White to move |

There are 3 separate subjects to count:

- Domination
- Tempo's
- Value of obligation

**Domination**

First, you count for domination. I don't know whether "domination" is the best term for it, but it seems appropriate. You count from

**-/-1 0 +1**(-/- is minus sign). -/-1 = you don't own the square. 0 = balanced, +1 = you own the square (and the piece upon it). Both a6 and f6 are balanced, but since the pieces on it are both defenders, black is weakened elsewhere if you capture them. Counting for domination gives you a sense of which targets play a role.

**Tempo's**

Second, you count the tempo change caused by a move. You count

**0, 1, 2**. 0 = no forcing move, 1 = single tempo move (places one obligation on the shoulders of your opponent), 2 = duple tempo move (places two obligations on your opponents shoulders).

**21.Bxa6**is a single tempo move. Black is obliged to take back a piece of the same value. Sooner or later. With a

*postponement move*, black can

*postpone*his obligations, but there will come a time that he has to comply with his obligations. In this position there are no postponement moves, so black must take back on a6 immediately.

**22.Bxf6**is a single tempo move, and black is forced to take back immediately.

**23.Nd5**is a duple tempo move which attacks two undefended pieces. Black needs a duple defense move to save them both. There are two of these duple defensive moves: 23. ... Qd8 and 23. ... Qd6

Both move has as drawback that the black queen is now overworked, it cannot defend both bishops on f6 and d7 at the same time. White finishes with the duple offensive move 24.Nxf6+, and since black hasn't an appropriate duple defensive move, he looses a piece.

Counting the tempo change of a move is a simplification of the tempo counting system. It is based on the assumption, that the obligations for both sides are in balance. If you play a game, you know that for sure, since if it were not, you would have gained or lost a piece already. If for a puzzle the obligations are not in balance, you simply gain the wood you dominate. Only if you have to analyze a position that is not your own game or a puzzle, you need an absolute obligation counting system. Since such system is rather complex, we should avoid it when solving puzzles. The relative tempo counting system I propose here should be sufficient. At least, that is what we have to test.

You must realize that you can have obligations already. This means, that if you attack with a piece that was previously under attack itself, you gain two tempi. One defensive, and one offensive. We must develop a sense for this.

**Value of obligation**

If you capture a rook, your opponent is obliged to take one or more piece(s) back of equal value. It doesn't suffice for him to take only a minor piece back. I don't like counting with numbers like 3, 5 and 9, since I easily overload my poor short term memory with it. So I'm going to experiment with Minor piece = 1, rook = 2 and queen = 3. I'm interested in the mechanism of the combination. Once I have unearthed the mechanism, it is soon enough to calculate the exact value for the gains and losses on both sides. When I don't have a clear sight on the inner workings of the combination, it suffices to know that if my rook is taken, I need at least a rook or two minor pieces back. It is just a precaution for overloading my STM.

Anyone who can count from minus 1 to plus 3 should be able to use these 3 counting systems.

Let's describe the moves by the FUNCTION concepts:

ReplyDelete1. BxN - removes the Queen's guard.

2. BxN - removes the Bishop's guard.

3. Nd5 - duplo attack at two pieces with the use of the pin

4. NxB+ and Queen is overload: Knight's take away the Bishop defender

5. RxB wins the piece for free

Now we can analyse and take conclusions what are the relationships between white and black pieces: what are their functions and how white destroys these (functions using captures) and what was/were the main motif/s.

BTW. In the original position there is Na5 instead of Nf3. Did you change it conciously or just a small misclick when setting the position?

I used the FEN that was provided by Robert.

Delete@ Tomasz:

DeleteGood catch!

This is an error in Averbakh's book.I copied the position given in diagram 67 into Fritz and then copied the FEN into the post. The White Knight is on f3 instead of a5 in that diagram. I then looked up the game and added the link to it. Funny but true: I actually played through the game, and didn't catch that the White Knight was misplaced. I have no idea why Averbakh's book has the Knight on f3. However, I have found many (way too many!) errors in the book, especially one touted as for "advanced" players. I have no idea if the position got inadvertently changed during translation, or if it was changed for pedagogical purposes. In any event, it does not materially change the "idea" I wanted to express regarding counting.Thank you, Temposchlucker, for another excellent elaboration of the idea of "counting." Sometime recently (perhaps in all your discussions), I came to the notion of merely "counting" interactions on squares, rather than trying to keep track of relative material gains/losses in the traditional "Reinfeld" value system (or some variant, such as Kaufman): P=1; N=3; B=3; R=5; Q=9. For the purpose of evaluating piece/square contacts and interactions, every piece has exactly 1 and only 1 capability to capture on any given square, IFF it can "attack" (move to) that square. It is a two-value system:

