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

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.

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.

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.


  1. I solved this puzzle 3 times and i blundered it 3 times in the last 4 years

    1. Did you learn something from the position and did you forget that, or did you not learn anything from the position at all?

  2. 2041.0 You are certainly not picking easy problems to demonstrate the concepts!

    The previous move was 1. N(a5)xNc4, putting White ahead (at least temporarily) in material, but there are three White pieces now directly attacked: WRc1, WRc6 and WNc4.

    I spent about 15 minutes trying to decide on an approach. White is ahead by a Knight (temporarily, at least): Knight for a Pawn. There appears to be NO immediate prospects for a checkmate, so Black will have to regain material. I considered 3 alternatives.

    (1) 1. ... bxc4 This appeared to be the least likely choice because it is very simple for White to remove the capture threat from BBa3 and the capture threat against WRc6 by simply recapturing on c4 with 2. R(c1)xc4, leaving even material.

    Can Black expect to get more from the position?

    (2) 1. ... Rxc6 I liked grabbing a "free" Rook (I'm a patzer, what can I say?!?), but is it actually "free"? Not really; White captures the Ba3 with 2. Nxa3, saving the White Knight and attacking the now "hanging" Black Rook at c6. If Black captures WRc1 with 2. ... Rxc1+, White "saves" the WNa3 with 3. Nxc1. (The Knight was indirectly protected by the White Queen.) This leaves White with two minor pieces for a Rook and Pawn (plus 2:1 Pawns on the Queenside) - even material.

    By process of elimination, we arrive at the final possibility.

    (3) 1. ... Bxc1. Here's where I (finally!) figured out why this was the move. White still has 3 pieces "attacked": WBf4, WNc4 and WRc6, whereas Black only has 2 pieces under "attack": BRc8 and BBc1. Consequently, Black still has the opportunity to end up with a material advantage. After 2. Rxc8 Rxc8 White still has 2 pieces "attacked" with only 1 Black piece "attacked". If White moves away the Knight with 3. Ne5 (or 3. Na5) then Black can eliminate his hanging BBc1 with 3. ... Bxf4. On the other hand, if White captures the BBc1 with 3. B (or Nxc1 then Black regains his material with 3. ... Rxc4, ending up with the Exchange, an extra Pawn and a 2:1 Queenside Pawn majority.

    So, the "key" appears to be counting how many pieces are under "attack" overall, and, if Black has an advantage, there must be some sequence which will allow him to make one more capture, regaining material.

    1. "2041.0 You are certainly not picking easy problems to demonstrate the concepts!"

      I do that because my gut feeling tells me that the position IS actually simple, and that I SHOULD be able to see it that way. What my gut feeling didn't tell me is that would take up three days to do so.

      "White still has 3 pieces "attacked": WBf4, WNc4 and WRc6, whereas Black only has 2 pieces under "attack": BRc8 and BBc1. "

      It suffices to count only the pieces that are hanging. Since the pieces that are not hanging, are simply exchanged. The adage of Tal is about hanging pieces.

  3. My move was rook x rook . I will need to read Roberts comments closer. But a thought as why the bishop take works is that the black a3 bishop is a sitting duck [for white] and its striking first takes it out of the role. Although i could be wrong.......

  4. Unsure of this but is this in a way of improving blacks worst piece ???

  5. A3 square has an exploitable weakness of only being protected by a queen.

  6. @ Jim Takchess:

    I know I thought about removing the Black Bishop from "attack" during the first moments of looking at the position. I kept "seeing" the LoA of the White Queen as well as the rescue of the White Knight at c4. You are also correct that it is a way to "improve" Black's worst piece. Good ideas!

  7. I solved it, took at least a good five minutes, but it's more of an observational exercise. Most problems in chess seem to me to be observational exercises.

    Threat recognition, and even material counting can be considered a threat if you can do it wrong, has been my weak point. I know players online do a better job of this than I do because they will pause, and I won't know why at first, but then quickly pick up on the threats and dilemma that they have spotted. How well you observe the board, and threat recognition are closely linked. Sometimes it's about spotting mistakes that haven't happened yet.

  8. I completely do not know how to express it clearly, but I CANNOT explain to myself why one move is better than the other in this specific position (BxR vs RxR).

    Anyway my unconcious mind gives me some directions (maybe you can use these anyhow Tempo):

    1) there must be some additional value (function) that one move performs while the other does not.
    2) it is connected with "Re-Loader" motif - coined by Weteschnik.
    3) it includes the hidden move function - leaving the square (with capture) with simultaneous opening/closing the lines of attack (defence).

