In search for the ultimate coat hanger

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This is about the 8th time that I look at endgames. It seems that the time is finally ripe now.

• My first attempt to get better at endgames was when I picked up an endgame book by Euwe. Euwe is one of those terrible endgame authors who wanted to give his book a whiff of science, I assume. Which meant that he tried to be complete in his writings. Well, sort of. The result is that his book started with 8 chapters with endgames that you get only once in a lifetime, if you are lucky. An author must protect you from wasting your time. As novice you look for guidance, not for completeness, of course. The idea of an encyclopedia is totally wrong for a novice in endgames.
• It took me about a half year of daily study to get an idea where to start with endgame study. That I count as my second attempt.
• The third attempt was based on my discovery that all endgames were judged by the underlying pawnending. So I started with SOPE of Muller and Lamprecht. That seemed to work well for some time untill I collided with the habit of those authors to put in lots of beautiful endgame compositions into their exercises with positions you will not even get once in 10 lifetimes. That is so silly in an endgame book when you are a novice and looking for guidance. I had to stop that spilling of my time in disgust.
• The fourth attempt was papa Polgars endgame brick which suffered from the same flaw.
• An endgame CD with 2400 exercises of Convekta: same waste of time
• Sixth attempt was PCT. Darn you, Gregoriev! Darn you silly endgame authors!
  
• My seventh attempt was Lars Bo Hansen's SOCES. Now that was a revelation! Finally a book that guides you in stead of being encyclopedic and wasting my time with beautiful studies! I had to stop that study though since my positional middlegame skills were so poor that I never reached an endgame that wasn't lost anyhow.

Now I have improved sufficient in positional middlegame skills, I picked up the study of Hansen's book again. I really love it! Hopefully I can find the ultimate endgame coathanger to hang all those bits of knowledge on which I have gathered overtime but forget to implement in my games.

From the middlegame into the endgame

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Blunderprone commented on my previous post:

"Being able to reach a middle game position and in my head run through a calculation only to mis-evaluate the outcome is an issue in my mind's eye. Visualization skills are critical for calculation of a position's value at the end of a variation. Much easier to see if it's forced moves with a distinct and clear advantage or loss ( material or space). But to reach a middlegame position and evaluate the correct course is most difficult in static positions. In it's simplest terms, the decision to play a minority attack or try to make your opponent advance a pawn in front of his king first, requires teh ability to see the resulting position and say " then what?" and " who is better?" That's where knowledge of typical endgames from your games could really come in handy. Recognizing a subtle panw structure in your minds eye can give you an advantage."

The improvement of my positional middlegame play happened as follows chronologically:

• First there were loose bits of positional knowledge with no interconnections in my mind. Knowledge about outposts, half open lines, king safety etc.. I used to forget to apply this knowledge in my games all the time.
• After a period of serious thinking and abstract arcane blogging I found the common idea behind all these different loose ends of knowledge: piece activity. That generalization made it possible to incorporate the knowledge into my play. That helped my positional middlegame play greatly.
• Then I found the relation between pawnstructure and piece activity. That it are the pawns which determine which piece is good and which piece is bad or ugly.
  
• Due to this new insight I often reached a middlegame position with pieces which were active like hell but is was not clear to what avail. Allthough it was possible that the pieces could do something "active", the concept of "something" wasn't clear. That is where my latest blogging comes in, it defines exactly of what the activity consists. What the pieces do by being active. And it defines the hierarchy of the moves which should be played first.

The problem is now that towards the transition into the endgame I am in about the same position as I was towards positional play two years ago. That means there are a lot of loose different bits of endgame knowledge which I forget to apply in my play. If the above list can be generalized into a recipe for improvement then that means that my next step should be to find the common factor in those bits of knowledge. Which is what I'm up to now.

If I return to the comment of Blunderprone, all this means that you can't evaluate a position until you have transformed the bits of knowledge into an applicable form. Only then evaluation becomes automated enough to be useful in a game. The visualization he touches upon has a close relation to this internalization of knowledge. If I translate it to my own situation, I have difficulties to visualize the cage. Which should be trainable separately perfectly. Visualization without a relation to internalized knowledge I consider to be luxury. It will have no effect on the outcome of the game. If you can't evaluate two different positions right even if you see them physically on a board, then you will not be able to do any better when visualizing these positions in your mind in stead.

Abstract

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Some fellowbloggers seem to tend to see my writings as abstract, arcane or theoretically. I'm totally to blame for that. I don't make any efforts whatsoever to make it look differently due to other priorities in using my time. Yet I can assure you that they can't be further from the truth and totally miss the point in my writings.

On the contrary, my musings have a 1:1 relation to the games I play. They form the actual guide for my moves during the middlegame. They are very, very concrete.

The past year a drastic change in my middlegame approach has manifested itself due to these very concrete musings. In 90% of the cases I reach a very good middlegame position. Even against players with a much higher rating. Most of my opponents agree with that judgement.

Due to this new middlegame approach, a new weak element has surfaced though. I can't finish off my opponents. I misjudge a position, I'm drawn into an endgame and lose the game, even without knowing why.

I had put the Secrets of endgame strategy of Lars Bo Hansen on the backburner because I had lots of positional middlegame troubles about a year ago. Now my middlegame troubles seem to be corrected, sufficient for the moment at least, it seems to be about right to switch places and put my middlegame computing algorithms on the backburner. Only for a while, of course, but there is a very concrete cause for this change: Corus is nearing.

concrete

A.C.I.S. Arcane Chess Innovation Society

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In a previous post I discovered that chess is the ultimate trap. You might think that that leads to a simple algorithm which closes the trap. Just take away as much squares as possible from your opponent's pieces and you're done.

