The logical and the psychological approach

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There are two area's where both my knowledge and my skills are substandard: middlegame and endgame. There are two approaches to fix these omissions. The logical approach is to start with endgame play and to work your way backwards to the middlegame. Because you can only steer the middlegame towards a favourable ending if you know which ending is favourable and which is not.
But there is a downside to this logical approach. Knowledge of theorethical endings bears much similarity with an encyclopedia. Nobody has ever mastered the knowledge in an encyclopedia by starting to read it from letter A to Z. Unless you are an idiot savant, maybe. The acquiring of knowledge without immediate application is experienced as dull and is prone to forgetting. If you know which endgame is favourable but you don't know how to steer the middlegame towards such endgame, your knowledge is impotent.

So for psychological reasons, it is better to start with the middlegame. In order to overcome the lack of knowledge which endgame is favourable and which not, I have to postulate some premises.
For the time being I will have to work with presumptions about what a won endgame looks like in stead of the real thing.

There is another problem that I should mention. When studying positions, my computer tells me which ending is won or drawn. But the one-eyed kings of this world get other results. Because they play against humans and not against computers. So I need some statistical information about how often certain endgames are won or drawn in practice. Is there a source where I can obtain such information?

A global game plan?

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I realize quite well that my previous post is hard to read since my thoughts are still brewing. I hope somebody will take the effort to formulate some answer to the question at the end of the post though. The idea of a closer study of the parameters that decide the game is very tempting. But take a look at the following three positions:

diagram 1


















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White to move: draw
Black to move: draw

diagram 2


















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White to move: wins for white
Black to move: draw

diagram 3


















=/-
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White to move: draw
Black to move: forced loss for black

This all looks rather esotherical.
Nunn wrote a book of 320 pages solely devoted to the KRp vs KR ending. His book makes it seem as if there are 3 levels of endgame knowledge:

• The totally ignorant patzer, among which I reackon myself
• The one-eyed king, who wins drawn endings against ignorant patzers
• The endgame tablebase assisted computer which draws lost games and wins clear draws

If I am going to study the parameters by working my way through Nunns book, I basically try to jump from level one to level three. Somehow I think that might not work.

But maybe it is possible to develop a global game plan for the moment. My previous posts seem to suggest that from all endings the ones with minor pieces are the most likely to have an outcome that is not according the tablebases. Where a one-eyed king can win from the total ignorant. So when I don't know what to do in a game, I follow my endgame maxims (see my sidebar) and head for a minor piece ending. Just for study purposes.

Parametrize this!

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Let's have a closer look at the endgame we studied lately. We found quite a few topics that need further investigation:

• With no pieces, the remaining pawnending was a win.
• With pieces, be it minor or heavy, the ending was drawn. On advice of Ed I have tested KNppp+KBpp on a wing in stead of the center, but that doesn't alter the outcome.
• Ed casted doubt on the accuracy of the computer which calculates the ending notouriously faulthy. He is right about that in the sense that I cannot say that the outcome is 100% proven. But different engines have calculated the position 30 ply deep with over 100 million tablebase hits. I am convinced. But I must admit I'm somewhat biassed since the outcome of the computer is according to my reasoning.
  
• Both Ed and Likesforests feel that white has great winning chances in practical play with N vs B. Are they one-eyed kings in the land where only patzers screw up this drawn ending?
• Both felt that R vs R was a clear draw. Why do patzers play this ending well?
• The fact that Ed made a difference between center pawns and wing pawns shows that he has access to some secret knowledge which I haven't.
• The relative difficulty for humans to keep the draw in a N vs B ending in comparison with the easy to draw R vs R is not shown in the figures the computer comes up with.
  

Time to have a closer look at the parameters at hand. Thus far I have found:

• Piece activity.
• Distance to the promotion squares.
• Amount of pawns.
  

Besides that there are parameters which interfere with general rules.

• Unexpected mates .
• Forced trade of pieces.
• Piece sacrifices.
• The rim of the board.
• Exact placement of the pawns.
  

Piece activity.
Added piece activity on both sides tends to change the outcome from a win into a draw.

• ppp vs pp = easy win
• added K = not so easy win
• added K + minor pieces = quite difficult draw
• added K + heavy pieces = easy draw

How does that work?

Distance to the promotion squares.
Let's have a look at the following diagram.

diagram 1.



















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White to move.
Parameters:

• distance to promotion square: 1 tempo
  
• piece activity: 2 tempi
  

The black pawn needs one tempo to queen.
The white rook needs 2 tempi to perform een action.
Een action is one of the following:

• take possession of the promotion square.
• take possession of one of the squares between the pawn and the promotion square (not possible here).
• conquer the pawn.

