Applying logic

At Whitsuntide we played a tournament of 7 long otb games. I used the games to check my latest findings. It greatly reflects that my theoretical findings are confirmed in practical play. I scored 4 out of 7 with no draws. TPR was 1754.

Winning by mistake.
All games had in common that the only way to win them is when the opponent plays a suboptimal move. This means you cannot win a game by finding a move where your opponent has no answer to, but you have to play optimal moves yourself all along until your opponent makes a mistake. Be it a tactical or positional mistake. Your opponent has to defy logic in one way or another.

Three areas of improvement.
I found three areas to improve my chess in my games.

• Learning unknown territory.
• Replacing unfruitful opening lines.
• Applying logic.

These three areas are not equal. The first two can be fixed relatively simple. Applying logic contains the real meat of the matter and has not an easy fix.

Learning unknown territory.
There are a few areas in chess that are relatively new to me. Mainly this consist of certain parts of the endgame. Basicly this is about good old school pattern recognition. The reason I haven't added the concerning patterns to my database yet is due to the low frequency of occurrence of the patterns in real play. Adding these patterns is just a matter of doing. It is an easy fix.

Replacing unfruitful openinglines.
I found a certain line in my openingrepertoire where I always come into trouble. Sometimes I win, sometimes I loose, but I feel uncomfortable and it feels like I'm gambling. I changed the order of the moves so I can now avoid this specific line in favour of a line where the queens are traded off very early in the game. This will be good for my endgame experience too, so I hit two birds with one stone. If my opponent avoids the queentrade I'm back in the old lines with changed move order.

Applying logic.
It turns out to be difficult to find the logic in a position. Things go wrong when I cannot find the logic or when it takes too much time and energy to find the logic. When I cannot find the logic I play like a headless chicken. This is not uncommon, by the way. When it costs too much time and energy to find the logic I will get troubles later in the game. I run into timetrouble or I become blunderprone due to lack of energy.

Let me give an example of not finding the logic in order to know what we are talking about.

White to move, I'm black.
My latest move was Qe3, in order to attack the pinned knight twice.
I totally missed that white can play Bd5 here.
Even after Bd5 black is still winning, but that is not the point. The point is that I missed a logical answer to the pressure on Nd2.

If I hadn't seen this position, and somebody described the position to me in a more abstract way, like "A piece is pinned and attacked once more than it can be defended, what can you do to free yourself" I certainly would look at ways to extinguish one of the attacking pieces. The logic is easy enough, but the mind isn't disciplined enough to always look for the logic.

This is really the way to go. Guide your thoughts and attention by logic in a systematic and disciplined way. Do it right first, speed will follow automaticly.

A few answers to Bright Knight

BK said:
It is not at all clear that it is easier to improve by a fixed percentage on harder problems than it is on easier ones. Back in the days of the Bain Experiment, I found that reducing my solution times by a fixed percentage for my first pass through the first batch of problems gave a good fit to my solution times on the first passes through the later batches of problems. That appears to be roughly right for Woolum too.

I advocate to train every specific task that you have to perform in a specialized way. Optimized for that specific task. Preventing diminishing returns.

The first thing to do is to determine which tasks we are talking about. Every tasks has its own specialized sets of patterns associated with it, and if you don't find out which patterns to learn, chances are high that you don't learn these patterns at all.

First task: 20 tactical elements.
The first task we have identified is that we have 20 - 30 elementary tactical themes, depending on the source. Let's round it off to 20 usefull themes. In my opinion these are trained best according to my speedtraining method:
Make per tactical element a separate problemset with rating <1200. Solve these problems as fast as possible, untill you reach a speed of <4 seconds per problem. 1000x per tactical element is probably enough to recognize it everywhere and fast. Let's say a problem takes 20 seconds at average. This leads to a total time of 20 elements x 1000 times x 20 seconds =  111 hours to master this task.

Doing the same with combinations I consider to be useless, since there are way too much combinations.

Doing problems higher rated than 1200 is useless for this task. Here the law of diminishing results sets in soon.

