Saturday, March 11, 2017

War on Trial and Error

While performing an investigation for the previous post, I realized how weak  trial and error actually is, in comparison to calculation in the direction of a goal. Just random trying in the hope for clues must be the last resort during a game. In the study room we need to eradicate trial and error.

Diagram 1 - white to move
2r2rk1/1p3pb1/p3bBpp/2p1P3/4NR1Q/8/1Pq3PP/4R1K1 w - - 0 1
[solution]

The black king looks like a duck, it sits like a duck and it quacks like a duck. So it is probably a sitting duck. So the main goal is clear: mate the king! If the opponent feels compelled to postpone his demise with a piece sac, I'm fine with that.

 I tried from here on to solve the matter with trial and error, but I failed. We need a clear goal here that gives direction to our calculations. What can that be?

What can we say in general about this position? White has 4 attackers (Bf6, Rf4, Qh4 and Ne4). Black has 3 defenders (Bg7, g6,h6). The most likely scenario is the trade of the bishops, saccing the rook or the knight for one or two pawns to get access to the king and give mate with the queen and the remaining piece. Beware that Qc2 and Rf8 don't enter the defense.

I'm not sure where this is going. I'm going to investigate it and will update this post later. Comments in the meantime are helpful!

UPDATE
Great comments! It took me quite a few hours before I even knew where to start. I think I have an idea now. The black king is protected by a fortress of 3 pawns: f7, g6, h6. The base of this fortress is f7, which is bolstered by Rf8 and Be6. We must ask the question: which defender is the weakest?

f7

At the moment f7 is well defended.

g6
g6 is protected by f7. Notice that f7 has a double function: protecting g6 AND Be6. So g5 can be weakened by attacking Be6.

h6
h6 is definitely the weakest point. If it is pushed to h5, g6 will get a double function: defending h5 AND keep the g-file closed.

1.Bxg7 Kxg7 is simply undermining h6

2.Qf6+ is designed for three things.
  • It prevents that f7 is pushed, which would open lines for black for counterplay OR for adding defenders from aside.
  • It clears h4 for the rook
  • It forces the black king in the path of the black rook, so it takes more time to let Rf8 defend h6
2. ... Kh7 must protect h6 (either by the king OR Rh8)
3. Rh4 Rh8 forgets its function to protect f7
4. Ng5+ double attack K and B the rest you can find yourself.

Now we have found already two universal questions to guide our calculation in the case of a mate attack:
1. Which piece is the sitting duck?
2. Which defender is the weakest?

Friday, March 10, 2017

Back to the future

This blog is not easy to follow. I fullheartedly acknowledge that. If you have become interested in the PLF (PoPLoAFun) system just lately, you probably have trouble to keep up with the details. If you are genuinely interested,  I advice you to go back a few months, and start reading from dec 3, 2016. It is worth the effort.

Going back in time
In fact, I'm doing so myself. Just to ingrain the knowledge that has been accumulated along the way. And to look if somebody has fallen of the bandwagon without me noticing it. A musician we can't do without in the future, for instance. This is what I have already found sofar.

The adult human mind is unsuited for chess calculation. This means, that if an adult tries to improve at chess, he must be clever enough to avoid calculation whenever he can. The plf system is designed for exactly that. It determines goals that lie in the future by their characteristics. Only when the goal is determined, we can go back from the future towards the present. From the present on we can calculate towards the future goal again by using our notorious beloved trial and error. Since our goal is already standing firm, the majority of the branches can be pruned beforehand, since they can't possibly lead to the required goal. This way, the adult brain doesn't become overloaded.

Sitting duck
The goal must always be immobile, to at least a certain degree. The goal will be an augmented immobile piece, or the rim of the board (which happens to be an immobile goal for the pawn with "lust zum wander"). Or it can be a square. It must be a sitting duck. Since if it isn't, it will be long fled when we arrive.

Beware of counterattacks
A square can be a sitting duck too. That might sound obvious to you, since a square seems to be glued to the board, but that is deceiving. The value of a square is determined by the pieces that are in contact with it. When those pieces are immobile, the square is immobile. When the pieces that are in contact with a square move, the value of the square changes. Squares give access to targets. Attacking squares move when the target moves.

We start at the end of the line, which is the sitting duck. The PoPs (Points of Pressure) and the LoAs (Lines of Attack) tell us something about the road from our attackers towards the sitting duck. Function tells us something about the immobility of the duck and its defenders. Function is, as you might remember, one of the causes of immobility.