The activity of a piece is reciprocal (1/x) to the amount of tempi needed to do something useful in preventing promotion. There are two area's where the rook is more active: on the e-file or the 2nd rank he needs only 1 tempo to conquer the pawn.

Amount of pawns.
What is the role of more pawns? The pawns are standing abreast at their initial squares to avoid complications as much as possible. Kings on e1 and e8 to elimante piece activity. Just to get a general idea:

• p vs - = mate in 22
• pp vs p = mate in 23
• ppp vs pp = +10.73 and moving up at ply 27
  
• pppp vs ppp = +2.25 and moving up at ply 28

The tendency seems to be that more pawns add complexity and put mate to the rear. This suggests that it is a good idea to trade pawns in order to try to win. You will probably have to wait with the trade of pawns until all the pieces are off. So the hierarchy of trades for the winning side becomes Q, R, BN, p. For the losing side it is either the other way around (p, BN, R, Q) or to avoid trades alltogether. Are there any maxims or rules of thumb that confirm or deny this?

This is chess

This post is some time overdue since I actually waited for a post of Phaedrus to throw this into the discussion. But since he needs more time I decided to make room in my head.

Quality and frequency.
I already told you about two important parameters of pattern recognition: quality and frequency.
Quality is about how decisive the recognition of the pattern is for the result of the game.
Frequency is about how often you encounter the pattern in a game.

Area.
There is a third parameter though: area.
Chess is divided in different area's like tactics, strategy, endgame and a lot where we have no name for. I'm pretty familiar with the most frequent patterns in the tactical area, but I used to be quite ignorant in other area's of the game.
Until lately I started to show some lapses in my ignorance due to study.
Yesterday I played a game against an opponent who is known for his tactical tricks. He had the following approach: he tried to lure me in a trick, and if that wouldn't happen he would try to trade off pieces in an attempt to draw. But I kept the complexity level low and simply avoided his tricks. He clearly had no clue what to do in such positions. He had no plan B. He wrecked his pawnstructure and started to trade pieces off towards what he thought to be a draw. But with no pieces on the board it would be a lost pawnending so I cooperated happily and won the game.

This shows that no matter how much patterns you know and how well, if it are patterns of the wrong area you will simply screw up. Even the little positional knowledge I learned from my latest experiments was a enough for a simple win. And he still doesn't know what hit him.
This is really satisfying. This is chess.

An article about the previous posts is in the making.

Investigating the parameters

I'm quite happy with the input of Ed and Likesforests, who force me to look deeper into matters. I'm investigating the general laws of the endgame and the parameters that play a role. That bears a suspect similarity with creating a few rules of thumb in order to get rid of some serious endgame study. But belief me, that's not what I'm after. So please don't be afraid that I shut down my mind while following ridgid rules.

You have to know the rules first before you can break them

I (the computer, that is) analyzed the following endgames with the aid of the Nalimov endgame tablebases. Only the first diagram has a forced win. All the other diagrams are drawn. White to move in all diagrams.

diagram 1
























Forced win for white

diagram 2
























draw

diagram 3
























draw

diagram 4
























draw

diagram 5
























draw

diagram 6
























draw

diagram 7
























draw

If you think away all the pieces and the kings, it is a simple promotion.
If you add the kings it is a not so easy forced win.
If you add the kings and two minor pieces black has difficulty to hold the draw.
But it is a draw.
If you add the kings and two rooks it is an easy draw.
If you add the kings and two queens it is an easy draw.

This suggest that the more powerfull the pieces are the more difficult it is to promote the extra pawn. I purposefully placed the pawns on their initial squares far away from promotion and the pieces on as inactive as possible squares. Maybe when you place the white pawns more forward and/or the white pieces and king on more active squares a forced win with pieces is possible.

All this seems to suggest a hierarchy in trades: the most powerfull pieces first. The problem in the positions above is that you cannot force the pieces to trade since they ar too volatile.

It's hard to be a penquin.

I'm experimenting a bit with templates since blogger keeps messing up my texts.


























Let's see if we can find some reasoning behind trading towards an endgame.

For reasons of convenience I start with the most common trades. That are the trades of pieces of equal value.


B x B
B x K
K x B
K x K
R x R
Q x Q

Underlying pawnending is a win.
Since the value of the pieces is equal, there must be something else that determines if a trade is beneficial. That beneficiallity is based on the underlying pawn ending. You have to ask yourself first "is this position won if there were no pieces on the board". I said a few things about that here and here some time ago. If the pawnending is won, you have a sustainable advantage and you can start to trade pieces until there are no pieces left.

