of Chess Endgame Strategy by Lars Bo Hansen, maybe. Which I will check out within two weeks (hattip to Blue Devil). Endgame books just treat theoretical endgames.

For the theoretical part of rook endings it suffices to know the Lucena attack, the Philidor defence and Vancura's schwindle.

Pawn endings.
What plays an important role in almost every practical endgame is the question "is the underlying pawn endgame won?". Since the answer to that question tells you if it is favourable to trade off the last pieces. The serious student must ask himself what he is going to do with pawnendings. I have choosen to study them thoroughly.

Most of the time that I have studied endgames, I have studied pawnendings. Most people think they are simple. They are not. Since most people have no idea how to play pawnendings they are not aware of the pitfalls. When you walk into a pitfall without noticing it and it is not punished by the opponent, both players will agree that there wasn't one.

Why are pawnendings so difficult? There is a whiff of magic in pawn endgames. Most of what is going on in a pawn ending is not visible with the naked eye. The structures are only visible to the minds eye, for the one who has learned how to see it.
The march of the king causes optical illusions, since in reality the diagonals are exactly of the same length as the rows and files. Zugzwang is another invisible weapon.

Corresponding squares.
Most battles are fought by the kings.
Not all. Breakthru and the pawnrace are weapons of the pawns, for instance.
But most of the time it are the kings that struggle to invade the opponents territory.
The attacking king strives in two different directions, the defending king tries to defend both.
There are two systems:
  • the Reti manoeuvre
  • corresponding squares
Both systems have in common the struggle with an eye on two targets. Targets in the broadest sense, so a target can be the defense of a pawn.
The Reti manoeuvre is based on the diagonal movement of the king which makes that the king can come closer to two targets at the same time with only one move.

There are a lot of techniques that fall under the common denominator corresponding squares. For instance all forms of opposition (normal, distant, virtual) and triangulation are based on corresponding squares. A thorough knowledge of the theory of corresponding squares is paramount.

There is a big but.
I couldn't find a useful explanation of the theory of corresponding squares. As described in SOPE the theory is incomprehendsible. Most descriptions on the web are even worse. Besides that, it is not practical.

In order to make it practical I must find out how the theory has to be applied in practice. How do you determine what the key squares are? Where do you start in complex situations? That is where the existing descriptions fail miserably. GM John Nunn even suggests to forget about the theory and to learn just a few tricks. I found it impossible to apply the tricks without understanding what I'm doing.

[disclaimer] Since my investigation hasn't finished yet, it isn't ready to explain the theory of corresponding squares to your mom. Yet. Technical ranting below.

I have written about corresponding squares before (a good read) and I intend to make use of the same position of Grigoriev:

diagram 2

Black to move and draw.
What are the invisible properties of this position:
  • The black king is bound to the rule of the square of d3 in order to prevent promotion.
  • White has two targets: he can try to invade into blacks territory via the left or via the right of the pawns.
  • If whites try to outflank black on the right side of the board, black can counterattack the white pawn on c2 and both black and white will queen a pawn in the resulting race.
Let's have a look at the key squares.

diagram 3.

If white can reach one of the blue keysquares of the first order, the black pawn will fall. Notice that d3 is a key square which white cannot use.

Black cannot defend the keysquares e3 and f3 by opposition, since he cannot make use of the square e4. So black has to shift the frontier one rank into whites territory.

diagram 4.

Black must prevent white from invading the green keysquares of the second order. Notice that that are all squares which are adjacent to the blue keysquares (d2, e2, f2, g2) but since d2 and g2 (counterattack by black against c2!) are not available for white, they are not colored green.

If there wasn't a second front at the leftflank it would suffice for black to take the opposition with Ke3. The problem is though that square d3 isn't available for the black king. If white heads to the left keysquares, and moves to c1, he is still in contact with the keysquare e2. If black moves to d4 at the same time, he fails to defend e2.

diagram 5

So black must make use of a trick. Since there is little space at the left, black can permits himself to shift his whole defense one file to the right. This way his king always stays one file to the right of the file of the white king.

diagram 6

That means that the first move of black from the beginposition must be 1. ... Kf3 in stead of 1. ... Ke3
The keysquares are still protected and black is just in time when white tries to invade the keysquares at the left. When both players have reached the utmost left of their defense (a2 for white and b4 for black), white can try to lure black into a trick by playing Ka1

diagram 7

Black must never forget that he has shifted his whole defense one file to the right. That means that if he plays Ka4 or Ka3, he will never be in time when white starts to run backwards for e3.
The same is true for the c-file. If black plays Kc5, he will be in trouble when white playsKa1-b1.
From c5 the black king can't go to the b-file (too much to the left) not to de d-file (too much to the right) and he cannot go to c6 (too far away from the battlefield).

So when white plays Ka2-a1 (the red arrow) black must stay on the adjacent b-file and play Kb4-b5

With this kind of reasoning the keysquares and the corresponding squares don't appear out of the blue any longer but it is a practical method how you can apply the theory behind the board.

Boy, am I running around in circles or what?



    Corresponding squares in chess are squares of reciprocal (or mutual) zugzwang. (Dvoretsky)

  2. HDK,
    thx, that are a few vague examples I was talking about. When the position becomes more complex the explanation tends to become even more obscure.

    The definition of Dvoretsky is in line with this. The term reciprocal zugzwang is useless when used in a game. Since in a game only one person is to move. It's just all too theoretical and not practical.

    The matter is how to find the keysquares yourself and how to find the corresponding squares yourself in an OTB situation. That is practical but not told by the books with their fancy definitions.

  3. Mind you, I'm not saying that the descriptions of the theory are wrong, my point is that they are insufficient for practical application.

    pgn of your endgame book is here. That is a big but lol

  5. after you left, your grand puba status was uncertain in the waffing silence. then much worked followed. and, with this post, that you are our grand puba cannot be in doubt. it is so.

    you do so much for us.


  6. A very interesting and illustrative post.
    I also have read you post about corresponding squares.

  7. CT,
    great! I was actually wondering how many people would have the patience to read this.