And God placed the middlegame before the endgame

Phaedrus added the following comment to my latest post:

"It is completely unclear to me why an "ideal game" should end with an endgame. It might well be possible that the ideal game (played by the super computer that "solves" the game of chess, is already decided in the middlegame. As your assumption of an ideal game is the foundation of this quest, I do not know if you have struck gold here. Yet I am very interested to see where it ends."
Disclaimer: warning, abstract ranting ahead!

There are 3 ways by which a game can be won.

• Winning a piece
• Mating the King
• Promoting a pawn

All combinations that win a piece can be devided in two seperate groups. The first group I have dubbed the duplo-attacks. These work by attacking simultaneously 2 pieces with only 1 move. Notice the similarity with my previous posts where one move served two goals. If the opponent of whom 2 pieces are under attack can only make a single-purpose move, he can only save one piece by making that move.

The question is, can you force that?
Imagine a middlegame position with no pawns. There is no way that you can win a piece by best play because the pieces are simply too volatile. Every attacking move can be countered by either a counter attack or a defensive move. You can only win a piece with a duplo-attack if the pieces are restricted in their movement. Pawns are the agents nec plus ultra to restrict pieces. So the question translates to can you force the restriction of pieces by pawns so that a duplo-attack is unavoidable?

The second group I have called the traps. A trap has as characteristic that you restrict the movement of a piece by moving your pawns forward. This leads to the question can you force the restriction of pieces by pawns so that a trap is unavoidable?

Given the similarity between both questions I think it is justified to say that if one of the questions must be answered with no, it probably means that the answer at the other question must be no too.

I simply cannot belief that the final frontline of the pawns will be far off of occupying about 50% of the board at average. I cannot belief that 1.d4 or 1.e4 give you such forced advantage that you will end up occupying say 75% of the board. A ship with two captains who want to head in opposite directions and where every captain can steer for 5 minutes will end up roughly at the same spot as where they started.

I cannot imagine that owning 50% of the board is enough to trap a piece or to force a duplo-attack. So, overall, winning a piece by force with ideal play from both sides is beyond my imagination.

Which leaves mate as the only method to win before the endgame. I consider mate to be a special instance of a trap. But there is a difference. First the value of the king is infinite, which means that every means is justified as long as it ends up as mate. Second, the king seems somewhat limping, because of old battlewounds, of course. He moves slow. Which makes him an easy target. I have no arguments that an early forced assault must be excluded. On the other hand I have seen no indication at all that such untimely assault is likely.

Because of the application of computers we can be sure that such assault will not take place in the first 12 moves. On the contrary, the longer I let a computer evaluate a position, the closer it gets to a zero advantage, usually. After centuries of chess no indication has emerged that an early forced assault is likely. But I cannot proof that it is impossible.

If it is possible, we are not able to find it though. Which is the same as saying for us humans, with the aid of computers, it is not possible. Yet.

As long as it is not proven otherwise, the ideal endgame will thus end in the endgame.

Combat the king

Now we know what the goals of the enemy king are, how can we prevent that he realizes his goals?

King vs King.
First there is the combat of king against king. These are the weapons of your king:

• Shouldering away
• Opposition
• Zugzwang
• Triangulation

All these weapons have time or tempo as common ground. Shouldering away means that the hostile king needs more tempi to get around you. You lengthen the path to the goal which costs time. Opposition dito, this works only if there aren't any spare tempi (pawnmoves) around. Zugzwang again means there are no spare tempi around that don't harm you. With triangulation you lose a tempo intentionally, thus bringing your opponent in zugzwang. Thus the parameters to combat the king are:

• time
• pathlength

Which are closely connected.

Pawn vs King.
The king has proven to be vulnerable when his parameters are manipulated.

Diagram 1.























It is possible for pawns to keep out the king. This is done by lengthening the pathway of the king to get to the pawns. In the diagram this pathway is infinite, so the time for the king to get there is infinite too.

It hasn't to be so extreme, of course. Even when fewer pawns are standing abreast, the king needs a lot of time to get there.

Diagram 2.























Of course the pawns have an extra weapon besides their ability to keep the king out for 4 moves in the diagram above: the king must stay in the square of the pawns to prevent promotion. But that is an old weapon which we already discussed.

Diagram 3
























If we think of holes in a position, we usually amagine that a knight arrives there at a certain moment. But the story above culminates into this: you must put your pawns in such way that they keep the king out. Here white can simply walk to b5 to penetrate into the enemy position. It is the pawn structure which allows this.

