Sunday, October 15, 2023

The final conundrum

 It took me 18 years to find the bottom steps of the ladder to chess improvement. Often I thought that I had found the beginning. But time after time, a close scrutiny of the results of my training sessions, tempered the initial enthusiasm. Usually after a month or three. Mr Glicko and Mr Elo are relentless.

I always managed to keep my mouth shut when I thought that I was successful. Until May this year. When I discovered the importance of chess logic as the base of transfer between chess problems, and as the base of analogies in chess, I felt that I finally was on to something. I felt that I was improving. Of course that is subjective proof, but since I don't was punished by disappointment after three months, that was good enough for me. It worked. So I finally found to courage to speak up a bit.

But it wasn't efficient. It started to dawn on me that still something was missing. I started to analyze my losses, and I was working on my five new openings as a madman. I noticed the weakness of my middlegame play, and I started to work on my positional play frantically. I discovered that result = what x how.

Another breakthrough came when I started to experiment with different problem depths. In May I started with problems of 5 ply deep. That was an arbitrary choice. When I tried problems of 7 ply deep, I felt I could still work on my logic, but my training sessions lost momentum. It became more difficult and daunting to make progress. That was the reason that I started to experiment with problems of only 3 ply deep.

I had done so in the past, and I had abandoned it because I thought it was too easy. But back then, I focused on pieces and positions, and nowadays I focus on logic, which has a higher level of abstraction. When I selected problems with a rating of higher than 2100 AND 3 ply deep AND mate, I thought I had found the holy grail.

But again I was in for a shock. Sofar, I only had focused on mate in 2. The golden standard is the performance of Susan Polgar during her simul. If I'm not at least heading in that direction, I am going nowhere. For the first time I had the feeling that a tenacious training might lead to a faster seeing of mate in 2. The choice to focus on mate in 2 solely, was arbitrary too. When I tried to do other tactics in the same manner, I all of a sudden felt totally lost. Since a mate in 2 ends after two moves, no matter what. But a non mate tactic doesn't necessarily end that way. You might find yourselves in the thickets of variations that are not clear at all. I called that the final conundrum that must be solved. "How to train tactics that don't end with mate?". 

While writing the previous post I had a revelation. Blogging does that to me, that is why I write everything down. It became apparent to me that you cannot begin with logic when you have no idea what you want to achieve. And that you can only know what you want to achieve when you see it.

When I started with logic, I had suppressed the vulture. But without the vulture, you have no starting point for your logic. This means that you must split the training in two. The vulture must be trained, and the logic must be trained.

Let me try to clarify that.

White to move

q2r2kb/1b3p1p/5PpQ/3np3/2p1N1B1/2N5/1P4PP/5R1K w - - 0 2 


Make a clear distinction between the salient cues and the ensuing logic. I said it often, I don't think it is important to find the solution ourselves. You can do so if you like, of course, but I consider it a waste of time.

In the previous post I made a difference between the executional move and the preparational move. The executional move has salient cues that must be learned by the vulture, while the preparational move must be used for training your logic reasoning.

What execution are you invited for in this position? The position invites you to play Ng5 and mate your opponent. Get a clear picture of the salient cues which gets you there if the opponent is not allowed to make moves.

Once you have a clear picture of what you want to achieve, you must ask yourself how your opponent is going to prevent it.

You will find that the knight on d5 is a very annoying beast. When it starts to move it unleashes blacks bishop, queen and rook.

You need some perseverance to get rid of the beast. When you find the move 1.Be6, you will find another salient cue. 1. ... fxe6 is impossible due to 2. f7#

The vulture might have missed that initially. Put that salient cue in your backpack.

It is a kind of Stoyko exercise, but then for tactics. In the end you will have a list of salient cues and a list of narratives. Take your time.

This is the direction in which I look for solving the final conundrum. Whether this conundrum is final or not remains to be seen. Time and again, the devil is in the details. But I feel very optimistic about it. But that never has proven to be a guarantee.


