Saturday, May 06, 2017

Harvesting subtleties

I'm slowly working my way through the 40 positions I have been investigating since Dec 3rd. Now I have a Tree of Scenario's, I have something to give the more subtle knowledge a place. It is remarkable how commonly usable this knowledge is.

Did you for instance know: A target is protected by two defenders. When you trade off one defender, the other defender becomes immobile.

When this kind of knowledge is discovered, it feels as being subtle knowledge. But when you think about it, it is actually rather surprising that you have never realized it before. It is no rocket science, and very obvious. And remarkably commonly usable.


Monday, May 01, 2017

TOS-1 Lack of space


The Tree Of Scenario's (TOS) has three main branches. Lack of space, lack of mobility due to function and lack of time. First I'm going to investigate lack of space. The typical examples of immobility due to lack of space are the trap and mate. For the sake of simplicity, I take mate as illustration.

Work on the box
We talked a lot about the imaginary box that is used to contain the hostile king. There are a few scenario's that are based on working on the box.
  • Work on the material of the box. Your own pieces are “soft”. Which means that the king can walk “through” them. While the king cannot walk “through” his own pieces. The “hard” pieces of the opponent are the perfect blockaders. Hence it is best to use the enemy pieces to build the box.
  • Plugging a hole in the box. Sometimes a king can skedaddle out of the box when he feels itchy. You must keep the box closed.
  • Breaking the box open. When the king is surrounded by its own pieces, you can't deliver the final check. In that case you have to pry the box open. With a sacrifice for instance.
  • Squeezing the box. When the king has too much room to manoeuver, you must shrink it.
For other pieces than the king, the box can sometimes be quite big. It can comprise the control of a whole diagonal or file.

Chasing the king
When the king is not in the box yet, you must chase him into it. Since the king is very sensitive for checks, you can chase him over quite a distance.

UPDATE

Function

What types of functions do we have? From the perspective of the opponent:

Defensive function

  • covering a piece
  • covering a square
  • blocking an attacker
  • keeping your attacker occupied with defense by attacking a piece that is defended by your attacker



Offensive function

  • Keeping your attackers busy with fencing off a counter attack.

 Scenario's
There are the following scenario's related to function:
  • Harass the functional piece
  • Exchange the functional piece for a less functional piece
  • Capture the functional piece, so you can exploit the fact that it can no longer exert its function
  • Win the piece since it isn't allowed to abandon its function
  • Deflect the functional piece by forcing it to exert one of its duties while abandoning the other duty
Somehow I have the uneasy feeling I'm forgetting something.

UPDATE II

Lack of time

Single target
In the case of a puzzle database like CT, a lot of problems are presented with a piece already hanging or being outnumbered. These positions are a bit unnatural, since they start in the middle of something. When you play a game, you know how the position came about. A single target has no time to escape since you have to move first. Usually there are two scenario's to complicate matters:
  • Before you can take the hanging or outnumbered piece, you must first fence off a counter attack
  • After you have taken the target, you have to fence off a counter attack

Duplo attack
A duplo attack has two targets which are attacked with just one move. The two targets and the attacker(s) have a complex geometrical relationship. The targets must be either unprotected or insufficient protected. Scenario's:
  • The targets can escape if one of them can make a tempo move
  • The targets can escape if one can protect the other while their value is equal or less than the attacker

Preliminary moves
Especially in case of a duplo attack, there are specific preliminary moves.
  • The target isn't yet standing on the target square, and is forced to walk the target square
  • The attacker isn't on the attacking square, and has to make one or more tempo moves to get there
  • The wrong target is on the target square, and by exchanging it, the right target is placed on the target square
  • Lines must be opened first with tempo
  • A combination of the above
Summary
A vast yet limited amount of scenario's is mapped out here. Of course the list is way too crude and bulky to be of any practical use yet. So that has to be the next step, summarizing this into a useful guide for the attention.

Saturday, April 29, 2017

Building the tree of scenario's

On December 3rd, 2016, I abandoned the salt mines and all other unproductive idea's for chess improvement, and started to build a logical framework where I can put my knowledge on. I finally found the tree of scenario's as a potential framework. I even heard myself say in the previous post something like "there is a limited amount of scenario's and a limited amount of questions that need to be asked to interrogate the position".

Since December 3rd, I have analyzed about 40 positions extensively. A lot of little gems were unearthed. Now it is time to go back to these 40 positions, in order to derive a decent tree of scenario's from it. Only with such coherent framework of chess knowledge, I can hope to begin some serious tactical training.

The first step will be to erect a complete tree with all crude observations hanged in it provisionally. The second step will be to optimize all observations, so that the tree will act as a handy summary of adequate and relevant knowledge. The third step will be to distill a training method from it.

I'm working on the first step right now.

