Thursday, June 15, 2017

Developing the RCCM

Robert Coble said:

"The exploration of the PoPLoAFun approach has produced some surprising results!

Temposchlucker has noted that we seem to follow a “spiral” of increasing sophistication as we learn more about how to “see” the critical aspects of any given position. We start at a very simple level, eventually embed the necessary “lessons” in LTM for that level, and then move up a level of abstraction. Some of us progress rapidly up through the levels until we reach a pretty high level of skill. Others of us advance to a certain (relatively low) level, and seem to get stuck at that level.

Let’s begin at the beginning – the formal rules of chess. We have a very clear-cut goal – checkmate. We have very specific rules for the movement of the pieces. But nowhere in the formal rules do we have anything that tells us how to get from the formal rules regarding piece movement to the ultimate goal checkmate.

We “discover” that mathematicians have developed relative values for the types of pieces, predicated (primarily) on the potential mobility of the individual piece located on various pieces of an unencumbered board with no other pieces on it. The so-called “Reinfeld” value system is Pawn = 1, Knight = 3, Bishop = 3, Rook = 5, Queen = 9, and the King = infinity, because when the King is “lost” the game is over. We ingest this STATIC EVALUATION system because it is a shortcut to determining when (and whether) to trade pieces through exchanges, or whether to “sacrifice” some units of material for some non-material (perhaps intangible) compensation.

Unfortunately, this very early acquisition of material “rules” becomes part of our subconscious (intuition). We then try to build on that very “shaky” foundation. We try to relate the various piece values by “assuming” that the Pawn’s value is the “basic unit,” and using the relative values as if they are absolute values.

Let’s examine one such assumption and then I’ll move on to the more cogent discussion. The two Bishops have an equivalent value in “points” to a Rook and Pawn. Yet, if the mobility of two Bishops is compared to the mobility of a Rook and Pawn, you will find that the two Bishops together on the edge and corner of the board have a minimum mobility of 13 on two adjacent long diagonals, and a maximum value on two center squares of 26. The Rook, on the other hand, has a mobility of 14 regardless of its position and a Pawn has (at most) 1 move, giving a combined value of 15 for Rook/Pawn pair. But the average value for the two Bishops is 19.5!

What conclusion can we draw for this simple example?

Basing our evaluation function on a STATIC evaluation system which is primarily AVERAGE mobility may be (and probably is) deeply flawed. And so our foundation for future skill development is grounded on very thin “air.”

But we have to have SOME basis for making judgments about moves, exchanges and sacrifices, or we will just be playing randomly.

Consider a more dynamic approach. A given piece can Attack, Block, C</>onstrain (Restrict), or Defend a specific square on the board 1 and ONLY 1 time at any given instant. It is not possible to develop an overall evaluation of the entire board position by simply “adding” up all the A/B/C/D “functions” for both sides, subtracting the combined value for one player from the combined value of the other player and declaring that we have an accurate “evaluation” of the position. In short, the maths approach using dynamics does not work.

So where does that leave us? Is there no way to use this notion of dynamics to assist us in evaluating our positions? I would emphatically state the exact opposite! And what does this do for the notion of the ubiquity of tactics?

This is where the idea of “spiral” levels of increasing expertise comes into play. Think of the A/B/C/D level as the equivalent of the machine hardware instruction set of a given computer processor. That is the foundational layer that undergirds all other (higher) levels. We do NOT want to “program” our subconscious to throw up signals to our conscious at this level; it is simply too crude to form the basis for useful (higher level) chess skill.

So how do we move “up” a level based on A/B/C/D? We combine one or more pieces in the given position which have an effect on a specific square. Here our maths approach works fairly well, provided we can “see” those combinations of A/B/C/D on that specific square. Those squares are the “points of pressure” (PoPs), which by definition are “weaknesses.” The “lines of attack” (LoAs) are the potential movements of the pieces so as to affect the specific “point of pressure” localized on that square. The “functions” (Funs) of each piece impacting on a given square must be examined to see if that same piece simultaneously has other functions (obligations) on a different square, because any multi-function that a piece has becomes a potential encumbrance which may negate its effect on the square in question. Thinking at this level corresponds to the assembler level of our hypothetical computer. We can now process the various interactions symbolically, but the level is still too low for skillful play. This is a tremendous advantage compared to machine language, but it is still too crude for high level chess skill.

We move up again to the motif level. This is an abstraction of the PoPLoAFun aspects combined with a descriptive phrase, i.e. “the encircling motif,” “the geometrical motif,” “the desperado motif,” “the promotion motif,” etc. This gives us much more power of abstraction and corresponds to the macro-assembler level of languages for programming. Macros give us the capability to encapsulate a recognition function in such a way as to reuse it in many different situations without having to work our way through each of the lower levels.

We move up to the tactical themes/devices level. We can now figure out “HOW” we should move the pieces in cooperation to accomplish high level goals. We can execute combinations! Note that one of the usual elements of a combination is a feeling of “surprise” to one of the players, not to both. The player who executes a combination is NOT surprised – he anticipated and planned it. This corresponds to the procedural language level of programming.

We move up to the strategy level. We now “plan” our next (relatively short) sequence of moves as short-term goals. We have now reached the non-procedural level of programming, where we specify “what” we want to do, but do not have to consider “how” to do it. The “how” is taken care of “behind the scenes” by the subconscious simultaneously working on all of the lower levels.

