## 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

1. The following line of thought merely expands on your succinct observations above.

(1) WBc1 is B.A.D. and absolutely pinned. (I presume that's what "(c1)" indicated.) WK cannot move out of pin and maintain protection of c1. Functionally, WBc1 does NOT "protect" b2. Apply encircling motif to c1 by adding another attacker; BQ or BR are the only potential possibilities.

(2) b2 is B.A.D.: WQ and WK "protect"; BQ and BR attack; b2 is also "pinned" (unimportant in this position because no more Black attackers available for encircling). WQ cannot move because of this defensive function.

(3) WRd7 is LPDO. Immediately springs into mind: can we combine these two things [(1) and (2)] into a duplo attack (against WBc1 and WRd7)? 1. ...Qc6 is the obvious connection square.

(4) Ooops! WRd7 IS "protected" indirectly by WNd4 (guarding the potential "attack" square c6 from BQ). WN has a defensive function and therefore cannot move; it is "pinned" by function. [BTW, this is another example of a "pin" that does not meet the classical definition of a pin.]

IMHO, this is the "hard" part of finding the solution QUICKLY!

(5) Ignoring "legal" (and "smart") moves, how can we "connect the dots" between adding an attacker to WBc1 (encircling motif) and LPDO WRd7? The common square is c6. Since the WN is "pinned" to d4 (by function of indirectly protecting WRd7), apply the encircling motif again: the new "target" is the pinned WN. "The attacker of the defender against my attack is my friend!" There IS an available Black "attacker" for WNd4: 1. ... e5. (Recall from (1) that WQ cannot move because of its function of guarding b2.)

(6) If the WN moves, then the exchange motif brings a more congenial (and absolutely REQUIRED) duplo attack. 1. ... e5 2. Nf5 Rxc1+ 3. Kxc1 Qc6+ followed by 4. ... Qxd7 picking up the loose WR.

2. Nf5 is better than 2. Nf3 because of a possible defensive trap (protecting the c6 square indirectly): it would be a suicidal mistake (after 1. ... e5 2. Nf5) to immediately play 2. ... Qc6 allowing the fork 3. WNe7+. This succinctly illustrates the assault motif: NEVER give the opponent a tempo to "recover" in a sequence of forcing moves! (It also illustrates the wisdom of Heisman's question to be asked, "Is it SAFE?")

(7) If the WN does not move, simply capture it, gaining material.

This illustrates the "chaining" together of motifs into a sequence of possibilities via logical thought. Eventually (and it usually does not take very many iterations, nor very much thinking time because the motifs eliminate extraneous moves while also aggregating several moves into a coherent whole), one side or the other runs out of attacking or defending resources. When that occurs, it is time to evaluate the relative gains/losses.

Black wins a minor piece in all lines.

2. Your elaborate story shows both what our problem is, and how to solve it.

There are only a few scenarios, yet the way they can manifest themselves is manifold. Somehow, I always associate a defender with a piece that defends another piece. But a piece can be protected in many (indirect ways) ways. It can protect an attacking square(as in this case), it can shield a line of attack, or in can block with tempo et cetera. But the scenario is the same: if a piece is (partly) immobilized ("pinned" as you put it): harass the defender. That shouldn't take a minute to realize, that should be the pavlov reaction.

b2 defended by Q can I harass the Q?
c1 defended by K can I harass the K?
d7 defended by N can I harass the N?

We have to familiarize ourselves with the few scenarios there are.

3. As we dig deeper into this process, I am much more appreciative of mister Lasker's insight that the "function" of the pieces is one of the critically important "cues" to understanding a specific position and what should be examined FIRST. It binds the various pieces/squares together into invisible relationships that may not be "seen" from the visible geometrical perspective. It doesn't mean that function will always give an immediate answer or even a final answer, but it's a good place to begin. I believe mister Lasker referred to it as "seeing" and understanding the complex operations that are GERMINATING in the position. In short, we should be "seeing" the potentialities as well as the actualities.

4. Encircling motif: "Where there is superior force at a given point and immobility within the defenders ranks a combination should be present.". That already implies the function motif to be extant.

PoP identifies the superior force. If you neglect the problems around it like the value and the amount of defenders, it gives you a glimpse into the future.