I'm not worried about the calculation from the present towards the future. When the goal is clear and the branches are pruned, we are perfectly capable to calculate the line at high speed. The determination of the "viable" sitting duck causes us more trouble.

Looking into the future
Sofar, we have found three ways to look into the future without calculation. Two of the three are musicians that have fallen off the bandwagon during our wild ride towards chess aptitude.



For the demonstration of the three methods to look into the future without calculation, I will make use of the original posts where we discovered the methods. So the positions might look familiar to you. Which is good, since you don't get distracted then by the variations. I will add the link to the original posts, for those of you who want a more thorough look at the positions presented.

First method: ignore obstacles
The first method to look into the future is looking at the geometry of the position. We look at a LoA without being bothered by the fact that there might be obstacles along the road. We trust that calculation will take care of these obstacles later. For now, we only want to determine the sitting duck.Take the following diagram.


Diagram 1. White to move
We talked extensively about this position here.
The square c8 is a sitting duck. There are two LoAs converging at c8:
  • a3 - c8
  • c2 - c8
For the time being, we ignore the blockading pieces Bc3, Nc6 and Nd7.
We can only reach c8 in the future. But first we must determine which pieces or squares are the sitting ducks. Since only sitting ducks are worth our efforts. Other targets are too agile.
Only once the sitting ducks are determined, we can go back from the future to the present, and calculate if we can free the LoAs with tempo. If we can, we can be reassured that the duck will still be sitting there when we arrive at it in the future.

Second method: ignore counterplay
Again you start with a sitting duck. See diagram 2

Diagram 2. Black to move
We talked extensively about this position here.
The white king is the sitting duck. It is waiting to be mated. White can drum up some counterplay, but that doesn't change the assessment. In the end the sitting duck will be murdered. The only way to avert an immediate demise for white is a sacrifice. Which is just a slower way of loosing in this particular case.

Chess moves come in pairs. That may sound silly, but just think about it for a while. A CCT move triggers an avoidance reaction. A check must be fled from. A capture must be equalized by a counter capture. A threat must be parried. Everything that can be stirred up must be answered first. But in the end the sitting duck will be still there waiting for you. Only if you have a clear picture of the sitting duck, you can come back from the future to the present situation on the board and start calculating forwards in time towards the duck.

Third method: ignore value and defenders
Have a look at the following diagram.

Diagram 3. Black to move

We talked extensively about this position here.
c1 is the sitting duck. To be able to see that, you must ignore the defenders of the road towards c1. Only when you have determined the sitting duck, you have a goal in the future. Only after you determined your goal in the future you can start the calculation of how to harass the defenders of the LoA.

Conclusion
 A sitting duck is a stable goal that lies in the future, and doesn't disappear overnight when we need time to get there. We want to determine the sitting ducks without calculation. We can do so by ignoring all kinds of things like obstacles, value of the pieces, defenders and counterplay. That gives us the clearest picture of what we want to accomplish. Until this point, we haven't loaded a burden onto the mind. Only when we have a clear picture of our goal, we can start to calculate. But it is no longer calculation at random in the deplorable tradition of trial and error in the hope for clues. It is calculation aiming at the removal of obstacles, harassing defenders and answering counter attacks until the goal is reached, or until the opponent needs to sacrifice wood in order to prevent you from reaching it.

The theory of looking into the future while ignoring all sorts of things is still in its infancy of course. A lot has to be done to make it more coherent and reusable. But I'm pretty sure that grandmasters prune the tree of analysis in a similar way. Conscious or unconscious.

The positions above might not be the clearest examples. I used them because they triggered the discovery of the methods. Don't worry, we will find better examples in the future.

We saved a few musicians that were fallen off of the bandwagon. We don't know yet who is going to play the piano and who is going to hit the drums though. But what we know for sure is that we are going to need them. In the future.





Wednesday, March 08, 2017

You had just one job . . .


Diagram 1. White to move
r3r2k/pp4b1/2q1Nppp/1R1Q1P2/2n5/2P5/b2NBPPP/4K2R w K - 1 1
[solution]

UPDATE
When you compare our comments, it looks as if we are looking at quite different positions. Which is a clear indicator of what our problem is. We see way too much possibilities. I saw an in essence simple position. Nc4 is hanging, and how am I going to round it up, with the knight or the bishop? Hence the title of this post. I had just one job. . . Choosing between 1.Nxc4 and 1.Bxc4
After thinking for more than three and a half minute I flunked it with 1.Bxc4. Based on some vague notion that "it was more active to attack Ba2".