  1. PART I:

    As we improve, there is a change in both what we focus on and how we think about each position. The “same” position (revisited after years) can reveal different “secrets”. In every case, there is a necessary deepening of “seeing” salient cues and the thinking processes that are triggered. As previously noted, skill in chess (and every other domain that I can think of) is not one but several mini-skills.

    A recent insight was that pattern recognition is, in essence, an implicit perception of similarity. Pattern recognition is NOT based on the concrete pieces-on-squares that formed the theoretical basis of “chunks” as originally proposed by Simon and Chase, nor the embellishment of “templates” added later to chunking theory. Instead, the similarity is between the current concrete situation and various abstract roles which have been ingrained into LTM through repetition. It is necessary but NOT sufficient to be exposed to a wide range of similar (at the abstract role level) positions, which may be totally different with no commonality on the basis of pieces-on-squares.

    One of the marvelous “skills” of the human mind is the creation and expansion of categories via analogies through a subconscious abstraction process. We often try to categorize positions by shoehorning a given position into a specific labeled category. This can actually be more harmful than helpful in developing skill. We ASSUME that because we have labeled it, we “know” it. Familiarity with the label breeds contempt for the deeper aspects that we did not “see” when we applied a label to it.

    I’m willing to bet that anyone who has spent as much time as we have studying chess can regurgitate on command a textbook “definition” of the various tactical themes/devices like forks, pins, etc. The problem is NOT that “we know it when we see it (visually)” but that we DON’T know it when we “see” it in the form of abstract roles based on piece/square relationships and trajectories, IE, the “dynamics” of the position. In short, the labeling process gives us knowledge but not skill. Instead of our knowledge informing our skills, we ASSUME that knowledge IS skill.

    This is one reason why an adult has more difficulty improving than a youngster. We have acquired many years of experience ingesting knowledge and regurgitating it on command; that is the fundamental process in formal academic education. We get rewards in the form of credentials certifying our “expertise”. As the old saw goes: “In theory, theory and practice are the same; in practice, they are NOT the same.” We “know” from experience that practice (applying knowledge in the real world) MAY be quite different from the theories we learned to repeat as mantras.

    I made a silly request earlier for information regarding your problem set; my apology – forget it. The SKILL to be gained is acquired from intense focus on PERSONALLY performing the abstraction process. Taking the results of what someone else has acquired through hard, intense focus identifying the salient cues and trying to remember it is nothing but another attempt to acquire knowledge. Such knowledge acquisition does NOT produce skill!

  2. PART II:

    You made a great point:

    Make a clear distinction between the salient cues and the ensuing logic. I said it often, I don't think it is important to find the solution ourselves. You can do so if you like, of course, but I consider it a waste of time.

    The only way to internalize the salient cues and the ensuing logic is to DO THE WORK INDIVIDUALLY. The given problem set is as irrelevant as finding the solution. As GM Nigel Davies put it (repeating from an earlier comment):

    “The HOW is more important than the WHAT. It really doesn’t matter what you study, the important thing is to use this as a training ground for THINKING rather than trying to assimilate a mind-numbing amount of information. The reality is that YOU have to move the pieces around the board and PLAY with the position [in your own head]. Who does that? Amateurs don’t, GMs do.”

    This advice illustrates how easy it is to misunderstand improvement advice because we ASSUME we KNOW what is intended. Our prior knowledge leads us to ASSUME meaning that may be considerably (if not totally) different from what was intended to be conveyed by the advisor.

    The HOW in this quote is NOT about learning specific techniques or thinking processes. It is instead how we approach our training with focus and attention. What are we really trying hard to “see” and how focused are we while trying to “see” it? That makes all the difference in the world in acquiring SKILL. I recall advice from Master Gichin Funakoshi regarding martial arts training:

    What you have been taught by listening to others' words you will forget very quickly; what you have learned with your whole body you will remember for the rest of your life.

    Memorizing the solution to 10,000 tactical problems will NOT necessarily provide any usable SKILL when faced with a new unknown problem or position. Memorizing the steps of a specific thinking process so as to be able to regurgitate them will NOT necessarily provide any usable SKILL when trying to determine the best move in a given position. The difference is between description and prescription. Descriptions are only useful for communicating with others during a discussion of theory or providing knowledge; they are otherwise useless for acquiring SKILL

    Note to self: FOLLOW YOUR OWN ADVICE!