0 = cannot capture/does not attack the square; 1 = can capture/does attack the square. It is then simply a matter of "counting" all attacks/defenses on a given square. The numbers involved remain very low. This applies even if contemplating the potentiality of an absolutely pinned piece. At a superficial level, an absolutely pinned piece has NO capturing capability. However, it still has "attacking" value in certain circumstances, especially when the opponent's King is part of the consideration.Consider the following position from this game:

Vladimir Andreevich Makogonov vs Vitaly Chekhover, 1937[FEN: 4r1k1/8/3R1Qpp/2p5/2P1p1q1/P3P3/1P2PK2/8 b - - 0 36]

(I checked the FEN against the actual game position this time!)

White “assumed” that he was “safe” if Black pinned his Queen with 36. … Rf8 because he had a counter-pin of the Black Rook with 37. Rd8, preventing capture of his Queen. Alas, he didn’t consider that the Black Rook also absolutely pinned White’s Queen, and so he lost his Queen after 37. … Qh4+ 0-1. Although the Black Rook is absolutely pinned, it still can create and hold a pin itself. It must have seemed like “brilliant” play by Makagonov. Sadly, it would have turned out so much better for White if he had played 36.Kf1 instead of 36. Kf2. It’s those little nuances that make all the difference in the world!

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.

I agree with that statement - you have to obtain an edge (advantage) over squares to be able to win the material or achieving much better position (positional advantage). And this finally leads to material gain - "capturing" the King as the extreme case.

DeleteAnyway I have never seen the refutation of pieces functions concept. I strongly believe it is internally connected to the squares superiority concept. That's why sometimes when one piece is one square away - you cannot win (or draw) the position. It must be some type of relationship between the pieces that we call "invisible interaction". And if we are playing on the board with squares as points - they must be the key to understanding the concept of gaining material advantage. No doubts about that.

After playing chess for some time I finally decided NOT to consider the piece "always [fully] pinned" as it is only a matter of capturing the pinning piece or cover its line by the other one.

Another observation that "simplifies" the process of "seeing" the "obvious" (I wish!):

ReplyDeleteI have observed that when the Queen is the defender against a duplo attack (which is quite possible given the Queen's unique power to move like either a Rook or a Bishop), the final result (successful or unsuccessful defense) depends on the relationship between the tow targeted squares. If there is a linear geometrical relationship, then the Queen will most likely be able to "protect" both threats without overloading her defensive capabilities. On the other hand, if the target squares are located apart by a Knight's move, then the Queen cannot defend both squares.

In the given position, Bf6 and Bd7 are separated by a Knight's move. Although the Queen can protect both squares from either d6 or d8, after the exchange on f6, the Queen must abandon one or the other. This can be "seen" rapidly, without calculating variations.

That "Knight relationship" idea crops up in many different situations involving a Queen, such as mating attacks with variations on the Epaulette or Gueridian or Dovetail mates. If you look at variations of these mates, you will find that the two squares that must be covered by other same-side pieces (or blocked by other-side pieces) are ALWAYS on the two squares that can be reached from the Queen's square with a Knight move. It is a fact that a Knight complements a Queen in an attack much more than a Bishop or Rook, because the Knight covers the only square(s) that the Queen cannot cover by itself.

Just another one of those mini skills to be learned and developed.

An aside: I hope I did not give the impression that "counting" is a universal panacea for solving all positions. For me, it is just another one of those mini skills that must be developed along with everything else (such as recognition of motifs as "signals" and knowledge of typical tactical themes/devices and mating patterns, and the corresponding move sequences). I make my comments in the spirit of finding and sharing these types of insights about "shortcuts" that I find useful for reducing cognitive load, resulting in a much faster "sight" of the solution for a given position. Think of it as simply another specialized tool in the overall toolbox; YMMV.

Hopefully, my sometimes dyslexic fingers did not distract overly from the point: "the relationship between

ReplyDeletetowtargeted squares" should read "the relationship betweenTWOtargeted squares." My apology for the "Fingerfehler".