Underlying pawnending is a draw.
If the pawnending isn't won but a draw, there are other matters that play a role to determine if a trade is beneficial:

• activity of the pieces.
• does the trade alter the pawnstructure.

Piece activity.

In the ending the piece activity is two fold: attacking, can a piece help to clear the road to promotion, and defensive, can your piece restrain or block an enemy pawn to prevent it's promotion. This piece activity is mainly influenced by the pawnstructure. Your own pawns block your own pieces, and squares that are under attack by hostile pawns are usually forbidden. The idea is to trade your pieces in such way that you keep the active ones while your opponent is saddled with the passive ones.

But before you can decide on trading you have to ask yourself wether the pawnstructure is fixed or volatile. If the position is very volatile because the pawns are not restrained or blocked, the piece activity can easily change by just moving pawns.

Pawn structure.

If a piece is defended by a pawn, the trade of equal valued pieces alters the pawnstructure. This can effect the outcome of the underlying pawnending and/or the piece activity. This should tell you if the trade is beneficial or not.

It is all so logical that I wonder why I haven't thought of this before.

No crenellation anymore

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I consider the metaphor of crenels and merlons to be busted.

There are two problems with it. The first thing is that you can't permit to use your pieces to do defensive work only. Like supporting the walls and keep an eye on the holes. If you keep your pieces behind your pawns, you leave the no man's land between the pawns to your enemy pieces. Which gives them the possibility to threat you without any risk. That's not good.

Secondly, when you keep pushing your pawns forward, your position becomes inevitably overstretched, sooner or later.

I'm always happy when I can formulate a verdict.

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I'm experimenting with a new method now. I focus on double purpose moves. I try to find moves that have both an attacking and a defending function. The idea behind it is that when you make a double purpose move while your opponent doesn't, you have effectively gained a tempo. Besides that I'm busy to map out which trades are beneficial and which aren't, in relation to the endgame.

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I will keep you informed.

Subscription

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I subscribed for a few tournaments: OSBO PK, Groningen and Corus. Time to boil the oil!

Johan van Mil

More about battlements

What a relief! A new system with most of my beloved gadgets and tools installed. Now I can catch up since I have thought alot about chess lately.

Maybe you wonder why I speak about battlements while I actually am studying the endgame. The reason is that I get a sense of what the endgame is all about. So I can't help to think about the middlegame and how it influences the endgame. And from there I start to think about the opening. I was never known for the habit of limiting my view:)

General scheme.

I use the metaphor of the siege as a guide to move. Sofar I encountered 3 idea's in practice. The first idea is:

Keep the intruders from the crenels.

Take the following diagram after 1. f4 e5 2. fxe5 d6 3. Nf3 dxe5 4. e4 Nf6 5. Nc3 Bc5 6. Bc4 O-O 7. d3 Ng4 the following position arose:

diagram 1

White to move.

Black plays opportunistic and tries to invade without preparation. If you can protect your invasionsquares well enough then there will come a moment that you can drive your enemy back. Here I played 8.Rf1. After black was expelled he was in some trouble.

The moving wall.

The second idea is to use your pawns as a moving wall. You keep your pieces behind your pawns, you keep an eye on the invasionsquares and you give the pawns extra support.

diagram 2























White to move.

It is my intention to play d3 and e4, thus moving my wall forward. How must I support my wall? If I play d3 right away, I lose a pawn on c3. I can't play d3 too early since I have to be carefull that there doesn't appear a black knight on e3. So I must find a move that protects both my existing wall (c3) and my future wall (d3 an e4). Qc2 is a move that accomplishes right that. In the game I played Qe1, which indicates that I'm not familiar with this line of though. The Queen doesn't protect d3 from there, and that got me into trouble later on.

Overstretching.

The third idea I encountered is overstretching. This is in fact the test of the viability of the metaphor.

diagram 3
























White to move

As you see I have moved the wall forward, keeping my pieces behind the wall and keeping an eye on intruders. The idea of this kind of play is to keep complexity low and to give the opponent a cramped position nonetheless. But when your opponent manages to create a breach in your wall all of a sudden your pieces who support the merlons and protect the crenels from invasion can become overworked since they have to assist in defending the breach too. Maybe that is why Nimzowitsch advocated overprotection? In the position above black played g5. White is still fine, of course, but in the following complexity I lost the thread and the game.

What should be the goal to strive for in a stretched situation where all of a sudden a breach occurs? Maybe the trading of pieces to take away counterplay? Since your pawns are closer to promotion they can become a power of their own.