  3. After reading your blog post, I started thinking about how to train tactics that don’t end in mate. I have been using for my training, primarily using Puzzle Storm.

    Problems that end in mate have a concrete ending; there can be nothing more to consider. However, tactics that gain some type of advantage (material, positional) that does not end the game immediately leave one with a feeling of uncertainty, and the necessity to decide what to do next.

    My approach to the “final conundrum” is to first, trust my intuition and judgment. Even if I can’t calculate forward sufficiently to reach a recognizable evaluation that I am definitely winning AND that I also KNOW how to proceed from the problem end point, I accept that it is sufficient (for that particular moment) to have improved my long-term prospects of winning.

    The process is fairly simple. Going back to Aox’s process, first try to get a “feel” for the goal of the problem (checkmate via a forced sequence of moves [without concern for how many ply it may take], or relative gain of material [which includes promoting a pawn]). That sets a goal for WHAT needs to be done and also constrains the means of HOW to go about it.

    Next, get a “feel” for the tactics that are available (on the surface). Mentally try out a few of them to “SEE” if they can work. This is not strictly calculation; some authors call it “short tactics.”

    Then, using the “obvious” tactics, begin trying them out mentally [Klein’s mental simulation] using intuition. If there is an obvious refutation, choose a different tactic and try again. Very important: include all refutations in all future simulations involving that specific problem. That provides a sharpening of the focus on how to make the tactics work favorably. Keep in mind that the best moves for the opponent sometimes can be more difficult to discover than my own moves.

    After deciding on a specific solution, enter it and see if it is the approved solution. Determine if the solution ends in mate or not; if it does not, don’t go to the next problem. Continue to look at the “end” position as a “stepping stone” [Tisdall]. See if you can figure out (NOT guess) how things will progress for the next few moves. When I am certain of how and why I will proceed AFTER reaching the “solution” position, then I turn on the Stockfish engine (the little slide button on lichess) and see what Stockfish suggests as the continuation for both players for the next few moves. I pay very close attention if Stockfish suggests a sequence that I did not “SEE” at all. I don’t leave that problem until I understand WHY that is a better solution. Sometimes, in order to get a better “feel” for the context in which the tactics arose, I will replay the entire game from the beginning, using Stockfish to tell me when there is a large switch in evaluation from one side to the other. It’s very important to “SEE” why and what the mistake(s) are that caused the evaluation to switch sides.

    At that point, I leave that problem and go to the next one.

    Lather, rinse, repeat.

  4. I just began rereading Gary Klein's book Sources of Power: How People Make Decisions, 20th Anniversary Edition, looking for more understanding of methods and approaches to improve decision making skills. Mapping across different domains sometimes requires mapping equivalences between the terminologies.

    Deconstructing the typical logical approach to calculation.

    We adult chess improvers know what that word means: “I go here, he goes there, I then go there, . . .” The “gold standard” (which chess “experts” love to either extol or denigrate) has to be GM Kotov’s thinking process. To save space, I’ll use GM Valeri Beim’s summary of the 4-step process, given in his excellent book How to Calculate Chess Tactics — A revealing look at the nuts and bolts of chess thought:

    First of all, let us consider what Kotov himself says about his theory of calculating variations:

    “1) In beginning our calculations, we must first of all list all the possible moves in the position — the candidate moves — so as to ensure that we do not overlook some important possibility.

    “2) Having done this, we then calculate each variation in turn. The order in which we do this depends on the character of the player and the characteristics of the position. Every player has his own way of doing this. One prefers to start with the most difficult lines, and only then turn to the easier ones, while another player prefers the opposite.

    “3) All of the possible lines can be pictured as a ‘tree of variations’.

    “4) The main rule in calculating is that the player must train himself during a game to go over each branch of the tree only once and must not be tempted to return to lines he has already looked at.”

    Criticism #1: Are we to look at “all the possible moves” or only “the candidate moves”?

