Sunday, January 15, 2017

It all starts with the targets

Let's have another look at the diagram we are investigating, and especially at the PoP a7. Btw, I changed the use of colors a bit, in order to take into account those who suffer from color blindness. I reckon most people should be able to distinguish between the colors now.

White to move
Legenda:
brown square: (potential) attacker of a7
blue square: defenders of a7
brown dot: PoP
yellow dot: colors brown during the investigation, since it turns out to be just another PoP
red dot: attacking square

B.A.D.
a7 is B.A.D. (Barely Adequate Defended). How can we exploit it?

First attempt: harass defenders
There are two defenders, K and B. They can't be forced to give up the defense of a7, while maintaining the same pressure on a7.

Second attempt: add attackers
How can we pile up against a7? The only attacker we can add is Qh7. Qh7 makes that a7 is outnumbered. But if a7 is outnumbered after Qh7, it is equally true to say that g8 and h8 are outnumbered after Qh7. So g8 and h8 are just another PoP, and should be treated accordingly.

Qh7 reliefs R e7 from its duty to defend b7, so now e8 is outnumbered too.

Of course the queen can't move to h7, as we already know.

Discovery
If you look close at the PoPs (Points of Pressure) in the position we are investigating, I can't help to get a feeling of randomness, when it comes to the choice of where to begin. Any PoP seems to be fine. But random choice must lead to redundancy. And redundancy costs time. Which costs rating points in turn. Some PoPs play a key role, while others are irrelevant. So how can we know where to start?

In the previous post, we found that a target is always geometrically connected to the PoP. Otherwise it wouldn't be a potential vulnerable target. No PoP, no chances.

Since PoPs and targets are connected, we can equally well start with the targets, and find from there the PoPs they are connected with. It doesn't solve the problem of redundancy though. You can't know beforehand which PoP is relevant and which is not. The same is true for targets. You can't know if a target is potentially vulnerable before you have investigated it.

But there is a big difference between targets and Pops. Targets have a natural hierarchy based on their value. Since their value is known beforehand, you know beforehand where to start. PoPs do not have such characteristic. So start with the target with the highest value and look for PoPs that are connected with it.

Starting with the targets and working our way back to the PoPs and from there to the attackers gives our serial mind a gripe according to its sequential nature. Time consuming parallel choices like "with what PoP should I start and which PoP should I investigate next" are avoided.



Friday, January 13, 2017

PoPeye

The PoP (Point of Pressure) has become the starting point of any attack. We need to develop an eye for PoPs. When I look at a new position, my approach is pretty incoherent. Time to have a closer look at the PoP. What are the characteristics, how do we recognize them?

Two (three) types
The first thing that pops into the mind, is that there are two types of PoPs.

PoP-P
The first type is where there is a a piece on the square which is under pressure. The first twenty positions in my database appeared to be of that type.  Only when I started to look at positions that have a 300 point higher rating, I noticed the first PoP with no piece on it. PoP-P can be solved with the three motifs encircling, geometry and function.

PoP-S
The second type has no piece on the PoP. It's just an empty square. For instance a7 in the diagram below is such PoP-S. To exploit a PoP-S, you need an extra motif: the assault motif.

PoP-PS
I theorize that there must be a third type, which is actually a PoP-S, but accidentally there stands a piece on the square. The main subject of the attack is not about the gain of the piece though, but about the assault of the king.

It is important to realize, that there can't be a combination without a PoP.

B.A.D.
A characteristic of a PoP is that it is always B.A.D. (Barely Adequate Defended), if it is defended at all. A PoP is about outnumbering the opponent on a square.

Contact with a target
The PoP must always be in geometrical contact with a target. Either by that the target stands on it, or the target has a geometrical connection with the PoP. Which means, that the target will be attacked directly from the PoP, when an attacker conquers it. In the diagram below, a7 is a PoP, the king is directly in geometrical contact with it. When white conquers a7, the king is attacked.

Contact with an attacker
The PoP must be in direct contact with an attacker. There is a geometrical connection between the attacker and the PoP

Exploiting a PoP
When you already outnumber the PoP, you can go on winning. But usually you are in a situation where the PoP is only B.A.D. (Barely Adequate Defended). Which means you have some work to do before you outnumber the opponent on the PoP square. Most of the time, it is necessary to make use of some kind of immobility.