LoA identifies the lines of attack. If you neglect the problems around it like blockading pieces et cetera, it gives you a glimpse into the future.

I think it is a good idea to keep PoP and LoA "as clean as possible". That means, no worries about if matters are actually feasible. Both PoP and LoA are directly visible.

The function motif divides the combination in potential building blocks. Function brings in sight what is invisible at first sight. It seems that Bc1 is protecting b2, but it is not, since the bishop has the function to protect the king. Within each block, there is an order. Target - defender - harass defender. Between the blocks, there is an order too. You start with the PoP, and work backwards from there.

5. I fully agree with your assessment above regarding PoP, LoA, and Fun. The "cleaner" the process, the easier to retain and use QUICKLY in the majority of positions.

One insight that I have gained from this discussion is this (from above): "no worries about if matters are actually feasible." Prior to beginning this latest investigation, I would think in terms of legal MOVES even when trying to think using "chunks" of tactical themes/devices. This resulted in rejection (without consideration) of ILLEGAL moves (in the specific position but NOT illegal in prospective positions in the future) without full consideration of the possibilities. In short, the mechanism that I was using eliminated the desired solution without being aware of it. As I've worked on this process, I've found myself much more open to visualizing pieces on squares that appear to lose them without compensation. I recall something (I can't remember where I saw it) that while visualizing, you can put pieces en prise without any fear whatsoever that the opponent can take them, because it's only "seen" in the mind's eye, not actually on the board. I guess this correlates with Tal's dictum regarding multiple pieces being en prise simultaneously: the opponent can only capture them ONE AT A TIME, and then ONLY WHEN IT IS HIS TURN TO MOVE.

The mental "baggage" that we accumulate (without intending to do so) is often a significant part of what restricts our ability to just "see" what is potentially available. Another liberating thought has to do with the material count (P=1, N+B=3, R=5, Q=9, K=200). Each piece has the capability of 1 to attack/defend a specific square regardless of the position of that piece. A piece sitting ON a square CANNOT attack/defend that square! The relative material value of the pieces is irrelevant to the attack/defend function. For example, in the position above, WQ+WK = 2 on b2; BQ+BR = 2 on b2; ergo, b2 is B.A.D. Same for WK=1 on c1; BR=1 on c1; ergo, c1 is B.A.D. This simplifies the process of "seeing" (very small numbers) and therefore makes it QUICKER. A B.A.D. situation should immediately "trigger" a [PRIMARY] search for additional attackers/defenders AND a [SECONDARY] search for possibilities to overload one or more of the defenders with additional functions. This brings into play a host of other tactical themes/devices such as distraction, diversion, etc.

Note that there is a hierarchy to the tactical themes/devices. Some are "direct" [first order] (fork, for instance) and some are "indirect" (diversion, for example [second order] or reloader [third order]). If we start with the direct and only then consider the indirect, I think that speeds the process of "seeing."

Your last paragraph above is PURE GOLD!!

6. I wish you all a happy and successful year of chess improvement!

7. If the chess puzzle is exactly the same as the previous one I have solved - there is no problem with retrieving this from mental database. I noticed a few familiar puzzles and the time reaction was about 2-3 seconds. The solution was retrieved in about 3-5 seconds after I recognized the identical puzzle from my mental database.

I am curious if anyone was wondering how do you know when the task is solved: if you gain a pawn, N, B, R, Q or give a checkmate? Or are we only considering the puzzles with THE ONLY solution? I am asking because I am currently struggling with such problems. And what I can confirm: when you recognize the important motifs in the position and the similarity to the position you previously solved (no matter how long ago), then the solution may be quite easy - especially in a comparison to the puzzles you have no idea and the specific one you haven't solved.

Happy New Year and all the best in the chess improvement world! ;) :)

8. I am not sure if we were discussing this hint, but it helps me solving the puzzles. What is it?

WRITE DOWN all the lines of action you feel/think interesting. In addition write the specific squares, too.

This way I found the solution after literally writing down the last square I know it is important. Before that I had been solving the puzzles up to 10 minutes!

I bet this method is very close (or the same, but the form is a bit different) to Robert's recommendation (mark the lines with the marker/pencil).