Matters are somewhat more complicated, though. As I stated in my previous post, you are dealing with a cage. A cage with walls that are closing in on the hostile piece. This are the problems to be solved:

• The walls of the cage have a freakish shape.
• The walls constitue of many different elements like the rim, own pieces, hostile pieces, covered squares and tempo's.
  
• The walls are partly invisible.
• The fabric of a wall can be made of tempo's. That means there are holes in the wall but the opponent cannot make use of it since it takes too many tempo's to walk through it so you can close it in time.
• The pieces that form the walls have to cooperate in order to close in.
• The walls can be attacked.
• Only cages that you can shrink to zero squares do really matter.

A very good example of all these elements of a cage is mating the king with bishop and knight.
I will not start with such complexity though. I start more simple with an algorithm to mate the king with two rooks in an attempt to optimize the coordinating of the pieces. I will not bore you with the details.

More boring stuff

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Writing the previous post I was pleasantly surprised that the proposed algorithm "The position to strive for is to maximize the difference between the current potential of your own pieces and the current potential of the pieces of the opponent" lead to a tendency to walk towards the center without any additional programming. After some thinking I realized that this very same algorithm would create a few other tendencies as well without extra programming:

• the tendency for a pawn to walk to the promotion square, which brings him closer to its full potential.
• the tendency to capture pieces.
• the tendency to trap pieces.
• the tendency to occupy open lines and outposts.
• the tendency to base exchanges on the dynamic value of a piece.
  
• the tendency to trap (mate) the king. Maybe this should be stimulated by letting the potential of the enemy drop to zero if that happens. This would cause the game to go in the right direction any time.

The programming of this algorithm will by no means be simple. It isn't guaranteed that it is even possible with less than an infinite amount of calculations. My attempt to avoid the tree of analysis will be based on formulating the ideal position and working backwards to the beginning.

First of all I have an important problem to solve. A problem that I haven't even formulated yet.

What is the exact relationship between tempo's and squares?
The fact that you can only make one move at the time makes that the squares don't have an equal value for a piece. The fact that you don't occupy a square 7 tempo's away is not as pressing on the performance of a piece as the fact that you don't own a square just 2 tempo's away. But how many squares of the 7th order have the same value as a square of the 6th order (=6 tempo's away)?

After some thought it becomes evident that it isn't sufficient to look at the future of one piece only. It is the combined effort of different pieces that constructs a cage in which pieces can be trapped. This needs separate investigation.

How potent is my piece?

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This is the hypothesis:
All kinds of positional topics like piece activity, king safety, outpost, color complex etc.. can be described using only a few elements. Space and time are two of them.

If I am able to express every topic in these same few elements than I can compare them on a realistic basis in stead of awarding them with arbitrary statistic bonuses. I want to stretch matters even further, even the tactical elements can be expressed using these very same few elements. Everything isn't worked out completely yet. That's the reason for this post. Let me give it a shot.

What happens when a piece is dumped on the board?

Diagram 1























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In 7 tempo's, the King can reach every square of the board. That must be his potential in the shortest time from his position on h8.
Potential from h8:

• Space = 64 squares
• Time = 7 tempo's

That shows immediately that there must be better squares on the board. If you place the king in the center of the board, for instance on e4, he becomes even more potent.
Maximum potential:

• Space = 64
• Time = 4 tempo's

Even if you give the king more tempo's, he cannot accomplish more than reaching 64 squares.

I'm a bit afraid that you might find these posts a bit boring. For me they are very important though. Without them I would never be able to find the third element as I just did:

• Position on the board.

Only on d4, e4, d5 and e5 the king will have his full potential and hence his greatest future possibilities.

What happens when other pieces are being dumped on the board? It is evident that they can only limit the full potential of the king by influencing the elements.

Diagram 2























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The blocked pawns are lengthening the pathways of the king. To go from h8 to g7 the king needs 15 tempo's. To go from h8 to h7 he even needs two tempo's more.
The king can still reach all 64 squares. But he needs an incredible amount of tempo's to do so.
It is possible to place the pawns in such way that a certain part of the board isn't accessible to the king at all.

Conclusion for now:
The position to strive for is to maximize the difference between the current potential of your own pieces and the current potential of the pieces of the opponent. Potential can be expressed in squares and tempo's. Not every square has equal potential for a piece. Hence the inclination for some pieces to head towards the center.

Hanlon's razor:
Never attribute to malice that which can be adequately explained by stupidity.

PGN viewer almost ready

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On my quest to find the pot with gold I'm almost ready with my new PGN-viewer. It took me 3 days of programming and I need another few hours. Of course only when it is finished the actual work begins: writing analysis-algorithms that answer my questions.

In the comments on a previous post there were different methods proposed to find the static value of a piece. A static value is some kind of average based on a statistical method. What I'm looking for though is the dynamic value of a piece. Based on what a piece actual does in a position. In the corner a rook sometimes has merely the same function as a pawn, just covering the pawn in front of him. Especially if he has little prospect in the future his value is about 1 (pawnunit, that is) . While a rook that is about to deliver mate has a value that approaches infinity. Usually the dynamic value will be hoovering somewhere in between and can change drastically during the game.

The algorithms I intend to write are meant to shed light on how it can be calculated what a piece actually does and how to calculate its future prospects. Since that is what you want to maximize.