    Criticism #2: NOT overlooking some important possibility implies an evaluation of all move possibilities – PRIOR TO deciding which moves are “candidates” and which are not. What is the basis of that evaluation?

    Criticism #3: Ordering the calculations implies an evaluation based on the characteristics of the position. There must be SOMETHING directly visible at the surface level to use as the basis. What lies on the surface that gives a reliable indication of the difficulty or ease of calculating a specific variation into the future?

    Criticism #4: No human will ever be able to hold an exponentially growing tree in short-term memory. How can a human be expected to hold the tree of moves AND the corresponding endpoint values, backed up through the interim nodes to ply 0? {As GM Lein lamented to GM Tisdall: “I don’t think like a tree; do you?”

    Criticism #5: How do we move ideas gleaned from one branch to previously explored branch?

    Criticism #6: Why are we exploring variations on the basis of individual moves? Isn’t this a case of “seeing” the individual trees and missing the forest?

    Criticism #7: Presuming that this process can be applied during training and analysis not during a game, how do we gain anything from trying to follow the process under limited time during a game?
    I’m sure there are other valid criticisms of this approach to calculation.

    As rational as this process appears to be (and it is very appealing in its apparent logical simplicity), NO ONE ACTUALLY USES IT DURING A GAME! If you try it, you will very rapidly get lost in the minutiae of just keeping track of everything AND you will consume enormous quantities of time doing it — and you will NEVER get close to coming to a rational decision on the best move to play for a single move, never mind the entire game.

    There MUST be some alternative that works; otherwise, master level players would not be able to play better than club players.

    So, what’s the alternative?

    I have some thoughts about that. Later. . .

  5. Prior to getting into an alternate reality (a different perspective on the calculation process), take a look at a relatively ‘famous’ example of starting the process by making a complete list of candidate moves from the Maestro himself.

    GM Alexander Kotov, Think Like a Grandmaster, pp 16-17.

    FEN: 1brr2k1/1b3pp1/pp2pqnp/4N2Q/3P4/1B4R1/PP1B1PPP/4R1K1 w - - 0 1

    (As an aside, this position is also analyzed by GM Andy Soltis in his book The Inner Game of Chess: How to Calculate and Win, pp 78-79. GM Soltis does a better job of identifying the critical candidate moves by identifying the winning move that was NOT even mentioned by GM Kotov.)

    The ten moves in the following list were proposed by GM Stockfish as the top ten ‘candidates’ (with the number of moves to be searched set at 20). Those moves are a superset of the moves proposed by GM Kotov. I have deliberately (randomly) rearranged the move order as evaluated by GM Stockfish, so as not to spoil the “fun” of figuring out the actual candidate list that SHOULD be considered. Recall from my last comment that the very first step of the Kotovian thinking process (at least for calculation purposes) begins with making a list of ALL potential candidate moves, “so as to ensure that we do not overlook some important possibility.”

    GM Kotov states:

    White’s attack on the king side looks very threatening, and naturally the master who was White tried to find a concrete way to shatter the enemy king or to get some decisive advantage. As it is not very difficult to SEE, this concrete line must involve a sacrifice.

    Making a list and checking it twice,
    gonna find moves which are naughty or nice.

    Santa Claus is watching YOU!

    1. Bxh6
    2. Nxg6
    3. Ng4 (intending Nxh6)
    4. Bc3
    5. Nxf7
    6. Rxg6
    7. f4
    8. Kf1
    9. Bxe6
    10. Be3

    Which move(s) did GM Kotov include in his list of candidate moves?

    What move was actually played by the master playing White?

    What order did GM Stockfish assign to the moves in the list, best to worst?
    What move should have been played according to GM Stockfish in order to gain a large advantage (+5.74 after 15 minutes of analysis)? Oh, by the way, this proposed ‘best move’ is the ONLY move that GM Stockfish ‘thinks’ gives White a significant advantage.

  6. The “solution” to the questions asked in my previous comment:

    GM Stockfish scores the top 20 moves this way, after 2.5 hours of “thinking”:

    [Note: Moves marked with an asterisk are the moves listed in my previous comment.]