Patience

Friday, April 28, 2017

Simplify this!

What do the three types of immobilization have in common?

Lack of space
When a piece is under attack and has lack of space, it has a lack of time too. Imagine that your opponent was allowed to do a few moves in a row, while you had to pass and wait, then he could free himself.

Function
When a piece is immobile due to its duties it can't abandon, it is comparable to a lack of space. Imagine that your opponent was allowed to do a few moves in a row, while you had to pass and wait, then he could free himself.

Lack of time time
When two target pieces are placed in an unfortunate way, they can be both attacked at the same time with a duplo attack. Imagine that your opponent was allowed to do a few moves in a row, while you had to pass and wait, then he could free himself.

What these three times of immobilization have in common, is that they are temporary. They all lack the time to do all necessary actions. That is why special moves, aka duple function moves, are paramount. Both for the defense and the offense.

Sitting duck
I have been inaccurate about the sitting duck. A sitting duck doesn't equal the target in al situations. In situations of lack of space and duplo attacks, it does. But when a piece has two functions which are mutual exclusive, the target is often not the sitting duck, but the pieces it is protecting.
So the question is: how to exploit the sitting duck.



Diagram 1. Black to move
r3k3/p4p1p/4p1r1/2p1n3/4nN1Q/P1PqP2P/3B2P1/2R2R1K b q - 1 1
[solution]

points of pressure d2; f1; g3
lines of attack g-file; d-file; d3-f1-diagonal
function c1 defends f1; black Q defends e4
sitting duck d2

How to exploit the sitting duck?
I will update later. Comments are already welcome.

UPDATE
The white bishop is hanging. It is the sitting duck. The thinking starts with the question "how to exploit the sitting duck". There is no reason to think about an other idea. Unless you can prove that the bishop can't be taken.

A hanging piece is a common situation on CT. Is usually the result of an incorrect sacrifice. It is a typical example of a piece that is immobilized by lack of time

The normal reaction to a hanging piece is to take it. Cash it in. But there can be situations where the the capture should be postponed, since you first have to deal with a counter attack. As is the case in diagram 1. Notice how backward thinking diminishes the amount of things to think about.

We can't avoid to think from the point of view of white here. What are the points of pressure from whites perspective?
points of pressure e4; g6; e7; e5
lines of attack h4/d8; h-file
function Q - e4; Ne5 defends g6; h7 defends h8

1. ... Qxd2 2.Nxg6 is a triple function move. It attacks e4; e5 and threatens Qe7#

That indicates the three things black has to prevent before he can take the bishop. He can use as much moves as he needs, as long as he keeps the initiative. Since whites threat comprises mate on e7, keeping the initiative can't mean anything else than giving a check.

1. ... Ng3+ solves the first problem: it saves Ne4 for the moment with tempo. What is more, it chases the white king to the line of attack e3/g1. Which gives black a chance to gain a tempo while defending his knight on g3. Notice how important this is.

1. ... Ng3+ 2.Kg1 Qxd2 3.Nxg6 Qxe3+ the knight on g3 is save and the king has to move to h2. The rest can be easily calculated.

Backwards thinking minimizes the calculation by pruning the tree of analysis drastically. You don't have to consider a lot of options. The prize for this is that you must be very accurate about what a move actually accomplishes. Especially what effects it has on the initiative

The questions you have to ask your self are not rocket science. You have to know the standard scenario's how an attack or defense develops. We need these questions to pop up automatically. There are not that many scenario's or questions. We need to cultivate our sense for the initiative. And we have to cultivate accuracy. Two skills that aren't acquired overnight.


Friday, April 21, 2017

Building the system

We made a quantum leap in understanding Tals adage in the previous post. His adage is based on hanging pieces, and I didn't realize how important that is. Despite I have postulated that in earlier posts, where I made a distinction between action moves and postponement moves (although I didn't call them action moves back then). Only now I start to appreciate how this distinction prunes the tree of analysis drastically. Postponement moves don't alter the outcome of the combination. They just postpone it. Postponement moves are normal moves on a tit for tat basis. A CCT-move followed by an answer in order to neutralize. The normal moves don't need calculation. We must be aware of the special moves. The moves with a duple function. Since they do change the outcome of the combination.

The tour the force I am trying to accomplish, is to merge the plf system with Tals adage. To that end I am going to investigate a few positions of which I think it should be possible to unearth their simplicity, although they now lead to failure or enormous time consumption. The goal is not to solve the position, but to bring the necessary logical reasoning in accordance with Tals adage.

Tals adage is limited to hanging pieces. Can it be extended to mate positions?