Second task: guiding your mind for duplo attacks.
I identified duplo attacks as one of the three ways to gain wood. Traps and promotion being the other two. This means that you have to scan a position for all its duplo attacks. There are 5 different duplo attacks (double attack, discovered attack, pin, skewer, rontgen attack). The recognition itself of these 5 patterns is already taken care of when training for the first task. You only have to make it a habit to scan for all of these duplo attacks in stead of stopping short once you get distracted by one of them which looks promising.
I use high rated problems for this for a starter. Once I have identified all duplo attacks I store both the position and the duplo attacks as a flashcard in Anki and train them further with the aid of Anki, without going back to CT anymore.

Third task: making one of the duplo attacks work.
At average there are about 6 duplo attacks in a >2000 rated problem. Only one of them is winning. At this stage is is my task to find out which one and how I can make it work. For this I need all tactical elements that I have learned already in task one and that can act as some prelimanary move. Besides that, some conscious thinking is probably needed here in order to make it work.


Fourth task: identifying the focal squares.
The fourth task is needed to assist task three.
Once I know the target, I must find the way back to the attacker, finding the focal points along the road. These focal points give me clues to the preliminary moves I ave to make before the combination will work. I must identify the defenders of the focal points and find a way to annihilate them. I must identify where my own pieces get in the way and clear them, etc..
I use high rated problems for a starter. Once I have identified the focal points I make a flashcard with the position and the focal points. From there I train it with Anki.

Fifth task: learning the mating patterns.
This has great similarity with task one.
If I'm not mistaken there are 29 different mating patterns that must be learned. Speedtraining with <1200 rated problems will do the job.

Sixth task: learning the patterns that are associated with promotion.
This has great similarity with task one.

Speedtraining with <1200 rated problems will do the job.

Seventh task: Chasing the king.
I just discovered this as a problem. It has its own associated patterns. First I must formulate a search algorithm. In order to find one I use high rated problems at CT which are mates. Usually> 4 movers.
Only once I have found a suitable algorithm, I can start to think about a method how to train them.
To give you an idea of the complexity of the matter: a search algorithm must guide you through this testposition in order to be usefull.

Eight task: positional play.
Under construction. See previous posts.

In summary:
Speed training with tagged low rated problems is suitable for most elementary patterns. High rated problems are used in two cases:

• As a starter to extract patterns that you will only find in complex problems. The actual learning is done with flashcards and Anki.
• During investigation. When you are investigating new tasks and defining new search algorithms. This is only temporarily.

It is true that you have an average of about 3 minutes per move in a standard time limit game, but how much time can you afford to spend on checking that your chosen move is proof against a tactical shot? I would have thought that 1 minute would be optimistic. Hoping for a sixty fold improvement in your solution time is too optimistic in my opinion.

That's all way too ridgid and too theoretical. We will find this out in an empyrical way.


What failure rate is acceptable when checking for tactical shots? 10%, 1% or less… There are typically about 40 moves in a game, and many or most of them could fall foul of tactical shots. If you accept a 10% failure rate, you are going to “blunder” once or more in most games. Even if you get your failure rate down to 1%, you will regularly lose to tactical shots.

Again way too theoretical. Not all positions call for an ability to solve tactics at 2300 level. But sometimes tactics just must work or you loose. If I look at the Polgar middlegame brick, I could flaw about 25% of the tactics that were presented there with the aid of Rybka. This means that both the grandmasters who played the game, the grandmasters that annotated the game in the Informator and Susan Polgar who checked the problems for the book overlooked the flaws. When both you and your opponent miss the same tactic, the tactic is irrelevant for the game.

Chasing the King

.
.
.
.
In order to enhance the speed of solving tactical problems as much as possible, I work with high rated (2300 - 2400 std rating) problems. These often take me half an hour to an hour to solve. If I can speed that up to under 3 minutes, I'm 10-20 x faster. With easy problems it is much more difficult to speed up the same percentage. 3 minutes is the average time you have per move in a long OTB game. Another advantage is that when you need an hour to solve a problem, you can use a stopwatch and a logbook to write down what it is what you are actually doing and what exact costs so much time.

My search algorithm is actually developed for duplo attacks and not for traps. And it shows. Whenever I have to chase the king, I'm starting to consume time and to make errors. (I consider a mate to be a special instance of a trap.) This means I will have to work out a separate search algorithm for chasing the king. I will make a set of high rated mates with >4 moves to test it.