    *#1: +5.94 — 1.Nxf7 [BEST MOVE – NOT included on Kotov’s list]
    *#2: +0.39 — 1.Ng4 [Third mentioned on Kotov’s list, and his recommended move]
    *#3: 0.00 — 1.Rxg6
    *#4: -1.18 — 1.Nxg6 [Second mentioned on Kotov’s list]
    *#5: -1.37 — 1.f4
    *#6: -1.53 — 1.Kf1
    *#7: -1.64 — 1.Bxh6 [First mentioned on Kotov’s list]
    *#8: -1.83 — 1.Bxe6
    #9: -2.17 — 1.Qe2
    *#10: -2.33 — 1.Be3
    #11: -3.35 — 1.Rf3
    #12: -3.40 — 1.Re2
    #13: -3.42 — 1.Nf3
    #14: -3.43 — 1.Rg5
    #15: -3.67 — 1.Rh3
    *#16: -3.67 — 1.Bc3 (Played by the master with White)
    #17: -3.68 — 1.Rc3
    #18: -3.72 — 1.Rg4
    #19: -3.86 — 1.h3
    #20: -3.81 — 1.h4

    Oopsies! A strong GM completely missed the strongest candidate move! A master level player did not even choose one of the top ten “candidates”!!

    GM Soltis asks a cogent question: “Why, if White is looking to sack a piece, didn’t he [either GM Kotov or the master playing White] consider one of the most natural moves in the position?

    Surely it cannot be because of any insufficiency in carrying out the logical process of calculation. Surely it cannot be any insufficiency of experience with similar critical positions. Something failed to trigger the appropriate response in System 1 to the initial vulture’s eye view. All the disciplined logic in the universe will not help to calculate moves and variations that you do not SEE as viable opportunities PRIOR to beginning the calculation phase/process!

    There are none so blind as those who CANNOT “SEE”!

  7. Part I:

    Reference: Sources of Power: How People Make decisions, Gary Klein, The MIT Press, © 1999

    Please note: the following is a DESCRIPTION (N-O-T “prescription”) of the mental simulation process used to project into the future, either to predict what is going to happen and perhaps to prepare for it, or to watch a potential course of action to find out if it has any flaws. [Both of these aspects are present in chess when trying to decide on the next best move(s) or, failing that objective, at least good move(s).] Mental simulation is a heuristic strategy, and is the ability to imagine people and objects consciously and to transform those people and objects through several transitions, finally picturing them in a different way than at the start.

    People in various domains construct mental simulations almost the way you build a machine: “Here is the starting point. Then this kicks in, which changes that, and then the other thing happens, and you wind u there.” Mental simulations are not very elaborate. Each simulation seems to rely on just a few factors—rarely more than three. The simulation seems to play out for around six different transition states. These restrictions may be caused by limited working memory. Ways to avoid these constraints include: chunking several transitions into one unit; treating a sequence of steps as one step rather than representing all the steps; using our expertise to find the right level of abstraction; or [not available during a chess game because of the rules prohibiting it] writing things down and drawing diagrams to keep track of the transitions.

    The person assembling a mental simulation needs to have a lot of familiarity with the task and needs to be able to think at the right level of abstraction. If the simulation is too detailed, it can chew up memory space. If it is too abstract, it does not provide much help. Experience in the domain is necessary for building mental simulations. There are cases where the people involved could not assemble a mental simulation.

    Novices are unable to construct mental simulations, whereas “experts” can do it almost without conscious thought. Without a sufficient amount of expertise and background knowledge, it may be difficult or impossible to build a mental simulation.

    Given the Blogger limitations on images or diagrams in comments, I cannot reproduce the diagram of the process of projecting into the future. I have converted the diagram into verbiage, which I hope adequately the essence of the process. I have elaborated on some of the steps for clarity (or obfuscation, if you can’t clearly “SEE” the ideas).

    For those with a structured programming background, I have made no attempt to “normalize” the process steps to eliminate some of the branching. I’d rather present it “as-is” than screw it up.

  8. Part II:

    Jumping right in:

    Step 1: Overall goal: Project into the future using a mental simulations.