What do you think about it? I will try this trick for the puzzles I failed and see what happens.

Summing up: I think we should list ALL the methods which work for us (among all of the tested ones). And after that we could try to solve some dozens of puzzles to see how much they help us in finding the best continuation.

What I miss the most is the bunch of examples (diagrams) of puzzles with step by step explanation. However they should be explained with discovering ideas and making questions. And the final solution should be based on connection (merging) of all the previous info we have discovered (written down) so far. This way we could learn A LOT. At least it is my idea.

I think it is high time to create such topic at my blog. Let me know if you would be interested at such support of our mutual discovery journey (the blog is in Polish, but you can probably use Google translate to understand all the ideas).

@Tempo: let me know if I can use your examples and articles my friend. And what are the conditions I can use these. It will be great to show your work to the people who are reading my blog (as most Polish people simply does not want {sometimes they cannot} to read anything what is not written in Polish). Thanks for your great work!

1. You can use any post/example you like, as long as you mention the source. Chłopiec, są tłumaczone na język polski. Fantastyczne!

2. @ Tomasz:

I think the process you have described is very similar to my suggested "marking the lines with a highlighter" approach.

Giving credit where it is due, GM Jon Tisdall in his book Improve Your Chess NOW! suggested a method of "analyzing" which he called "variation processing." Here is his description:

My theory contends that a combination of the natural human approach to the position, tempered with some of the discipline advocated by Kotov, [the Tree of Analysis approach] is more effective. The components of this technique are (in this order):

1) To aim towards the choice of a single critical variation (heresy!). Branches are dealt with when unavoidable, and primarily to navigate the chief variation.

2) The constant application of abstract assessment.

3) A scan for critical candidates.

Step 2 is a verbalization (silently, if actually playing a game) of the "cues" that one discovers while surveying the position.

You propose writing these discoveries down; I prefer to mark them on a diagram without verbalization. My reason for this is because visualization is a visual (non-verbal) process. I wanted to avoid (as much as possible) any reliance on logical SLOW thinking processes. Perhaps it is only me, but I find that if I start writing down specific variations while examining a position, I very rapidly lose myself in trying to account for everything that is POSSIBLE, not just the things that appear to be PRACTICAL. In short, I lose sight of the "forest" because I'm too closely examining and trying to classify every single tree.

In summary, I'm a firm believer in "doing what works - for YOU!"

3. @Tempo

Thanks for your permission! I will try to make my articles as interesting as yours! And I hope more people (who are reading my blog) will start reading your articles... as they are simply GREAT! And you have so many articles, you made so many expertiments that I could use your blog's food for though... for a year! ;) :)

Writing down in an interesting style about chess tactics is not that easy. I admire your approach and the way you realise this! I am convinced you could write a book related to tactics - in a very similar way as FM Weteschnik did! Of course it would require a 2-3 years of writing (especially if you would have to analyze and compare at least 5-6 books related to tactics), but the final result would certainly be amazing!

@Robert

Yes, I fully agree "marking the lines with a highlighter" approach is much more efficient (especially for kids!). Anyway for me "marking lines" is very close to writing down the letters related to lines (vertical, horizontal and diagonal).

And no doubts visualization is a visual (non-verbal) process... and it takes a tiny range of (mental) energy.

And to make things clear: what I mean is to write down ONLY the lines or squares, not any variations. This way it may help to trigger important cues to start working. In my case (while I was solving one original chess tactics puzzle) I knew the solution was not that difficult, but I could not "break through". After I wrote down "the lines and squares of interest" the solution IMMEDIATELY popped up on me! It was so shocking (unbelievable) that my mind simply rejected it on the spot. Anyway I strongly believe that finding the right cues and the ways how to trigger these (without wasting much time and energy) is the right way to make QUANTUM leap at tactical (solving puzzles) field of activity.

By the way: GM Jon Tisdall's book "Improve Your Chess NOW" is a really refreshing one! Probably most people miss this book is a few things: its cover is awful and the author is not widely recognized. Anyway I remember I read some fragments of it about 14-15 years ago and I was really shocked how original approach the author presents! Now I come back to this book as my chess understanding is at the lowest level I can understand the value are intention of this book. It can hide some amazing ideas we can try to validate and see which ones work for us! :)