Diagram 1 black to move
2r3k1/5ppp/p7/1prRq3/4n3/P1N1P2P/1P3PP1/2RQ2K1 b - - 0 1
[solution]

UPDATE
points of pressure c1; c3; d5
The most juicy point of pressure is c1. Is does not only contain a fat rook, it is the entry point to the line of attack  c1 - g1, where a duplo attack (pinning the queen to the king is waiting to be exploited.

lines of attack c-file

functions
Knight defends c1 and d5
Queen defends c1 and d5
Both pieces are overloaded, since they can only perform one of their function while neglecting the other.

Counter attack chances
Black must prevent the entry of white to the line of attack 8th rank

Sofar for the initial scan of the position
The sitting duck is the white knight. It cannot move due to Rxc1.
This means that Rd5 is outnumbered. But how to take? Normally you would take the lowest rated piece, and normally that would work, but here it gives white a counter attack by entering the line of attack to the black king.

1. ... Rxd5 2.Nxd5 Rxc1 3.Qxc1 gives white access to the 8th rank

So 1. ... Qxd5 is the move. Normally you wouldn't use the highest valued piece for the capture. But since c1 is the entry point to the line of attack against the white queen and king, the black queen can be regained under all circumstances.

To link this to the adage of Tal would lead to a rather far stretched and artificial sounding explanation. Yet my gut feeling tells me that there is a connection. Just give me some time to gather my faint thoughts.

Saturday, April 15, 2017

They can only take them one at a time

There is a special breed of positions that gives me the feeling that I have a special talent to make the wrong choice. That is probably not true, but it certainly feels like it.

The past investigations made me hypothesize that the prodigy in chess has learned some tricks how to prune the tree of analysis. My remedy based on this hypothesis, making a good habit of looking for the convergence squares of the second order when you are stuck, does certainly work. But not in every position! I will give an example of a position that needs another way of pruning.

Diagram 1 black to move
r1r5/4qppk/p1R1pn1p/1p6/2N1PB2/bN3Q1P/P4PP1/2R3K1 b - - 0 1
[solution]

The title of this post is the adage of Tal concerning the pieces he left hanging. This adage tells me that he had a way to prune the tree of analysis in a drastic way. That must have made his calculations a lot easier for him. If you don't worry about things that don't need worrying, then the mind will be fried for more constructive work. I'm going to try to find out what his pruning method comprises. What does his adage mean in practice?

Feel free to comment already, I will update the post later.

UPDATE
Mutual captures are difficult to assess. For long, I'm looking for methods to simplify the thought processes involved. The capture is the standard move here. I'm looking for moves with a duple function. Captures that capture an attacker. Captures that capture a defender. Captures that attack a new piece. That kind of stuff. So I made a provisional list with extra functions that can be performed besides the actual capture. It are the moves with duple functions which play the decisive role.

The move 1. ... Bxc1 performs a double function. It captures the rook, and it saves the attacking function of the bishop, which otherwise wouldn't be preserved due to 2.Nxa3, which is a duple functional move too: it saves the white knight and captures a black attacker thus saving Rc1.

There is another move that has a double function which does roughly the same:
1. ... bxc4 captures the knight, and it saves the attacking function of the bishop, which otherwise wouldn't be preserved due to 2.Nxa3
 The problem with 1. ... bxc4 is that is allows 2.Rxc4 which is a duple function move:
It saves Rc1 and Nb3 with one move. This duple function is not yet found in the scheme though.

So I haven't found anything substantial yet, but at least you now know in what direction I'm looking. To be continued.

CONCLUSION
It took quite a few days of struggling, but finally I have seen the light. Let's see how we can apply the adage of Tal here. "Both you and your opponent can take only one hanging piece at the time."

Black has 3 pieces under attack. i.e. 3 white pieces are hanging.What is the most likely outcome of that situation: Black can round up 2 pieces, while 1 white piece will escape.
  • First ply: black takes a hanging piece
  • Second ply: white saves a hanging piece
  • Third ply: black takes another hanging piece
This totals to +2 pieces for black. Since black started with 1 piece down, the net result for black will be +1 piece.

That is, when normal moves are played.
What are normal moves? I call single function moves normal moves. When a move accomplishes exactly 1 thing. In opposition to special moves, which are duple function moves. A duple function move accomplishes 2 things.

In fact it doesn't matter which piece is taken first by black, since after 3 ply, he will have taken 2 pieces, while white has saved 1. But only when normal moves are played.

In this position, white has a few special moves up his sleeves. That makes the choice of the first piece to take not indifferent. In two of the three lines, white can save two pieces with one duple function move:

1. ... Rxc6 2.Nxa3 the last white move accomplishes two things with one move:
  • it saves the white knight
  • it captures the attacker of Rc1
1. ... bxc4 2.Rxc4 the last white move accomplishes two things with one move:
  • it saves the hanging Rc1
  • it captures the attacker of Nb3
1. ... Bxc1! 2.Rxc8 It saves Rc6, but at the cost of NOT taking the bishop on c1. It's a single purpose move.
2. ... Rxc8 and now white cannot both take the black bishop on c1 AND save his knight with one move.

