Monday, December 18, 2006

Back To My First Love

«Endgame was my first love, and it will be my last. Endgames of the future, and endgames of the past.» (Original lyrics by John Miles)

When I recall my first encounter with chess I see my daddy explain me the rules, and I see myself most fascinated by the pawns arriving at their last rank, becoming a queen. A real miracle: The least piece becomes the most powerful.

He also showed me how I can checkmate him with my queen or with my rook. I preferred the rook because it cannot let you stumble into a stalemate.

Then, finally, we began to play. I always had a very simple strategy: Moving the knights around the board, always looking for possible forks. After some pawns had gone, I also watched for possible skewers with my bishops. If I found no such opportunity, I tried to trade the useless pieces in order to get an endgame where I hoped to get my new queen faster than my daddy. Most times it was he who got it first.

I loved the endgame because it is simple and very tactical, and very fascinating, and because things may turn very quickly from win to draw to loss. Middle game tactics and let alone strategy was much more difficult to understand.

When I now, decades later, look again at the endgame, the old fascination returns. Of course I know now that endgames are not simple at all, even pawn endgames are not. These are the things I am dealing with these days: key squares, mined squares, corresponding squares. With these three all operations in pawn endgames can be explained, such as opposition and triangulation. The theory itself is quite simple, but the application is not. There is a lot of hard work to be done.

Thursday, December 14, 2006

Does The Theory Apply?

The theory of corresponding squares is a fine thing, this is for sure. If it applies, it allows to determine the right move for attack or defense in any position and without any doubt and with mathematical precision. A wonderful thing, this theory.

Two difficulties. First it is important to know whether the theory applies in a given position or if it does not apply.

Well, maybe not so difficult to find out. It must be a king and pawn ending. No other pieces. Has the defender any pawn move? If so, the theory does not apply. Has the defender a counter-attack? If so, again the theory does not apply. In any position with no pawn moves (spare tempi) of the defender and with no counter-attack, the theory of corresponding squares applies.

So far so good. But now comes the real difficulty: How can we find the corresponding squares? This question is far too premature. Other questions have to be answered first. I'll deal with them in another post. Just that much: Kings must fly by helicopter, just as kings of real countries use to do.

Monday, December 11, 2006

What Makes The Chess Game Work?

Mousetrapper's Claim: Chess would be a drawn game without the pawn promotion rule, all other rules being equal.

In pawnless endgames at least the advantage of a rook's value is required to win a game.

Many games are won by checkmate in the middlegame, but the main reason is that every side has to take care of their pawns, because losing them means losing the endgame. Therefore, some compromise has to be made between protecting the King and saving the pawn capital.

Pawns are the soul of chess, Philidor said.

Saturday, December 09, 2006

Hello Patzer, We Are Corresponding Squares!

Would be a great help in pawn endgames. But unfortunately, squares do not talk to us. Yesterday I had a sudden feeling that I have no proper knowledge about corresponding squares.

This is the state of my ignorance: Two kings struggle to get to a so-called key square. If the attacker gets it, he will win. If the defender gets it, he will draw. The means of this fight is opposition, a special kind of zugzwang. The geometric opposition is a special case of corresponding squares, if there is only a single pawn around. If there is a pawn landscape, the simple geometry is somewhat distorted, because certain squares are blocked to the kings. Therefore the corresponding squares cannot be recognized by simple means like in short, distant or diagonal oppositions. I have to find out in every case, asking a square: Hello, are you a corresponding square, and where is your counterpart? Not so easy!

I asked Google for help. And I found it at an unexpected place: Wikipedia. Wikipedia, it seems, is one of the best chess books, at least as far as pawn endgames are concerned. The authors reference to one of the leading experts, Karsten Müller. All very compact, math style. Clear rules. Exceptions. Excellent for brushing up knowledge, but maybe also for learning from scratch.

The most important concept I learnt yesterday was that you cannot figure out corresponding squares without knowing the key squares. These are the goal, and the corresponding squares are the way to the goal.

The second most important concept: There are key squares for attack and key squares for defense, and these are not the same!

In principle, I have got this stuff. But I know quite well that real understanding is a long-distance journey. It must lead from single pawns to simple pawn landscapes with very few blocked squares to complex landscapes with secret king pathways through the jungle. I want to become a jungle fighter. Wish me luck!

Saturday, December 02, 2006

The Fine Art of Defense

There has been much debate in the chess blogosphere about the «dull» games between Kramnik and Deep Fritz. This tells me that endgame lovers are a tiny minority. Months ago I would have joined the chorus. But now I begin to discover the beauty of endgames. This position, for example, is much more interesting than it seems at first sight:

It is quite obvious that Deep Fritz is better. Firstly because his King is in the center and the black King is not. Secondly due to the weak pawn c6. Thirdly because Black has 4 pawn islands and White has only three of them. Fourthly because pawns are on both wings which favours the Bishop over the Knight.

All grandmasters expected Kramnik to move f7-f6 to build a fortress. One even said «please not f5». All wondered why Kramnik used so much time on the move. Then Kramnik moved f7-f5!

Arthur Jussupov explained why this is better: White can infiltrate the «fortress» with Ke3-f2-g3-h4-h5. Now Black has the problem of defending three weak pawns. Thus it was much better to get rid of one of them.

A general rule says that in a minor piece endgame the defender must try to trade as many pawns as possible. Kramnik just has applied this rule. Can chess on the highest level really be so simple?