Tactics flow from a positionally superior game

In my quest to define an intelligent search algorithm for positional chess I had to swallow another disappointment.
I bought the book Chess Blueprints: Planning in the Middlegame of Nikolay Yakovlev.

I intended to make flashcards of the 188 blueprints he provided. Until I discovered that the author didn't computercheck his book. What's the use of learning the blueprint of a positionally won game when in reality you are loosing the exchange in that particular position. I didn't expect that anno 2010 (the date of publishing).

So once again I will have to think for myself. Let's see if we can find a natural hierarchy for chess moves. What do you think about this:

• Tactics.
• Targets.
• Invasion points.
• Open lines.
• Space.

Tactics.
In the end, you will win a game by executing a tactic. If there is a tactical combination around, it usually has the highest priority. Fisher said: Tactics flow from a positionally superior game. How does that work? How does one prepare a position for that?

In essence the pieces of the enemy are too volatile to catch them. Under normal circumstances you will never be able to force an enemy piece into a tactical combination. Unless our opponent makes a clear mistake we never can win a piece this way. This gives the first clue for what we should try to accomplish. We must enhance the probability to get a combination flowing. In order to do so we must restrict the possibilities of the enemy pieces while at the same time we must enhance the possibilities of our own pieces. There are three fundamental different ways to restrict the enemy pieces. In order of hierarchy:

• Tactics. Your opponent cannot place a piece on a square where it can be forked by a pawn. If a bishop in front of a king is pinned, it can't move etc..
• Obligations in relation to targets. If you can bind an enemy piece to the defence of a weak pawn, you effectivily have restricted it's possibilities.
• Space. When there are no tactics around and there are no weak points to attack the only way to limit the possibilities of your opponent is by gaining space. Of course you have to be careful that you don't overstretch the position by claiming more space than you can defend.

Targets.
Since pieces are too volatile, the  natural targets of the chess games are the weak pawns. Piece activity is closely related to targets. No target, no piece activity. These are the stages of handling a target:

• Induce a weak pawn.
• Fixate the target.
• Attack the target.
• Conquer the target.

In the middlegame you seldom manage to actually conquer the target. But the obligations that derive from the defense of the target limit the possibilities of the defending pieces. That can become killing by itself.  The more targets there are, the more difficult it is to defend them all in time.

The road to the targets.
In order to attack a target, the road from the attacker to the target must be cleared. That road consists of the following elements:

• Open lines and diagonals.
• Invasion points.

Both are useless when they are not in connection to a specific target.
Both are useless without an attacker that makes use of them.

Terminology.
I reserve the term target for a piece or a pawn.
The term weakness I reserve for a weak pawn, an open line or diagonal or an invasion point.

Space.
When there are no targets to work with you will have to work with space. Occupying the center, for instance, is meant to improve the manoeuvring space for your own pieces, while it denies space from your opponents pieces. Pawns are the pieces that divide the space between you and your opponent. They decide between your own pieces too which piece has mobility and which piece has not. As long as pawns are mobile, there is no definite advantage for one piece above another. Only when the pawns have become blocked, the position of the pawns has become static. Only then you can value the mobility of a piece in a more definite way. I.e. say which piece is good and which is bad.

Conclusion.
We have said enough about tactics already.
The next logical step is to look at weaknesses as defined above: weak pawn, an open line or diagonal or an invasion point. We have to master the patterns that govern these weaknesses and define a logical search algorithm. It all starts with targets and their stages, of course. Then the fight for open lines and invasion points in order to attack them.
With space we can deal later. Maybe in combination with the opening.

New ATH FIDE estimated

.
.
.
.
.
.
.
Since my new approach to study tactics my FIDE estimated ATH increased from 1798 to 1844.
The graph above gives you a clue how to interpret these figures.
46 points in one week, not too shabby!

My new approach doesn't cover long king chases very well.  I'm very bad at it either. Maybe I must find an apart search algorithm for that.

Applying the method to positional chess

Cure tactical flaw.
In the previous post I found a major flaw in my approach to tactics and I belief I have found the way to cure it at the same time. The flaw is that I act as a headless chicken when investigating a tactic. The cure is to look in a systematic way. I expect that it will take a few months to cure.