Immobility
Chess pieces are volatile. In a balanced game, any attack can be answered. This means that you can only find a combination in an unbalanced position. When, for some reason, the pieces of the opponent are hampered. Only then it might be possible that your attack can't be answered. The main cause for lack of possibilities is immobility. Only when your opponents pieces are immobile to a certain degree, there is a chance to carry out your vicious plans. Immobility must be seen in the minds eye. Looking at the pieces alone can bring you only sofar. But what is directly visible on the board, might be deceptive. You look at a knight, you see where it can move to. But when it is immobile, it can no longer do its knightly things. The ability to see immobility before your minds eye is paramount. That can't be stressed enough. This way you can win games. When you see things your opponent doesn't. There are three categories of immobility.
  • Immobility by function
  • Immobility by lack of space
  • Immobility by bad piece placement

Immobility by function
When a piece has a function to fulfill, it must stay in contact with its function.  The white queen in diagram 1 has to stay in contact with b2. So it is partly immobile. The queen can't move along the c2-h7 diagonal. So the interesting attacking squares e4 and h7 are out of reach.

Immobility by lack of space
The black king in diagram 1 has lack of space. When it is attacked, it can't flee into safety.

Immobility by bad piece placement
The black pieces are well placed for an attack on the white king, but badly placed for defense of the black king. The road from defender to PoP is too long. I.e. takes too much time.

Diagram 1. white to move

How to exploit the PoP
As you see, I use the same position as in the posts before. It shows both types of PoPs.
c3 is a PoP-P square. Black is outnumbered on c3, and there is a piece standing on it. But immobility vision will change this assessment.

Look at the defenders
When you consider a PoP,  you must first look at it's defenders. c3 is B.A.D., and the first attempt to exploit it is to have a look at the defenders. The defenders Qa5 and Rb5 are partly immobilized by function. Qa5 must stay in contact with c3, and Rb5 must pin b2. But there is no time to harass the defenders, since the white queen is hanging.

Add attackers
You always start with looking at the defenders, since they are partly immobilized already. Adding attackers can only be successful when your opponent can't keep up by adding defenders. Here you would like to unpin the pawn for instance. But that can't be done together with preserving the initiative. It stumbles upon the same problem: the white queen is hanging. So c3 is not the PoP that is going to lead you to glory.

I will continue with the other PoPs in the next post.


Monday, January 09, 2017

A closer look

The problems with the application of PLAF (PoPLoAASFun) need further elaboration. We can use the same diagram.

White to move


k7/1R2R3/pb3p2/qr6/5N1p/2r3P1/PPQ4P/1K6 w - - 0 1
[solution]

PoP (Point of Pressure)

a7. What do we want to know about a PoP?
  • How many times is is attacked? 2x
  • How many times is it defended? 2x
  • Can I add attackers? Yes Qh7
  • Can I harass defenders? No
That Qh7 isn't viable, isn't immediately clear. Only when the Function of the white queen is examined, we will find that it is immobile along the c2-h7 diagonal, since it has a defensive duty against the black rook sac on b2.

a8
  • How many times is is attacked? 0x
  • How many times is it defended? 0x
  • Can I add attackers? Yes Qe4 Qg2
  • Can I harass defenders? No
At first, I thought that when we look at the PoPs, we must keep it as clean and simple as possible, we don't look at the Function of our attackers just yet. That must be done at a later stage. But now I think about it, it seems more logical to see a PoP as a unit of assessment, and start the backwards thinking process right away.  Both Qe4 and Qg2 outnumber the PoP a8. In that case the following step must be to examine the mobility of our queen. In other words, we must answer the question "what is the function of the white queen?" Answer: to protect b2. Next question: "how does that function influence the mobility of the queen?". Answer: it must stay in contact with b2. This already tells you everything you need to know.

This leads to an important conclusion:
It is not first investigating all PoPs, then all LoAs, then all AS (Attacking Squares) and then all functions. The PoP is the unit of investigation. So far, I haven't seen a single tactical problem without a PoP playing a crucial role.