Now let's have a look at this position in the light of my next post. Which black piece is the most immobile? Answer: the black knight. Why? It is hanging and immobile due to lack of time. White is to move first. That may sound silly, but that is because this is a silly position, with a knight already hanging. We start in the middle of something.

In order to decide between taking with the bishop or the knight, I must look at blacks possible counterplay. According to my hypothesis in the next post, counterplay can be only viable when it is geared around a sitting duck of mine. What is my most immobile piece? Definitely Ne6!

Counterplay will be directed to undermining e6. I must use Be2 as a defender of my king OR as a defender of e6. What I must definitely NOT do is exchanging my bishop against the desperado on a2.

Finally the position has become quite simple indeed.

Sunday, March 05, 2017

Augmented immobility

You might have noticed the past weeks, that I augmented the term immobility. I discriminate between:
  • Limited mobility due to lack of space
  • Limited mobility due to function 
  • Limited mobility due to lack of time
Space
Usually the term limited  mobility is associated with immobility due to lack of space solely. The
trapped piece and the mated king are examples of lack of space.

Function
Lasker added function as a cause of immobility. If you loose a piece when you move a defender, you cannot really move that defender, albeit it is allowed by the rules. The defender has limited mobility due to its function.

Time
I extended the term immobility with limited mobility due to lack of time. This means that all duplo attacks fall under this description. If you must save two pieces but you have only time to save one, the other piece remains on the board as if it is frozen.

Augmented immobility
This augmented immobility as I defined it, comprises almost every possible technique you can throw at your opponent. All 30 or so tactical themes, and all 30 or so types of mate. I hypothesize that you can't find a combination that is not based on this augmented immobility. Or maybe you can, but at least the bulk of the problems at CT has this augmented immobility at its very core.

There is of course a reason for that. In a balanced chess game, there are always several answers possible to any move. To any attacking move. A combination is by definition not balanced. A combination works, due to the fact that the options of your opponent are limited, one way or another. These limitations are always based on augmented immobility.

Sitting ducks
This means, that for a combination, you must identify the sitting ducks. Flying ducks have to much options to circumvent an attack. I have analyzed dozens of positions of CT lately, and sofar I haven't been able to falsify this hypothesis.

Augmented immobility

Saturday, March 04, 2017

Plugging along

Diagram 1 black to move

2rr4/1q3pkp/3p1n1R/1p2p1p1/1P4P1/1BP4Q/5P1P/3R2K1 b - - 1 1
[solution]

UPDATE
This position  is not about winning a piece in all variations. Often, two pawns are enough for a sure win. I kept looking for winning pieces or mating the king. So this position revealed a fundamental flaw in my approach. I don't know when to stop calculating.

In the comments we toss around a lot of HE's, targets, PoPs, LoAs and Funs. Most of them are not very relevant, and confuse our view. In the past weeks we have found a method to sift the relevant targets from the irrelevant ones. That sieve is called immobility. You can't shoot a mobile target without hail. Hail is  T and E (Trial and Error). This blog has become a rehab for those who want to quit from their T and E addiction. To avoid shooting with hail, we must focus on the sitting ducks. We have a few of them.

Diagram 2. Sitting ducks. Black to move
White
  • Rh6 is immobile due to lack of space
  • Qh3 is immobile due to function
  • Qh3 and Bb3 are immobile due to lack of time (duplo attack Rxc3)
  • g4 is immobile due to lack of space
Black
  • Nf6 is immobile due to function
  • Kg7 is immobile due to function
  • h7 is immobile due to lack of space
  • f7 is immobile due to lack of space
 How to take advantage of the white sitting ducks and to protect the own sitting ducks at the same time?
1. ... Qe4 has it all. It transforms the black knight from a defender into an attacker. It tales control of the LoA (Line of Attack) c2 - h7, it relieves the black king of a function. And it attacks the B.A.D. (Barely Adequate Defended) pawn g4 twice, thus adding an extra function to the white queen.

White is paralyzed, which means that you have to watch out for desperado's. That's where a little calculation comes in. The defense 2.f3 opens a LoA against the white king, allowing a duplo attack against c3. Two pawns ahead in a position where you remain the most active is enough for the win.

Sunday, February 26, 2017

dear Liza, a hole

When a position is very crowded, I have often problems to find the right continuation. The next position took me 14 minutes to find the wrong move.