I'm pretty sure that Tal has used this kind of simplification in his thinking.

Wednesday, April 12, 2017

Convergence squares

If I look at the diagram of the previous post, I find it difficult to express what is needed. After studying this position for quite some time, the moves are so evident that I simply cannot understand why I didn't see the simplicity of the position before. At the mean time, I fully acknowledge that there is no guarantee at all, that I will able to see the simplicity of similar positions in the future. I can impossible tell what I need to learn from this position that will be transferable to other positions. It seems that words are a too lousy vehicle to do that.

Maybe that is a positive sign. When something descends from the conscious to the unconscious, we don't know how that happens, and words cannot express how it works. You learn how to push the breaks and to shift gears when you turn right, but you can't possibly tell how you calculate the right speed, how you judge the right noise of the engine and how you calculate the correct power to apply to push the steering wheel. But then again, maybe I'm just deceiving myself here.

One point springs out, when I considered 1. ... Ne6, I didn't realize the importance of f7. The alternative point of pressure f7 gives white a counter attack (1. ... Ne6 2.Rd7). This means that it must be good to cultivate the habit to look at the points of pressure

And maybe that is how we should formulate it. We have to develop a few good habits. These habits are mainly visual, it seems. Aox said:

"This "splitting of the whole problem in a sequence of sub-problems and then to solve them" costs---->time!!"

He  certainly has a point here. We must not look for an algorithm that guides our logical thinking. I have tried that a few times in the past, and the trade-off between better thinking and time usage has always been negative. Not to mention the drain of mental energy.

This means that it is not quite clear how to proceed. As said, it is probably best to cultivate a few good habits. The algorithm I'm busy to develop isn't a goal in itself. It is meant to identify the habits we need to cultivate.

Take for instance the following position:

Diagram 1. White to move


4r1k1/pqr1pp1p/p1Nn2p1/3P4/5QP1/8/PP1R1P1P/4R1K1 w - - 1 1
[solution]

What habit do we need to cultivate in order to transfer something from this position to similar positions? Feel free to comment already. I will update this post later.

UPDATE
What do we fancy that our RC-chess module should shout in our ear here?: Rb8!!

I have seen this mechanism working over and over again the past months. The moment my attention is guided to the right place of the board, the missing piece of the puzzle immediately pops up.

Every square of the board is screaming for our attention. Some squares shout harder than others. b8 is not screaming hard enough, so its sound drowns in the overall background noise, and is overpowered my the squares that seems more interesting.

What is so special about b8? What makes it different from c8 or a8? The difference is of course that the white knight and the white rook converge at b8. Chances that you can post a rook on b8 safely are higher than that you can post it on c8 or a8.
We can know beforehand, that converging squares are going to play a crucial role in any combination. So if you are stuck while forward thinking, you can start to look at the converging squares of the second order. If the squares of the first order don't work. There is no reason to look at non convergence squares.

The unconscious mechanism to let pop up the right solution is already well developed and put into place. The only thing that is missing  to ignite it, is the little spark of attention that leads us to b8.

Of course it would have been nice if the black queen was recognized as a sitting duck during the initial scan of the position. But I already identified the points of pressure and the lines of attack as a toolkit to help to find the most immobile pieces. The black queen has five squares where it can stand safely, so it doesn't look immobile until a rook appears on b8.

Robert Coble cited mr. Lasker:

THE METHODS FOLLOWED IN THE ANALYSIS OF A GIVEN POSITION BY COMBINATION AND BY THE CREATION OF PLANS ARE DIFFERENTIATED BY THE DIRECTION OF THE UNDERLYING THOUGHT. THE COMBINATION-PLAYER THINKS FORWARD: he starts from the given position and tries the forceful moves in his mind; THE POSITION-PLAYER THINKS BACKWARD: he conceives a position to be arrived at and works toward that position of which he is more conscious than the one on the board. He "sees" successive stages of the position aimed at and he visualizes the stage in a reverse order. If one position, according to his plan, is to follow another he "sees" the one that is to follow first and he deduces, as it were, the anterior position from it.

 To be honest, I was a little worried by this citation. It seemed as if the adult-chess-tactics-improvement-method I'm developing is different from the young-prodigy-way-of-chess-tactics-improvement-method. It is unlikely that nature is so prodigal that it allows two different ways, one by forward thinking and one by backward thinking, to learn the same skill, and that the end product of both ways will be equally effective.

But Aox put me on the right track again by pointing out the danger of introducing slow thinking into the method.

I'm sure that the young prodigy has picked up a few obvious idea's along the way, and has made looking for convergence squares of the second order a habit long ago, while even not remembering that fact consciously later on. And we should do the same.