You start with these questions about a PoP:
  • How many times is is attacked
  • How many times is it defended
  • Can I add attackers?
  • Can the opponent add defenders?
  • Can I harass defenders?
 The first two questions tells you if you already outnumber the opponent on a PoP. Usually, the plus and minus score will equalize to zero. Zero is an indicator the PoP might be B.A.D. (Barely Adequate Defended). The second two questions tells you if and how you can exploit the PoP.

If you can add attackers, you must continue with questions about the attackers
  • Does the attacker has a Function?
  • How does this Function influence the mobility of the attacker?
Further you must ask the same kind of questions about the defenders
  • Does the defender have a Function?
  • How does this Function influence the mobility of the defender?
  • Can I harass-block-capture-deflect the defender? 
 We need a tree of questions.

Sunday, January 08, 2017

Obstacles

I expected the application of the three motif system PoP LoA Fun (PLF) to have some obstacles. And indeed there are. Let us talk about that.

I solve now problems from the standard problem set at CT in stead of problems from the blitz problem set. That presents me problems which have a 300 points higher rating. Since I want to become 300 points stronger, I wanted to know which problems I encounter when applying the PIF system to higher rated problems.

Problems include:
  • Higher amount of PoPs, so it is difficult to choose the critical PoP.
  • Higher amount of LoAs, so it is difficult to choose the critical LoA.
  • More than one attacking square on a LoA, so it is difficult to choose the critical square.
  • Motif assault
  • Motif promotion
  • Counter attack 
  • Quiet moves (non CCT)

Higher rated problems contain more problems with the motifs assault and promotion. There is additional knowledge needed to handle these motifs. Theoretically, the preconditions from the Art of Attack of Vukovic should be a great aid here. But I never have internalized that knowledge. High time to make that knowledge more practical.  The diagram below shows 6 of the 7 problems mentioned above (no promotion motif). Can you find them all?

White to move


k7/1R2R3/pb3p2/qr6/5N1p/2r3P1/PPQ4P/1K6 w - - 0 1
[solution]

PoP
a7, a8, c8, e8

LoA
7th, 8th, b file, c file, e file, g2-a8

AS (Attacking Square)
a7, b8, e8, e4, g2, h7

Fun
a5 protects c3
b5 protects c3 indirect
b6 protects a7
a8 protects b8
c3 protects c8 by shielding

Motif assault
The new motif here is the the assault of the king. The preconditions state that you need a surplus of 3 extra pieces for an assault. One to sacrifice, and two to deliver mate. Usually the mate is delivered by the queen. Here the surplus is two rooks, so I need to add the queen to the attack. But from which attacking square and why? I gambled wrong.

Counter attack
There is definitely a counterattack going on.  This means I must make an attacking move that at the same time defends against the counter attack.

Quiet move
The actual move loads the battery against the king, but further is a non CCT move.

Wednesday, December 28, 2016

Modeling combinations

The first six positions of my database of doom are perfectly solvable with the aid of PoP, LoA and Fun. This raises of course the question if this is going to help to build the cues I need. For this six position this is probably the case. I missed a few PoPs, and a few LoAs, and some Fun. I used some bad methods like capturing with the cheapest piece first without further thinking. Those methods will render themselves useless when confronted with the logic of PoPLoAFun, so within this very limited sample the answer to the question is a resounding yes.

Time to enhance the sample. Today I did a few exercises in standard mode in stead of in blitz mode at CT. Those problems are higher rated. I found problems that are not covered by the PLF method (PoP LoA Fun). There are problems with other motifs, like the promotion motif and the assault motif, which are not covered by the three motifs of the PLF method. But besides that, the PLF method seems to work well. Albeit I have to learn a lot  new ideas. Especially I have to enhance my rigid ideas towards a more broader view.

Modeling the combination
From time to time, I'm able to model the combination. Which is very satisfying. For the first time I have the feeling I play chess in stead of reacting with trial and error to a position without a clue (cue). Let me give an example.

Black to move
 1r4k1/3R1pp1/1q2p2p/p7/3N4/P5P1/1P2Q1P1/1KB4r b - - 1 1
[solution]

PoP
b2, c1, d4

LoA
b-file, c-file, 1th rank

Fun
e2, b1, (c1) protect b2
b1 protects c1
b2 is pinned to the king
d4 protects c6 and b5
d7 protects d4

The best candidate to pile up your pieces against, seems to be c1. But without a gain of tempo, white is in time to build up the defense. It is interesting to see how the knight protects the rook. Not by directly covering it, but by covering the potential squares of attack c6 and d5. That is what I meant by a less rigid view. A piece can protect another piece in an indirect way.