Diagram 1. White to move

 r5r1/3b1nk1/p2p1ppb/1ppPp3/4PqP1/2P1NPN1/PPB1QK1R/7R w - - 1 1
[solution]

I'm going to ponder about what exactly is the cause of my failure, and which knowledge is needed to prevent such debacle in the future. Feel free to comment already, that is helpful.

UPDATE
It took quite some time to grasp what is going on exactly in this position, but with the  aid of the comments I was able to unravel it in the end.

The problem with  this position is, that with  T+E (Trial and Error) you soon dismiss 1.Nef5+ Bxf5 2.exf5 as too slow. Aox even called this move "silent", albeit between quotes. Only when everything else fails, you might come back and have a deeper look. And that is exactly what we try to avoid. How can we think about this position with as less calculation as possible?

Somewhere I defined the PLF (PoPLoAFun) system as a method to get on the track of the most immobile pieces. There are two completely immobile pieces here, the black knight and the g-pawn. When they move, a piece is immediately lost. They are immobile because they have a Function to fulfill. All other pieces can move a bit, as long as they stay in contact with their Functions. Have a look at diagram 2.

Diagram 2. The knightfork or duplo attack. White to move
Legenda:
Square = target
Circle = attacking square

The duplo attack is pretty easy to spot. It makes g6 an immobile defender. With a duplo attack, you have no free move. You have to attack two targets with one move. Since the opponent can only move one piece out of the way, the other piece is lost. Immobility due to lack of time.

But why does 1.Nef5+ Bxf5 2.exf5 work? Why is it not too slow?


Diagram 3. The triplo attack. White to move
Legenda:
Square = target
Circle = attacking square 


The point is, that fxg6 is a triplo attack. It attacks the knight (1), which has a function as defender of the B.A.D. (Barely Adequate Defended) bishop (2), and it captures g6 which has the function as the defender of the attacking square h5 (3). Thus making the knightfork possible.

 With a triplo attack, you have one free move. That is exf5. Which looks silent, but isn't. Black has 3 defensive task to fulfill:
  • Get the knight out of harms way
  • Get the bishop out of harms way OR defend it extra
  • Get one of the targets of the knightfork out of the way OR defend the attacking square h5 extra
3 defensive  tasks takes black 3 tempi to accomplish. That gives white 2 tempi to carry out his attack. Black cannot accomplish his 3 tasks in 2 tempi. White's tempi: exf5 and fxg6.

The plf system provides everything you need to know to focus your attention on the relevant squares and pieces. With hardly any calculation at all.

Friday, February 24, 2017

Another hole

When you come close to the endgame, the rules of chess seem to change. I don't know what causes that feeling. While the amount of pieces diminishes, the amount of space increases. The net result being that the amount of possibilities doesn't become lesser when you near the endgame. Only the nature of the possibilities changes.

The diagram below is a type of position that is continuously spilling my rating points due to my talent to find the wrong squares. Let's see if we can expel some calculation by logical pondering.

Diagram 1. Black to move

6r1/1p1b3p/3P4/2P2k1P/1P2p2K/5B2/5P2/4R3 b - - 0 1
[solution]

The last move of white was 1. Bxf3, taking a pawn.

Feel free to comment already. That makes it easier for me to get to the essence of the position, since you guys think differently.

Update

After 2.exf3 Re7 we reach the position that gives the most problems. How to judge it? Materially, black has a bishop for two pawns.

Let's have a look at the critical position.
Diagram 2. The critical position. Black to move
If you want to force the game in your direction, it doesn't make sense to chase a mobile piece. The white rook for instance is very agile. What is white's most immobile piece? Definitely his king. It has no duties to perform, no functions that is, but due to being sandwiched between the rim and the rook, it suffers lack of space. In fact, if black was allowed to move three times in a row, Rg1, Kf4 and Rh1# he would mate the white king. Since it is blacks turn, he comes up short two tempi. For the mate it is necessary that the black king can remain on the f-file, and go to f4 in due time. The move Be6 is designed to prevent the white rook to hinder the black king. If white follows up with a normal looking move like 3. ... Le6 4. Rxh7 or 3. ... Le6 4. Rxb7, he gets mated. To abandon immediate disaster, white must deflect the black pieces by sacrificing his main asset, his protected passed pawn. 3. ... Le6 4.d7
 
Diagram 3. Black to move

After 4. ... Rg4+ 5.Kh3 Rd4 black can pick up the passed pawn in due time. When white is robbed of his protected passed pawn, blacks extra bishop starts to count. When the rooks are traded, it is over. As you see, it wasn't necessary to keep the criminal behind lock and key. Mere police surveillance was enough. Due to the mate threat.