    Step 2: Specify the parameters:
    Initial state — the current position
    Final state — a desirable position
    Causal factors – Vulture’s eye view

    Step 3: Assemble the action sequence(s)
    3 causal factors
    6 transition states - between the initial state and final state (calculating ahead)

    Step 4: Perform an internal evaluation of the action sequence(s)
    If acceptable, go to step 5; otherwise, go to step 6.

    Step 5: Run and review the action sequences
    Go to step 7 (if problem areas found) or step 9 (if no problem areas found).

    Step 6: Failure to assemble a mental simulation. Go to step 1 or step 2.

    Step 7: Identify problem area(s), if any asking three questions:
    Does it make sense (coherence)?
    Will it get what I need (applicability)?
    Does it include too much or too little (completeness)?

    Step 8: RECURSIVE: Perform a mental simulation of the problem area(s). [Use stepping stones to keep track of where you are as you drill into the problem area(s).]
    Go to step 9.

    Step 9: Evaluate the outcome.
    If unacceptable outcome, reject the course of action and start over at step 1.
    If somewhat acceptable outcome (perhaps requiring “tweaks” or minor changes), modify the course of action and go to either step 1, step 2, or step 3 and repeat the simulation.
    If acceptable outcome, go to step 10.

    Step 10: Prepare for implementation.
    Predict the outcome.
    Estimate the data.
    Generate a course of action.
    Evaluate and inspect the risk(s).

    Step 11: Implement the planned course of action.

    This process is applicable to all aspects of determining the next move, regardless of whether it is a strategical plan, or a tactical plan with a clear-cut result (mate) or an indeterminate result.

    Here is a key point: this process is NOT based on individual moves and trees of moves! It is primed by System 1 (pattern recognition; experience; knowledge). As noted earlier, the “units” can be at any level of abstraction. The “simulation” is performed by System 2, guided by System 1’s intuitive suggestions at each step in the action sequence(s).

  9. Here I walk out on thin air like Wily Coyote chasing Road Runner.

    PART I:

    In a previous comment, I opined:

    There MUST be some alternative that works; otherwise, master level players would not be able to play better than club players.

    So, what’s the alternative?

    GM Susan Polgar’s simul performance is the gold standard for making consistently good moves under extreme time pressure (usually varying between 2.6 and 5.0 seconds per move ON AVERAGE). Our working hypothesis is that she (somehow) “SEES” the appropriate line of play based on internalized pattern recognition, without having to do very much calculation (if any at all). In a given position, she “knows” which move is best and just plays it.

    In contradistinction, I propose that she DOES “calculate” ahead, BUT she does NOT do it on the basis of individual moves. I think it is more of a “feel” which guides her to the rapid conclusion that “in this TYPE of position, this SEQUENCE of moves is the best line of play.” In short, she is NOT playing on the basis of “general” principles or “rules,” nor is she magically endowed with a super fast brain that emulates a special purpose computer chess engine. She is “merely” thinking like a highly skilled HUMAN. Experts in all domains do the exact kind of thinking, using similar processes (see my previous comment regarding Klein’s model of mental simulations). Glimpses of “glitches” occur whenever she is faced with a situation that is just a little outside of her internalized (and extensive) pattern base; this show up whenever she has to pause at a given board for just a little longer than average, using a conscious “search” for the closest pattern (NOT an individual move!) that works in that given position.

    To use a worn philosophical simile, for GM Polgar “it’s turtles [patterns] all the way down.” [See Bertrand Russell.] I think she traverses the pattern category hierarchy (up, down and across) at the speed of synapses. Her “calculations” are actually real, but based on higher level patterns instead of individual moves.

    Look at the description Tempo has given for the problem in this blog post.

    What execution are you invited for in this position? The position invites you to play Ng5 and mate your opponent. Get a clear picture of the salient cues which gets you there if the opponent is not allowed to make moves.

    Once you have a clear picture of what you want to achieve, you must ask yourself how your opponent is going to prevent it.

    You will find that the knight on d5 is a very annoying beast. When it starts to move it unleashes blacks bishop, queen and rook.