Preventing radio silence.
Since I don't want to have a radio silence during these months, I will think out loud about the ensuing step. Can we deploy this method to positional chess too? I see no reason why not.
Today I read all my posts I have written sofar about positional play (quite a lot!).

What is the goal?
The first problem we have to solve is to find out the core of the matter. My breakthrough in the previous post came about when I realized that I must be on the lookout for one of the six methods to gain wood. Without one, there can be no gain of wood hence no tactic. Can we find an analogy in positional play?

In my blogposts I found no less than six different appoaches to the matter. Six schools of thought. We must indicate one as being the best or find a way to reconcile them.

• Improving chance.
• Pawn targets.
• Accumulating little advantages and convert them to one big advantage.
• Preparing tactics.
• Treat a positional target as a tactic.
• Fixed list with positional elements.

Let's investigate this list.

Improving chance.
The pieces in a  chessposition are fast and volatile. Too fast and volatile to get them. By denying the pieces space their possibilities are limited. Limiting the possibility of pieces to react to attacks enhances your chances. This is closely related to piece activity. The pawns dictate which piece is active and which not. With pawns you can take manoeuvring space away from the hostile pieces. Overall this seems to be a good strategy. It is not a basic positional element. It consist of basic positional elements though.

As long as the pawns are mobile, it is difficult to say whether a piece is good or bad. Only when the pawnstructure is fixed you can say something about that.

Pawn targets.
Both the King and the pawns are slow moving. They are the natural targets of the chessgame. The pawns especially since their mobility is limited to 3 directions at most, often less. The King is vulnerable since every piece can act as an attacker. The stages are:

• Induce a weakness.
• Fixate the weakness.
• Exploit the weakness.
• Conquer it.

Attacking two weaknesses alternately is best.
Attacking a weakness leads to obligations for the enemy pieces. That is another way to enhance chance and limiting posibilities.
Looking around for the possibility to create weak pawns definitely is a basic positional element.

Accumulating advantages.
Accumulate many little advantages and convert them into one big advantage is an idea from the Botvinnik school, if I'm not mistaken. I read somewhere an article from a grandmaster lately who said that this idea was outdated. I tend to believe him. At first the idea of accumulating advantages  sound very logical. But in practice it is much less clear how to work with that. For now I forget this idea.

Preparing tactics.
How do tactics come about? Where do you have to place your pieces?
Must you set up a battery beforehand?
Improving piece activity in itself is a pretty vague description. Sometimes your pieces seem to be active like hell but they accomplish nothing. Piece activity without a relation to a specific target is useless.
Due to the fact that pieces are so volatile I don't think you can prepare a specific tactic by setting your pieces ready for it. That idea is usefull for slow moving targets like a pawn or the king, but the other pieces are too fast. You cannot force them into a tactic. Unless of course their mobility is greatly reduced due to lack of space or obligations.

Treat positional target as a tactic.
It is a charming idea. Just like you can win a piece with a knightfork you should be able to make a knightfork where one of the targets is replaced by an outpost square.
Allthough charming, I don't think it works that way.

Fixed list with basic positional elements.
Such list could look like this for instance:

• Open up lines/diagonals.
• Occupy an open line.
• Challenge the hostile occupation of an open line.
• Create outpost.
• Improve your worst piece.
• Sac pawn to open line or clear square.
• Restrict opponents pieces.
• Claim space.
• Create pawn targets.
• Sac pawn for passer.
• Color complex.
• Lead in development.

Summary.
From the given schools of thought I think that a fixed list with basic positional elements resembles a list with basic tactical elements the most. The can have the form of patterns. Hence we can learn them the same way as we learn the tactical patterns. If there are any usefull idea's in the other five schools of thought we can decompose into new basic positional elements and add them to the list.

A systematic approach to the move order problem

The move order problem.
In the previous post and its comments we saw what the core problem is when calculating. We recognize all kinds of patterns, but we have trouble to find the right move order due to the vast amount of possibilities. It takes too much time to investigate all possibilities.

Brute force.
Munich proposes to solve this problem by brute force. This means that he still wants to investigate all posibilities by trial and error, but tries to speed up the process by learning all kinds of patterns by heart.