Extrapolation to the rest of the game.
Again we can extrapolate this principle to the rest of the game. When pawns are preventing each other mutually from promotion, which is the case right from the opening until the creation of a passer, often not before the endgame, there can be only one method to decide the game: penetration into enemy territory in order to attack the pawns from behind. It is the pawnstructure that allows or prohibits this. This is in no way contradictory to my findings in the past about the middlegame: the importance of piece activity and invasion squares.
As I have said in extenso, I'm talking about the ideal game here, that is with no accidents like gaining wood or mating the king by tactical mistakes. Tactics are overrated LOL.

The influence of the King

Any pawngame without kings can be evaluated to the end. There are mainly two parameters for a pawn:

• What is the distance to the promotion square
• Are there impediments on the road to the promotion square

The weapons of the pawn are:

• Restraint
• Blockade
• Zugzwang
• Sacrifice
  

What happens when a king enters the arena? What is the influence of the King?
When there are two kings on an empty board the result is a draw. This means that the influence of the king is derived from how he effects the parameters of the pawns:

• Attack: can he free the road to promotion of his own pawn?
  
• Defence: can he impede the road to promotion of the enemy pawn?

This gives the king clear goals to head for. The power of the king is that he can make multipurpose moves. He can head for two (or more) goals at the same time.
The most famous example of all is of course Reti's position:

Diagram 1.























White to move and draw.

When there would be no kings on the board, this would be a clear win for white. It is very important to take note of this advantage for white (which I hadn't realized before).
When evaluating the kings you must first have a clear picture of the potential targets of both the kings and the pawns.

Black:

• Attack: de black pawn can promote on its own.
• Defence: the black king is already in the square of the white pawn and he must keep it that way.
  

White:
The white king has two targets.

• For attack: the key square d7, where the total path to promotion is protected.
  
• For defence: the square of the h5 pawn. Notice how big that target area is.
  

Multi-purpose moves.
Multiple goals add a whole new element to the battle. White has 4 moves at his disposal:

• c7 (serves 1 goal)
• Kg8 (1 goal)
• Kh7 (1 goal)
• Kg7 (2 goals)
  

Black has 5 moves at his disposal:

• Ka7 (0 goals)
• Ka5 (0 goals)
• Kb5 (0 goals)
• Kb6 (1 goal)
• h4 (1 goal)
  

The goals of black and white are mutual complementary by nature. Every attack (pawn promotion) has a defense attached which is mandatory. The one who makes a move which serves more goals than his opponent, comes one step closer to the realization of one of them.

Let's see what happens if we make a quantum leap and extrapolate this conclusion to the whole game.
In the startposition both players have 16 goals each. 8 attacking goals (pawn promotion) and 8 defensive goals (prevent the opponent's pawn promotion). If the game is not decided by accidents, like winning material or mating (winning) the king, one of the pawns will have to do the job. The pieces are circling around the pawns either assisting them or impeding them. Every multi-purpose move that you make (in relation to the 16 goals) while the opponent makes single-purpose moves, will bring you closer to the realization of one of the goals.
The value of each piece movement must be seen against this background. Thus fullfilling the words of Philidor which always seemed incomprehendsible to me until now.

There is more to say about the king and pawn, but I must digest this unsuspected conclusion first.

emagdne ehT spelled backwards

To me, a middlegame position is a bunch of positional topics which have almost no relation at all. They just happen to me in a game. My contemplations in the past about piece activity has provided some sort of cohesy. Of course there must be some hierarchy in the characteristics by which a position is evaluated, but sofar this structure remained obfuscated to me. In order to find out, I start at the very end of the game and work my way back to the middlegame, or maybe even to the opening. I will focus on how matters are interwoven. Maybe it will take me more than one post, I don't know, but I'm not going to hurry. I hope to be able to find the "ideal line" of the game. Which things should be evaluated first. Of course there are often shortcuts in a position due to accidents, like winning a piece or mating a king. But assuming that both opponents are able to avoid such accidents (or don't recognize them as they occur), what should you look for and why? And how are the topics logically related?

There we go.
To get a clear picture of every influence solely, we must isolate it's effect as much as possible. The first thing I'm asking myself is what influences play a role for the pawns alone, if the effect of the kings is taken away from them. See the following diagram.

Diagram 1.























The pawnrace.

What you see above is the pawnrace.
Decisive parameters:

• De road to promotion must be free.
• The distance which each pawn already has traveled.

Those parameters allready play a role in the transition from the middlegame to the endgame. Create a passer, how far have you pushed your pawns already.

Diagram 2.























The blockade.

In this position there is only one outcome possible.
Parameter:

• The road to promotion is blocked.