    Ng5 is mentioned as a potential first move – based on an evaluation that White should be attacking the Black king. What precursor patterns were triggered and evaluated that produced that suggested move? Perhaps it is that the Black king CANNOT move – always a trigger for the pattern “always check—it MIGHT be mate!” Perhaps it’s the fact that Black’s queen is way over on the queenside and unable to come to the defense of the Black king. Perhaps it’s that a TYPICAL queen+knight mate pattern exists for White in the near future, and Black’s defensive resources seem to be somewhat weak. Perhaps it’s “SEEING” that the White Rook is supporting the White Pawn on f6 in its “lust to expand” [Nimzovitch]. Perhaps it’s Lasker’s attack motif, derived from Nimzovitch’s “rule”: “Thou shalt NOT shilly-shally!” Perhaps it’s because White has local superiority on the kingside [5:3] and that the White Bishop needs to find something “useful” to add to the attack. Whatever attentional “cue(s)” were triggered, the search for the bluebird [Tal] begins.

  10. PART II:

    In our previous ruminations regarding the chess “thought process,” we have concluded that the starting point in analyzing a given position is the vulture’s eye view. It is assumed (and accepted) that the vulture’s eye view is an overview of the “forest,” performed from a high level of abstraction and prior to swooping down toward the more concrete view of the “trees” (perhaps even down to a single tree, its bark, any insect infestation, etc.) It is “triggered” by “obvious” (surface level) cues which are an amalgamation of knowledge and experiences which have been internalized, categorized and analogized. Some of this “knowledge” is in the form of heuristics (“general” principles or “rules”) which offer some aid in determining typicality – there is something “obvious” (to US) that is lying right out in the open which “clues” us (directing the focus of our attention) to what we should be anticipating in the near future.

    I suggest that as we gain SKILL, we utilize that approach more and more as we drill into a position. The vulture’s eye view is NOT a “once and done” thing, but it is utilized throughout the entire process of figuring out what to do in the given situation.

    Going back to Klein’s description, the causal factors are [RECURSIVELY] the “triggers” for the “candidate moves.” The initial surface cues start a recursive process, “looking” for IDEAS/CONCEPTS and evaluating them in terms of the goal(s) we first SEE. As we traverse the search space using patterns (NOT necessarily individual moves), we encounter leverage/choke points which cause us to form new sub-goals and evaluations. We may even change our initial goal(s) as a result of what we SEE as we go through the process. The entire process occurs pretty much subconsciously, although we may intentionally direct our focus to specific factors. We usually report our awareness of what’s happening internally in terms of the moves we become consciously aware of, even though the actual process is NOT performed down at the concrete move level.

    Novices (and less skilled performers) gain great benefit from using logical checklists to structure their thought processes. They also gain “shortcuts” (in lieu of expertise) by basing play on “general” principles or “rules” which allow them to pretend to higher levels of skill. Unfortunately, that “crutch” will only take you so far. Think of it this way: how many times have we “memorized” a sequence of opening moves, only to reach the end of our “knowledge” and then proceed to fall apart because we do NOT have a clue as to what to do next?

    I have had the experience of glancing at a position and KNOWING instantly what to play several moves into the future. I’ve played simuls several times against lower (or equal) rated players, including one in which I played 9 boards (average club players) at sight plus 1 board blindfold, winning all but one (and I won the blindfold game). There is no “feeling” of having to calculate each individual move in every game. Instead, there is a feeling of “SEEING” at a higher level, perhaps using what could be considered “chunks.” The interesting thing is that while conducting a simul, there is no time for introspection to determine how I was actually doing it.

  11. PART I:

    Let’s look at the “final conundrum” through the “eyes” of the Patriarch, surely an “expert” on chess.

    [I’m repeating some of the things I’ve used in previous comments, collecting together what I believe is apropos to the final conundrum.]

    M. M. Botvinnik, Computers, chess and long-range planning:

    "Dear reader, only when we firmly decide, together, to reject all this mystical nonsense [miracles, geniuses, incomprehensible laws, and other kinds of 'creativity'] can we put the question: what, properly speaking, goes on in a chess game?