    I have no clue HOW to express it as best as I can, but my dear Tempo - you should check out the following two articles (and respective positions):

    1) the position that even masters (or players 2200-2300) failed to play correctly. It was the position with Nxc6 motif and both queens were attacked in the same time (it was opening part position - probably after 8-10 moves)

    2) the article related to the position (at endgame part) with destroying the defender motif - when one side plays "safe" move, but the other sacrifices the Rook (for Bishop)... and after that BOTH white and black rooks are in direct contact (if white takes 1st rook, black takes the 2nd and the inverse scenario, too).

    It you merge (connect) all of these parts you can make next step forward. I think it would be a good idea to notice after each ply (half-move) what functions are gone and what new functions appears.

    I am not sure if this helped you in any way, but at least I tried! :). Keeping fingers crossed. The topics you are presenting nowadays are simply AWESOME (even if some of these damn hard!). I love it! Thanks! Keep up going great work!

    1. @Tomasz, interesting stuff. do you have links to the articles?

    2. @takchess

      All of this stuff I was reffering to is available at Tempo's blog. However I think the author will be the most fluent at finding (pointing to the links) these specific articles.

  9. I have seen so many calculation explanations of games' moves, that calculation isn't as much a weakness lately, for me, as say it feels like it is for my online blitz opponents.

    My number #1 issue/weakness is threat recognition. If I spent 7 minutes on this problem, I simply didn't _see_ the NxBa3 threat for the first 4 minutes. At first, I just said "duh...why can't I play 1...RxR(?)"

    Since I knew this position was a problem (for somebody, else I wouldn't be looking at it), I did a material count, then saw the threat of NxBa3, and could see right away that ...BxRc1 was correct, by following the simple threat trail.

    Okay, let me back up, when I first looked at this position the major thing that stuck out to me was that Black's king and queen were not threatened, so then I knew that it was a simple calculation exercise, and that Black finds nicer threat trails against White than vice-versa.

  10. It finally dawned upon me. I added a conclusion to the post in green.

  11. Excellent addition (in green). That's what I was reffering to! I am really EXTREMALLY curious how much influence does strategy and positional understanding to chess tactics. I bet it MUST be quite important as masters and grandmasters while playing bullets and ultra-bullets (half minute or even 15 seconds for a whole game!) must use much more than simple "fast counting". The tactics at an easy level may be understood with the use of "simple logic and some puzzles solved", but at the level 2000 and above simple means like we can see... are no sufficient enough to make a success!

    What do you think about the role of strategy (elements) to the tactical fluency?

    1. "What do you think about the role of strategy (elements) to the tactical fluency?"
      I think that role is non existent.

      Given the speed of positional decisions of grandmasters during blitz play, they must have an equivalent system for pruning irrelevant lines as they do have for tactical decisions. Based on positional knowledge in stead of tactical knowledge.

  12. A very nice post. As I do my own saltmining again with ctart . I am seeing how the theme of giving your opponent too much to do - overloading them with responces is prevalent. Given too much to handle and chasing shadows where the pieces once stood.

  13. I like your distinction between "normal" (single function) and "special" (double function) moves. Obviously, there is a connection between "counting" the function(s) of the involved pieces, and also "counting" the quantity of such pieces for each side. As you noted, once you "see" these "functions" clearly, then the position does become "simple" (in the appropriate sense).


  14. PART I:

    I've been thinking about a phenomenon that has puzzled me: the more advanced players (master and above) seem to play (almost exclusively?!?) on the basis of intuition - certainly much more than the class players do. Yet, if this is so (and I have no reason to doubt the many masters who have stated this to be true), then what are they doing for so long on each move when playing at slower time controls? If the intuition (System 1) is reliable, what takes the masters so long to finally make a move?

    I found a succinct answer on the accompanying link to Path to Chess Mastery: "How do you know you are becoming a stronger chess player?"

    To quote Magnus Carlsen: "Of course, analysis can sometimes give more accurate results than intuition but usually it’s just a lot of work. I normally do what my intuition tells me to do. Most of the time spent thinking is just to double-check."

    The "fast" System 1 (intuition) provides the "right" moves. The "slow" System 2 (logical thinking) confirms/disproves the intuition, changing or overriding it if needed. That's why the masters can play so fast (at a very high level) at blitz and also why it takes so long for them to make a move at classical time limits. In both cases they are using intuition as the basis for their move selection. At longer time controls, they are merely(!) performing more detailed logical checks, based on the amount of time available. Logical thinking requires considerably more time.