If there is no help by other pieces this is a draw.

Diagram 3.























Zugzwang.

Parameters:

• The road to promotion is restrainted.
• There are no other moves.
• You have to move but you would rather not.

Diagram 4.























Breakthrough.

This is the same position as diagram 1. By sacrificing a pawn you can create a passer. You lure away the blockading or restraining pawn, thus freeing the road to promotion for another pawn of yours. The interesting thing is that you can do that alone by freeing the road for your opponent too, thus starting a pawnrace similar to the one on diagram 1. Hence the same parameters play a role:

• De road to promotion must be free.
• The distance which each pawn already has traveled.

Diagram 5.























One stops two.

Capablanca teached us that it is not the amount of pawns that count, but the amount of pawns that you can prevent to promote. In the diagram above the 2 white pawns are controlling 8 pawns of black.

Logically this must be your startpoint at all times when evaluating an endgame or even a middlegame position: imagine that all pieces and the kings are gone and that only the pawns are left. What would be the outcome? Only very few parameters have to be taken into account to answer that question. Next post: what is the influence of the kings?

Mind stalling

When a position becomes more complex the time I need for a move grows exponentially. My short term memory is generating overload errors and I feel paralyzed. The effectiveness of my thinking comes to a grinding halt.

The past 8 years I have focussed on improvement in the right area of the graph above. In terms of the graph I have shifted the point that indicates how much complexity I can handle in 3 minutes considerably to the right. My approach has been multifold. I have tried to increase my ability to handle more complex stuff (probably to no avail) and I have simplified complexity by breaking it down (probably the most fruitful direction to head for). At the moment I don't feel I make much progress in the right area of the graph anymore.

The problem with the right area of the graph is that you have only time to calculate variations. There is no time to contemplate about the finesses of the position. About the pawnstructure, the strategical issues or whatsoever. When every move counts, can decide the game at once that is, then mere calculation is the only thing to embark on. The general advice is to calculate until quiescence. Or even better, to quiescence + 1. Speaking about nonsensical advice, here you have it. I am only able to calculate till my mind stalls. If every move seems to lose I even calculate till the mind stalls + 1. Where the + 1 stands for losing 1 hour on the clock. When I don't want to lose on time I have no other option than to gamble. Complexity downgrades chess to a game of chance.

In order to master complexity I had replaced my opening repertoire by gambits only. For years I haven't played different. With gambits complexity starts at move 3. So gambling and time trouble has been the bane of my play past years. With the acquiring of nerves of steel as added bonus. Of course I have made little progress on the more subtle side of the game. During the games I had simply no time to think about that. There is another side to it. In order to win from a lower rated opponent with a gambit you have to play much better than him. The gambitplayer has taken the responsibility to make the game. You must create the threats. While your opponent has only to react. To only parry all threats in the reassuring knowledge that one slip of you results in a won endgame. He will suffer much less from time trouble than you. On the other hand, the gambitplayer will blow away a much higher rated player every now and then.
There is another disadvantage with playing gambits and that is that you are not free to play in whatever direction you like. You can't trade off to an ending at any moment and you cannot trade queens for instance.

But playing the Polabia, as GM Danielsen pronounces it (the Polar Bear), has shown that it is possible to stay clear from complexity and to steer the game into the left part of the graph. This is by the way a proof of the steerability of a game, about which we discussed much in the past. Of course, if my opponent insists in complexity, he can create it. But the gambits against the Polabia don't look all that rosy and premature attacks are, well, premature. And remember, you have to play much better when playing a gambit, for reasons described above.
And, I might add, I'm not afraid of gambits since I know what a gambitsplayer hates the most:)
Thus my opponent can only steer into complexity with the odds against him. Which is fine with me. Complexity was the bane of my play, after all.

In the left part of the graph there is time for contemplation. Here I refind the issues that the positional chessbooks talk about. The subtleties for which I had no time in the past, busy with complexity as I was.

The Polabia with both white and black has replaced 75% of my gambits. Now I have to find something against 1.e4 which keeps me on the left side of the graph and which suits my taste. Maybe the Scandinavian with 3.Qd6? The rumours of the demise of that opening are clearly exaggerated, according to Rybka. Usually such rumours are of great help to prevent people from preparing themselves against it.

1%

Only 1% of the chess advice which mankind so unselfishly and abundantly provided to me survived the test. When you write something like that there is always somebody who asks what that 1% is. To be honest my first reaction was somewhat itchy. Man, don't be lazy and read my blog! On the other hand I realize that I just said in an implicit way that 99% of my blog is BS. Combined with my difficult way of saying things it is no wonder that somebody loses the thread. To take distance from the past I will try to formulate what that 1% is. To be exact, that 1% of good advice is actually non existent, since the advice was of no help at all and I had to think for my self.