Tactical elements are connected via squares. In this case, the square c6. Qc6 would be a double attack on the rook and the bishop. But c6 is protected by the knight. With e5 you can harass that very knight. This way you are modeling the combination.

Modeling


Sunday, December 25, 2016

Intermezzo

My own scheme of a complete direct attack would be as follows
One attacker, one target.
  • Attacker
  • Road to attacking square
  • Attacking square
  • Road to target square
  • Target square
  • Road from target to target square
  • Target
With this scheme it is possible to describe every obstacle in an attack, and every preliminary move.
  • Is the attacker already on the attacking square?
  • Is the road to the attacking square blocked?
  • Can the attacker reach the attacking square with tempo?
  • Is the attacking square free from defense?
  • Is the road from attacking square to target square blocked? 
  • Is the target square free from defense?
  • Is the target already on the target square?
  • Is the road from the target to the target square free?
  • Can I force the target towards the target square?

With a duplo attack the scheme gets more complicated.
One attacker, two targets.
  • Attacker
  • Road to attacking square
  • Attacking square
  • Road to target square 1
  • Target square 1
  • Road from target to target square 1
  • Target 1
  • Road to target square 2
  • Target square 2
  • Road from target to target square 2
  • Target 2
And a discovered or simultaneous attack is even more complicated.
Two attackers, two targets
  • Attacker 1
  • Road to attacking square 1
  • Attacking square 1
  • Road to target square 1
  • Target square 1
  • Road from target to target square 1
  • Target 1
  • Attacker 2
  • Road to target square 2
  • Target square 2
  • Road from target to target square 2
  • Target 2
I left the trap out, but even then the schemes are already way too complicated to be handled  adequately by the human mind. This means that we must be prepared to sacrifice completeness for manageability. That is exactly what the system with the three motifs of mister Lasker does.
  • PoP
  • LoA
  • Fun
By the way (btw), you can always find the commonly used abbreviations via the list in my sidebar. I introduce new terminology here and there. That frees my mind from a too rigid approach to Laskers system.

PoP
In the passed week, I had analyzed six positions, and every position has showed 1-3 PoPs. I think it is a safe bet to assume that there always will be at least one PoP in any tactical problem. Theoretically I can design a tactical combination with no Pops, but I don't think that has a practical  value, since the chance that you encounter such combination in practice will be very slim.
I associate a PoP with a piece. That piece can be a target or a defender (a piece with a function)

LoA
As with PoPs, I probably can design a combination without any straight LoA. Strictly speaking, Lasker says nowhere that a geometrical motif means a straight line of attack. But in practice, that is where you look for. But then again, such combination without any straight LoA would be extremely rare in practice. For now, I simply ignore those. Every position had 1-4 LoAs.

Fun
Pieces don't have necessarily functions. So a combination without any defending piece isn't necessarily rare. Yet beyond a certain complexity, you will not found combinations where no piece fulfills a function. Analyzing the functions is crucial to interpret what is going on. PoP and LoA are just identification methods of targets and roads, function describes the alteration of a piece. Unseen limitations of pieces.

Saturday, December 24, 2016

Opening the line of attack

It is surprising to see how fast a LoA that seems totally obstructed, can be opened. That's why you have to follow the LoA to the rim of the board.

Black to move





2k2b1r/1pp3p1/p1p3qp/4Pn2/N4Bb1/1P1r1N2/P3QPPP/R4R1K b - - 0 1
[solution]

Encircling
f3

LoA
g6-g1
f3-h1

Function
d2, g2 protect f3

Error
1. ... Bxf3 seems a double attack on Q and M#1, but gxf3 gets rid of the attacker which can cover h1.

Missing
cue: Nd4 is the way to add to the superior force against f3 with tempo (double attack)
cue: importance of keeping an attacker for the LoA f3-h1

In general: a piece that is B.A.D. can be encircled by harassing a defender or by adding an extra piece to the attack with tempo (which means a duplo attack)