    We adult class players depend on "seeing" logically based on KNOWLEDGE, not intuition. That's why we are so S-L--O---W to "see" what is important and what "needs" to be played. The important SKILL is to build the intuition, not to develop and utilize a multi-step logical thinking process. I think recognition of PLF must become second nature (and NOT consciously and logically thought through) in order to harness its power to the intuition. This can be done by consciously (at first) working through ever more complicated positions, stepping through the process, until the process itself becomes ingrained in the subconscious. We know we will have achieved the required inculcation into the subconscious when we stop thinking logically about PLF and can glance at the board, "SEEing" the PLF (and the ramifications such as motifs and tactical themes/devices) without being consciously aware of them. Until we reach that intuitive level, we will struggle to "see" the requirements of the position - and we will not improve our skill.

  15. PART II:

    The Zen Buddhists refer to this desired intuitive state as "Beginner's Mind." I had not previously connected that concept to what is required in order to gain SKILL in chess. This explains why young prodigies grasp so quickly and easily the things that we adults struggle to "see." Our knowledge and our reliance on logical thinking actually hinder us from just "seeing." We think that if we just learned a few more things (knowledge), we would play better. We ASSUME that more knowledge translates to more skill; THIS IS NOT TRUE! It is the ever accumulating knowledge and reliance on that knowledge through logical thinking that blocks us from just "seeing."

    It is a direct illustration of the "streetlight" effect, a type of observational bias that occurs when people are searching for something and look only where it is easiest.

    A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, "This is where the light is".

    Our "streetlight" is all of the various sources of knowledge that are so readily available: books, DVDs, articles, etc. We are searching for SKILL (the lost "keys") but looking in the wrong places (KNOWLEDGE). Unfortunately, most of the well-intentioned advice given in all of those sources simply leads us farther and farther away from where we should be searching.

    "THE ROAD TO HELL [the difficulty of adult chess improvement] IS PAVED WITH GOOD INTENTIONS [in the form of readily available KNOWLEDGE, logical thinking and advice]."

  16. PART III:

    All of that “theorizing” sounds great because it’s so “logical” and fits what we expect to “see” as adults. It’s also WORTHLESS for direct improvement of chess SKILL. Let me try to illustrate. Please keep in mind that I am NOT trying to increase your KNOWLEDGE; instead, I am merely trying to illustrate the thesis with simple examples.

    Most of us (perhaps) are familiar with the “rule” of the “square of the Pawn” in Pawn endgames. (If you are not familiar with this “rule,” no worries; hopefully, you will still be able to “see” the point of the examples.) The “question” (requirements of the position) is very simple:

    Can an unopposed (passed) Pawn advance to promotion unaided by its own King, or can it be stopped by the opponent’s King?

    Example 1: 8/7k/8/8/8/8/P7/7K b - - 0 1

    The answer to the “question” can be found in various ways.

    (1) We can logically “count” the number of moves for the Pawn to advance to the 8th rank. We can then “count” the number of moves for the opponent’s King to reach the promotion square. If the opponent’s King can reach the promotion square before or right at the moment of promotion, then the Pawn can be captured. In that case, we must look for some other way to exploit having a passed Pawn.

    (2) We can “learn” (KNOWLEDGE) the “rule” of the “square of the Pawn.” Draw a diagonal from the square in front of the Pawn (use the square that is two squares in front of the Pawn if it is still on its original square; already we find an “exception” before we have completed our “rule”!) to the 8th rank. Count the squares along this diagonal. Create a “square” from the origination of the diagonal with the sides equal in length to the number of squares on the diagonal. If the opponent’s King cannot move into this “box,” then it cannot stop the Pawn from promoting. If it can move within the “box,” then the Pawn can be stopped – in that case, we must look for some other way to exploit having a passed Pawn.. (And here’s another “box” to learn to deal with!)

    It is important to pay attention to that phrase: in that case, we must look for some other way to exploit having a passed Pawn.. We have formulated a logical “rule” and also what to do if the “rule” does not apply. BUT (and it’s a BIG BUT), we have lost sight of something very important with our “rule” making. We focused primarily on the Pawn, but ignored that larger context containing either or both Kings. It is just as important to “see” the implications for the Kings! The Pawn advance does not occur in a vacuum. We just don’t place as much importance on the Kings as on the Pawn.

    Consequently, we don’t “see” the potential movement(s) of the King(s) as being of equal importance – and we “drop” that little bit of “seeing” down the memory hole. The crucial piece of information that is overlooked is that the distance along the diagonal is exactly the same as the distance along the sides of the square. This conflicts with our geometrical KNOWLEDGE of the “rule” for the Pythagorean triangle: c^2 = a^2 + b^2. This “rule” is stated as: the sum of the squares of the sides of a right triangle are equal to the square of the hypotenuse. Because there is a conflict between our two “rules,” we subconsciously discard the demonstrable “fact” that in chess, c^2 = a^2 = b^2, or actually: c = a = b. In words, that means that the path along a diagonal for a King is exactly as long as a path along either side.