I previously noted the viewpoint of Teichmann and Petrosian regarding the ubiquity of tactics in chess. I’ll repeat those quotes for easy reference:

"Chess is 99% tactics" - Richard Teichmann
 Amended by Dr Dave at the Exeter Chess Club: ...Although it has often seemed to me that the remaining 99% must be all strategy :-)

In general I consider that in chess everything RESTS on tactics. If one thinks of strategy as a block of marble, then tactics are the chisel with which a master operates, in creating works of chess art.” – Tigran Petrosian

An earlier post by Temposchlucker (05 NOV 2006: “Is the method of MDLM flawed?”) offered this considered opinion based on experience up to that date:

I’m going to try to lay out why I think those two assessments (especially Petrosian’s) are correct, based on the preliminary background discussion above. It may take me to places that I really don’t understand fully, but I hope you get the idea as expressed.

3rd. The idea that chess is 99% tactics (not heralded by MDLM but by Teichman!) is definitely busted.

As I looked over the latest incarnation of the Tree of Scenarios (ToS), I remembered something that Temposchlucker had earlier observed (with an apparent sense of “Surprise!”):

A target is protected by two defenders. When you trade off one defender, the other defender becomes immobile.

As expressed, Temposchlucker’s observation is at a low level of tactics, perhaps down at the level just above the A/B/C/D level. It seems surprising that we don’t “see” that immediately as a truism and try to remember and apply it. But let’s try to move that same notion up through some levels and “see” what happens as we abstract the idea to the fullest. I’ll forgo a detailed discussion of the in-between levels required to perform the abstraction.

We “know” (from Temposchlucker’s description if not from our own experience) that we can remove a defender, which effectively adds an attacker, when we exchange off a defender of a particular square. We can accomplish this same relative increase in attacking power on a given square by decoying a defender away, or adding another task somewhere else to one of the defenders. This puts us at a higher level of abstraction than the level at which the observation was made.

One of the things that one notices about Nimzovich’s My System is that it is broken down into two levels: the elements and position play. He uses very simple examples to define and describe the elements of strategy. He then revisits those ideas at a much higher level of abstraction with regard to position play.

Consider Nimzovich’s idea of “overprotection.” We should (but often don’t) consider (some of) our important squares and provide an excess of protection for them. Obviously, this enables us to avoid B.A.D. squares (and pieces) but we often don’t “see” the even higher level of strategy that is involved.

By “overprotecting,” we enable ALL of the pieces involved in the interaction on a given square to become mobile. Any one of them (provided we have more “defenders” than the attacker has “attackers”) can freely move as needed elsewhere, without any concern that the attacked square will suddenly become critical (a “point of pressure”). That mobility gives us options which we would not have otherwise.

Lasker opined that the strongest attack moves along the “line of least resistance.” This is nothing more than saying that the attack aims toward the weakness(es) in the position. An overprotected square avoids this possibility of allowing the opponent an attack. Unfortunately, because each piece operates in one specific function on one specific square at a time, there is no such thing as a “weakness-free” position. There will ALWAYS be weaknesses in any given position! What we want to drive into our subconscious is the recognition of the patterns to “see” those weaknesses AND how to take advantage of them!

This is a case of observing that the lower levels provide the functional basis for the highest levels. This implies that the aphorisms of Teichman and Petrosian are actually true:

Chess IS largely tactics, IFF all levels of abstraction are considered simultaneously!"


  1. I define tactics as the forced gain of wood. This means that the game is already out of balance. I concern strategy with the preliminary phase. In this preliminary phase you try to saddle your opponents pieces with the three types of immobility. This means, that in every move, tactics plays a role as the purpose for your move. You try to work yourself towards tactics.

    Furthermore, if you have devised a plan, for instance to manoeuvre your knight towards an outpost, you must be constant on your guard for tactics. Most tactics aren't executed. But they limit or extend your amount of possible moves.

    1. Re: "I define tactics as the forced gain of wood."

      You're in good company! GM Botvinnik had this to say (in Computers, chess and long-range planning):

      "The algorithm that we are to work with rests on two principles. The first is that both sides in the end have to strive for material gain (this is not in the rules of the game, but is true in practice). It follows that everything begins with the attack, and the attack defines the trajectory (the path) of the attacking piece."

      "The second principle amounts to saying that we must find an approximate solution to limiting the problem. If we are to consider all possible attacks, the problem becomes impossibly difficult to solve."

      I think one of the limiting factors for class players is thinking of tactics PRIMARILY in terms of material gain, which is a manifestation of relying on the "point count" system for measuring relative gains/losses. I "get" the notion that attacking the King is (in a very real sense) is about "gaining wood." I also think we overlook the very desirable possibility of utilizing "tactics" for purely positional purposes. Ultimately, of course, that will result in gaining wood, but that is usually beyond human powers to foresee clearly.

  2. Some time ago I was investigating a position with the aid of Stockfish. Stockfish just crunches numbers when it comes to judging a position. That evaluation has very little depth. But since he can crunch numbers for possible future positions too, he can find the lines that are profitable.

    I realized that I gave the (series of) moves a meaning. Which is what we people need to do. I was surprised that I could devise a meaning for every move and every line. How can there be a meaning in the lines while Stockfish isn't constructed to build meanings? People need meaning to direct their thoughts in the right direction. And apparently we are very good at that.

    Albeit meaning falls short when the computer looks further into the future. Meaning that our chess reasoning is still in its infancy. Even for grandmaster who are being pummeled by the best engines.

  3. I used to play chess as a game of chance. I never found that very satisfying. The tree of scenarios adds some very basic chess logic. I like that very much. I'm not a gambler.

  4. In keeping with the discussion : What Soltis called Petrosian's Law is a very interesting observation / . Cheers, Jim