Let me try to explain what I have found. After a break of four months lately I had the feeling that I had forgotten all the details of what I had found out about chess the past years. During the first game after the break I felt what made the difference between my opponent and me. The only thing that was left from the past was my franticly scanning of the board. Automaticly and unconsciously. All the chess knowledge and chess skills finally cristallizes in this complex motor skill, this automatic scanning of the board. Knowledge that hasn't made the transformation into scan habits is virtually useless. Simply because you forget to use it. The trigger of this revelation was described here.

There are 3 parts to it.
The how = scanning
The what = quality
The how often = frequency
Scanning is the method. But with playing Troyis you learn a skill that is of little importance in winning a chessgame. It is a scan of low quality. You seldom decide a chessgame by only manoeuvring a knight in a limited space. Imagining the beams that come out your pieces is an example of a high quality scan. Besides a high quality it is important that you need the skill often. If the frequency of what you have learned to scan for only plays a role once every twenty games, it is too seldom of help. You have to identify those skills that you need almost every move.

In search for high quality scans with high frequency of occurrence I followed the blitz games of GM Danielsen. I could follow the tactics usually quite well but his positional decisions were acabadabra to me. I figured that that meant that my tactical scanning is reasonable but that my positional- and endgame scans are virtually non existent. Hence the first thing I'm going to work on are the 15 endgame principles of Lars Bo Hansen's book Endgame Strategy. Trying to transform those principles into scan habits.

To Alastair:
I put it in the refrigerator means: I don't do it now, but later.

Full throttle ahead

Today Margriet and I studied a few hours in Hansen's book, in preparation for the Corus tournament in januari. He has identified the following 15 key principles for the endgame:

• Pawnstructure
• Two weaknesses
• Space advantage
• Control of squares and files
• Grip and suppressing counterplay
• Domination
• Time: hurry or not?
• Making the right exchanges
• Transformation of advantages
• Two bisshops
• Bishops or knights?
• King activity
• Rook activity
• Initiative and attack
• Mate and stalemate.

I realized that all these topics are familiar, but in a way unlike tactics. It is pure theoretical knowledge, without a relationship to practice. I dare to say I have past the sea of openings and tactics safely. For my level and for the moment these two topics are relatively well covered. Which feels as if I'm freed from a burden. But from the endgame I have only experienced stage one: the ridgid application of rules. After the initial excitement of new knowledge, already years ago, the ridgid application of the rules caused the inevitable disappointment. Now it's time to go ahead on this road and to transform the theoretical knowledge into practical experience. Seeing the 15 principles in action must become as familiar as seeing a pin or a discovered attack.

It is remarkable that Hansen often starts to talk about the endgame already when the queens and only one set of light pieces are traded. Probably that is because the principles of the middlegame and of the endgame don't bite each other. The essence of the difference seems to be the safety of the kings. After years of going for the kings throat only, I have to learn to look in a quite new way. Which is thrilling.

It begins with the end.

Once I drove along a quite big mushroom. It was half a meter wide. The next day Margriet and I decided to have a look at it. We were very disappointed to see that somebody had kicked it to pieces. In stead we were looking at a broad boring lawn. At least, that was what I thought at first. All of a sudden I realized that there were very tiny fungi amidst the grass. When I had a closer look I saw a wealth of wee mushrooms. Most of them had beautiful shapes and there must have been at least a hundred different kind of species.

That's the art of life. Learn to not fall for the freak things with their easy satisfaction, but to sharpen your eyes so you can see and enjoy the little things where everybody else sees just a boring field of grass. Boredom that prevents a second look.

It's the same in chess. The break has done me alot of good. I realized that the freak gambits and the freak tactics alone are no longer able to satisfy me. It's time to sharpen my eye and to learn to enjoy the seemingly boring. I already start to see the glimpses of beauty neglected by many.

What is more logical than to begin at the end? How can you conduct a middlegame if you have no idea what you are heading for? I have 1.2 meter bookknowledge of the opening and more than average experience with tactical problems. It has become somewhat unlikely that I fall for a simple trap in the opening or a cheap trick in the middlegame, allthough accidents do happen. But my opponents have become stronger and tend not to fall for all too cheap tricks either. So what should be the plan as long as my opponent fails to become the victim of an accident? The answer is of course: get a favourable ending. Does the enemy make a mistake along the road to the ending? Of course I will not hesitate to punish him. But if his game hasn't serious tactical flaws, the ending should be the goal. Capablanca advocated exactly this.