    In my opinion, the process of playing chess (and probably any game) consists in a generalized exchange. By this term we mean an exchange in which (in the general case) the values traded may be tangible or positional ("invisible," situational). The goal of a generalized exchange is a relative gain of these tangible or positional (situational) values. There are not and cannot be other goals. In the end, this generalized exchange process must lead to the winning of infinitely great tangible value (i.e., to mate).

    The proof that something like this goes on in other games is outside our task. But we may remind ourselves that in a game as far from chess as soccer there is an exchange of tangible values (fatigue will change the effective strength of the player) and positional values (conjunctures). Independently of whether the player has the ball or not, he moves with respect to the ball, the goal posts, and other players so that the position of the team shall become more favorable. The objective [in chess], which ends the game if it is attained, is to win an infinitely large material value.

    The tangible [AVERAGE] values of the pieces in chess is well known to all beginning players. But what of the invisible, conjunctural (positional) value of the pieces? This value depends on the position of the piece and on the role of the piece in the general combat then taking place on the board. The positional value of a piece is subject to sharp changes: the intangible value of a Pawn can be very great, for instance when it mates the enemy King."

    If we assume that GM Botvinnik is correct that the objective of the game is (ultimately) gain of material, it does not change the fact that the mechanism of gaining material value is based on FIRST gaining superiority on one or more squares, relative to our opponent. If we cannot gain superiority (somewhere!) on the squares FIRST, then we cannot gain material. It is much simpler to count attacking/defending contacts than material values, and it is more useful for figuring out the available tactics of a position.

    This is where the solution to the “final conundrum” lies. A mating attack has a finite termination point, based on the rules of the game. A tactical sequence (including combinations) aimed to gain material has a finite termination point—but only if we can “SEE” the ending position (determining quiescence is the usual problem which sets the “horizon”) AND properly evaluate it. All other tactical sequence have a fluid termination point, based on our personal experience and judgment.

  12. PART II:

    GM Botvinnik's suggested approach is:

    "A simile may help clarify this notion of the horizon and its determinants. Let us suppose that a parachute-jumper has come down in a bog [swamp] and wants to get to solid ground. The bog is wide; its edges are hundreds of yards away. How does our hero proceed, if he cannot find a clear path from where he is to where he wants to be? He cannot take in the whole plot at one coup and pick out the entire path . . . he must act soon . . . darkness is falling!"

    "In all probability, he will inspect the bog in some given direction [DETERMINED BY THE PATTERNS ACCESSIBLE FROM LONG-TERM MEMORY] for the first five to ten yards, choose a path from hummock to hummock, as safe a path as he can find [JUDGMENT], and TAKE THE FIRST STEP. [You have to “step out on faith” in your intuitive “feel”!] He will make the next step after a similar preparation. Our hero again inspects the five-to-ten yard horizon. It will already have changed because of his action. He accepts the solution to the second-step problem, and so on until he clears the bog."

    I once suggested in a speech before the USAF 15th Air Force Leadership School the following idea:

    "How do you eat an elephant? One bite at a time. Pick a spot that looks tender and juicy, and chow down!"

    I respectfully suggest that you just take a small “bite” of something that YOU can easily "SEE", make a judgment as to the relative benefits/drawbacks in terms of improving the position/prospects of that piece in conjunction with other pieces [IMPROVE THE WORST PLACED PIECE] and then use that new position as a stepping stone. The first thing to do in the “new” position is to look around for any deadly “snakes.” At some point in the process, TRUST CAISSA that if you keep gaining small intangibles without doing something egregiously stupid (like a blunder), you WILL end up with a winning position (or at least not a losing position). You do NOT have to calculate everything out to a tangible conclusion—CERTAINTY is N-O-T AN OPTION!

    According to Mark Twain, "Good judgment is the result of experience and experience the result of bad judgment." Good judgment leads to success and happiness, while bad judgment leads to experience. However, to gain experience from bad judgment, you have to MAKE THE JUDGMENT and (hopefully) learn something from it. To continue to make good judgments, you have to act on your experience.

    So much for generalities.