  17. PART IV:

    Bringing that “fact” back into consideration is the “point” of Richard Réti’s famous 1921 endgame puzzle.

    Example 2: 7K/8/k1P5/7p/8/8/8/8 w - - 0 2

    Black just played 1. … h5. White is to move and draw in this position. At first inspection, it appears that White has no hope in drawing. His king is well outside the "square" of the black pawn and the king is a long way from supporting his own pawn. However, White can draw by making KING moves that have two purposes. One goal is getting in the square of the black pawn, so it can be intercepted and the other is getting to the d6 square to support the promotion of his pawn. The black king will have to spend two tempi to stop the white pawn from promoting, and this is the number of tempi the white king needs to gain in order to get into the “square” of the black pawn.

    If your KNOWLEDGE contains the “rule” for the “square of the Pawn” then you may despair of solving this problem. If your KNOWLEDGE includes calculating how far away your King is from your own Pawn (and how close the Black King is to it, within the “square” of it), you may despair of solving this problem. It becomes logically “impossible.” It is only when you “SEE” that you can approach BOTH possibilities SIMULTANEOUSLY that you realize there IS a solution. THAT “insight” is NOT the same as the “rule.”

    The “point” is that there are several things going on simultaneously. The White King must use the “square of the Pawn” rule to get inside the “square” of the Black Pawn. At the same time, it must threaten to promote the White Pawn, forcing Black to expend the two tempi to stop it. In short, it is a duplo attack, using the exact same “idea” underlying the “rule” of the “square of the Pawn” – the distance along the diagonal is the same as the distance along the sides of the square in chess.

    In our haste to acquire KNOWLEDGE in the easiest possible way, we internalize the tidbit regarding the Pawn, but do NOT internalize the same concept regarding the King movement. Yet, I believe that the internalization of the “square” of the King is arguably just as important as learning the “rule” for the “square of the Pawn.”

    In any event, I think it illustrates that in our pursuit of KNOWLEDGE, we often gain AND LOSE vital information at the same time. We build a “model” based on our knowledge. As I have stated many times, the value of a model is predicated on what is left out of it as well as what it includes. If vital information is lost, then the “model” becomes less than optimum, and is (perhaps) worthless.

    Gm Rowson asked a question: Why is adult chess improvement so elusive?

    He answers:

    To my mind, the problem can be distilled into two main parts:

    1) Most players seek to increase their KNOWLEDGE by learning new positions, and tend to study by "reading and nodding" as Nigel Davies put it. What they should be doing more often is honing their SKILLS, however meagre, BY FORCING THEMSELVES TO THINK THROUGH TRAINING AND PRACTICE.

    2) KNOWLEDGE OFTEN GETS IN THE WAY OF SKILL, because it's not 'innocent' - and has to be constructed. This means that there will be limits to what you can learn by passive absorption and that you are more likely to make progress by UNLEARNING some of your existing ideas primarily through the honest and rigorous analysis of your own games.

    Chess for Zebras: Thinking Differently about Black and White, Jonathan Rowson, C 2005

  18. I see it as an attention guidance problem. We have a fully fledged unconscious pattern recognition system. We only have to spark it, by guiding the attention to the right square of the board.

    The problem is, that we are easily distracted and disturbed. The reason for that is that the numbers of the tree of analysis grow rapidly.

    Due to the easy distraction and the turbidity we tend to think about the wrong things. Even the simplest chess logic takes ages to formulate when in that state of mind.

    The knowledge we are talking about is not rocket science. It is of the level of "when a piece is defended, you have to shift your attention from the target to the defender". Robert calls it seeing, I call it attention. We mean the same.

    If we dive into the tunnel of reasoning, it is a matter of chance whether it is the right tunnel.

    To avoid the threefold state of rampage of the mind, namely distraction, turbidity and tunnel vision, we need order in the mind. The only way to get to that order, is by pruning the irrelevant. Thinking about what is relevant doesn't take much time. It is the irrelevant which consumes us.

    This means that the knowledge and rules I'm interested in are always related to pruning the tree of analysis. One way or another. In chess, most rules translate to geometry. Geometry can be seen. The rule of the square of the pawn can be seen as a geometrical square. The rule of the square dismisses us from the need to imagine the sequential steps to promotion while the opponents king runs to the promotion square. All steps are summarized into the geometry of the square. We need this kind of knowledge, translated to geometry. The sequence in time must be translated to a geometrical picture that is seen at once. Thus freeing up the STM.