I have broad experience with the wrong way of endgame study. The way which is advocated by most chessauthors, by the way. They propagate to acquire an encyclopedic knowledge of the ending. Which is as nonsensical as learning openings by heart. In stead I'm going to focus on general endgame strategy. Because when I play an ending wrong, I can look after the game in my "encyclopedia" (a bunch of books) for how I should have played. You don't start to read an encyclopedia right from the latter "A" to the letter "Z", but you use it when you need it.

The Polar Bear is a solid base for a good middlegame, so no worries there. It seems to soothe my lower rated opponents into sleep since it isn't all too obvious what the opening is about. As you can see in my first game of the season here.

Why the best fit is better than the just fit (it's faster)

Read the following article from New Scientist:

Superstitions evolved to help us survive

• 00:01 10 September 2008
• NewScientist.com news service
• Ewen Callaway

Darwin never warned against crossing black cats, walking under ladders or stepping on cracks in the pavement, but his theory of natural selection explains why people believe in such nonsense.

The tendency to falsely link cause to effect – a superstition – is occasionally beneficial, says Kevin Foster, an evolutionary biologist at Harvard University.

For instance, a prehistoric human might associate rustling grass with the approach of a predator and hide. Most of the time, the wind will have caused the sound, but "if a group of lions is coming there’s a huge benefit to not being around," Foster says.

Foster and colleague Hanna Kokko, of the University of Helsinki, Finland, sought to determine exactly when such potentially false connections pay off.

Simplified behaviour

Rather than author just-so stories for every possible superstition – from lucky rabbit's feet to Mayan numerology – Foster and Kokko worked with mathematical language and a simple definition for superstition that includes animals and even bacteria.

The pair modelled the situations in which superstition is adaptive. As long as the cost of believing a superstition is less than the cost of missing a real association, superstitious beliefs will be favoured.

In general, an animal must balance the cost of being right with the cost of being wrong, Foster says. Throw in the chances that a real lion, and not wind, makes the rustling sound, and you can predict superstitious beliefs, he says.

Real and false associations become even cloudier when multiple potential "causes" portend an event. Rustling leaves and say, a full moon, might precede a lion's arrival, tilting the balance toward superstition more than a single "cause" would, Foster explains.

In modern times, superstitions turn up as a belief in alternative and homeopathic remedies. "The chances are that most of them don’t do anything, but some of them do," he says.

Michael Shermer, publisher of Skeptic magazine, has proposed a similar explanation for such beliefs, albeit in less mathematical language.

"Our brains are pattern-recognition machines, connecting the dots and creating meaning out of the patterns that we think we see in nature. Sometimes A really is connected to B, and sometimes it is not," he says. "When it isn't, we err in thinking that it is, but for the most part this process isn't likely to remove us from the gene pool, and thus magical thinking will always be a part of the human condition."

Scientific superstition

Yet not all superstitions persist because of their evolutionary kick. "Once you get to things like avoiding ladders and cats crossing the road, it's clear that culture and modern life have had an influence on many of these things," says Foster.

"My guess would be that in modern life, the general tendency to believe in things where we don't have scientific evidence is less beneficial than it used to be," he adds.

However, Wolfgang Forstmeier, an evolutionary biologist at the Max Planck Institute of Ornithology in Starnberg, Germany, argues that by linking cause and effect – often falsely – science is a simply dogmatic form of superstition.

"You have to find the trade off between being superstitious and being ignorant," he says. By ignoring building evidence that contradicts their long-held ideas, "quite a lot of scientists tend to be ignorant quite often," he says.

In chess, and in real life, people are succesfull when they are able to draw conclusions fast in a complex environment. Let me try to translate the essence of the article beyond superstition:

It is not possible for the human mind to draw a conclusion fast and to be right all the time. But often it is more important to be fast than to be right. Those who simplify matters can draw conclusions much faster than those who want to be right all the time. Simplifying matters adds an element of gambling to the conclusion. If you are gambling the statistics determine who is succesful. If the benefit of being accidentally right outweights the consequences of being wrong than you are succesfull. That explains the succes of following rules of thumb. Developing your knights before your bishops isn't necessarily always the best thing to do. But the damage of being wrong by moving your knights first is usually very little.

My trouble is that I can't stand being wrong. I hate it to be right only by accident. Hence I'm way too slow to draw a conclusion. That's why I'm not succesfull in complex situations. Like chess. Or life. What Transformation tried to explain to me here. To no avail. Due to my character.