Search strategy.
What I propose here is to add intelligence. Can't we find an intelligent strategy here that outperforms the brute force method? I have tried the brute force method myself for years and walked into the law of diminishing returns. If we are able to prune branches we can speed up the process by not calculating some lines. In stead of running around like a headless chicken (which is my usual state when in trial and error mode).

Of course I can't present you a ready to roll method straight from the start. But if we join our efforts we might be able to crack the problem at hand.

Automation of the strategy.
Once we have found a strategy we will of course find new ways to automate it and we will discover patterns that are related to this strategy and that can be learned by heart. But later is early enough to worry about that.


3 types of tactics.
There are only 3 types of tactics. Methods to gain wood.

• The duplo attack which is based on performing two attacks at the same time while the opponent can defend against only one.
• The trap which is based on lack of space.
• Promotion.

These 3 methods have in common that they all work with attackers and their matching targets. Lets see if we can work out an example.

White to move. You can find the solution here.

First step: identify the attackers and their targets.
I  use the following method: if an attacker was able to make two moves in a row, which pieces would he grab? If an attacker can't grab a piece within two moves I consider it to be irrelevant.

 

Attacker	Path	Target
Ra8	-	Bc8
Ra8	c8	Qd8
Ba3	-	Nf8
Ba3	f8	Bg7
Ba3	e7	Dd8
Nd5	e7	Kg8
Nd5	e7, b6	Bc8
Nd5	f6	Kg8
Nd5	f6, c7	Re8
Nd5	b6, f6	Nd7
Nf3	e5	Nd7
Bg2	h3	Nd7

We don't know yet which of these attacker-target combinations play a crucial role, but the combinations that do must be part of this list. This means we have ruled out a whole bunch of pieces that aren't worth investigating. Hence we pruned a lot of branches already. We can prioritize this list. The combinations with the highest target value and the lowest attacker value are the most interesting.

Step 2: Identify the duplo attacks, traps and promotions.
We know that in order to gain wood the attacker-target combinations must be part of a duplo attack or a trap or a promotion. It is easy to see that there are no pawns ready to be promoted. There are two pieces about to be trapped: the black queen and Bc8. There are the following duplo attacks possible:
Pin Ra8 Bc8 Qd8.
Knightfork Nd5-e7-Kg8-Bc8
Knightfork Nd5-f6-Kg8-Re8
This leads to the following shortlist:

Attacker	Path	Target
Ra8	-	Bc8
Ra8	c8	Qd8
Ba3	e7	Qd8
Nd5	e7	Kg8
Nd5	e7, b6	Bc8
Nd5	f6	Kg8
Nd5	f6	Re8

Again we managed to prune a whole lot of branches.

Step 3: Identify problems on the route.
We start with the highest rated targets.
Knightfork f6.
Let's investigate the knightfork on f6. If you look at the defenders and attackers of f6, black has the upperhand. There are 3 defenders against 1 attacker. There is no way to annihilate those 3 attackers.
Knightfork e7.
There are 2 attackers and 2 defenders. If I manage to annihilate 1 I have the upperhand.The Queen is overworked since it has to keep an eye on both Bc8 and e7.
Pin Bc8
In order to take advantage of the pin I must attack the bisshop one more time extra. I can do this only with the white knight on d5. There are 2 routes: via b6 and e7.
Black defends b6 twice so I can't get the upperhand there. e7 has already been investigated.
Taking the bishop with Rxc8 forces the queen into the knightfork e7 and diminishes blacks control over e7.
Trap Qd8.
With Be7, the Queen is trapped. The problem is that I don't have the upperhand on e7 yet.

Again we managed to prune a few branches.

Step 4: Identify the candidate moves.
The candidate moves that are left are now:

• Ne7
• Be7
• Rxc8

We can be sure that if there is a winning tactic that it must start with one of these three moves.
From this moment on I'm inclined to use brute force and find out which move is the strongest by trial and error.

Conclusion.
By not starting to calculate as a headless chicken right away we managed to prune the tree back from the 41 possible legal moves to 3 serious candidates. Without any serious calculation yet. We have needed pattern recognition along the way, but the pruning itself happened by reasoning.
The reasoning itself is at this moment a slow process. The next step is to automate whatever is possible from this process of reasoning. I'm sure if I do 100 problems this way, my mind will automate parts of this process. The move order problem isn't quite solved. But we have pruned largely the possibilities to investigate.