Saturday, January 11, 2020

In the beginning there was function

Aox provided me with a playlist about square strategy theory. Which handles about the method of Bangiev. The videos describe the how of this method. I try to re-engineer the why.

The PoPLoAFun system tells us:
  • duplo attacks appear at random
  • traps appear at random

There are three bases for a tactic:
  • lack of space
  • lack of time
  • lack of freedom due to function
Only the latter can be used as a guide from move one.

Pawns are the natural targets for positional play due to their limited mobility. All pawns on the 7th rank can only be defended by pieces or by pushing them forward. The f7 and c7 are weakest in the start position because the king and the queen are bad defenders.

In the opening phase, the position is very fluid. This means that the least defended pawn can change rapidly. Until there comes some fixation of the position, positional targets can change from move to move. When the enemy pawns become less mobile, it becomes time to pick your target. Bangiev helps you to focus on the weakest base pawns.

Diagram 1
  • You look at the base pawns. That are the pawns that cannot be defended by other pawns on the square which they occupy.
  • Then you look at the base pawn that can drum up the least amount of defenders.
  • Then you look at your own pieces. Which one can attack the pawn of choice?
So it is a matter of balance between potential attackers and potential defenders. Which base pawn is B.A.D. (Barely Adequate Defended)?
In the position above, that might well be the b7 pawn. Because the light squared bishop is outside the pawn chain, it cannot assist in the defense of the b pawn.

Putting pressure on the b-pawn ties the defenders to it. Tactics might arise spontaneously from this very fact. But the b-pawn itself has also two functions: defending a6 end c6. When you put so much pressure on the b-pawn that it no longer can be defended on its base square, it might feel compelled to move forward. Thus forsaking its duty to defend a6 and c6. After b6 or bxa6, we all of a sudden notice to have a weak color complex. A weak color complex is a  way to infiltrate into enemy territory. Think of it as a matrix of lines of attack.


  1. Re: mirsultankhan’s elucidation of GM Bangiev’s “square strategy theory”

    I watched all the videos in the series. I readily grasp the concept of using a triangle with apex at one of the 4 central squares as an indicator of the direction to pursue IAW “the requirements of the [Pawn] position.” However, I’m confused as to how to correlate this to a weak color complex. The highlighted squares are white, with the d5-square a particularly strong square - for Black.

    In the hypothetical position, I think of the c6 square as one of the principal weak squares. In the given position, it is “protected” twice – by the BNb8 and b7-Pawn. However, whenever the Black Knight “develops” to either c6 or d7, the c6-square loses one of its protectors. The Black Knight on either c6 or d7 can be pinned by a white-square Bishop against the King (presuming, of course, that Black delays castling).

    The b7-square (as you detailed) MAY become weak as a result of piece pressure on the b7-square. If it advances (in order to be protected by the a6 Pawn), it does weaken the c6 and a6 squares. It also weakens a7, because the a7-Pawn is now “defending” b7, which gives it a function - and any piece which acquires a “function” automatically goes onto the list of potentially useful targets.

    My understanding of a weak color complex is that the “weak squares” reside on the color OPPOSITE to the color that the Pawns are fixed on. (Since there are no Black kingside Pawns, I will ignore the possibility of a weakness there, for example, Pawns on f7-g6-h7 with the black-square Bishop already exchanged.) In the example given, the potential “weak” squares are those on the BLACK squares in or near the center: d4-e5-c5-d6, where a White piece may sit without being necessarily “molested” by Black Pawns. A White Knight on e5 “attacks” the c6 and d7 squares and tempts Black to advance the f7-Pawn to force the Knight away, thereby weakening the e6-square. It also means that c6 becomes “B.A.D.” once the Black Knigh moves. A White Knight on c5 “attacks” the b7-square, and tempts Black to advance the b7-Pawn or to exchange the black square Bishop to remove it. A frontal assault on b7 is only possible if one or more major pieces can either directly attack it (presuming the b-file is half open for White) or if White can place major pieces on the c-file, with intent to penetrate to the 7th rank (an “enveloping” attack, in GM Nimzovich’s terminology). The c5 “outpost” becomes the means to increase pressure on the c-file, possibly forcing a weakening of the dark squares, which facilitates the 7th rank invasion. A White Knight may also invade on the d6-square (an “octopus”), depending on what White has on the e5-f4-g3 and a3 squares. A White Knight on d4 “tempts” Black to advance in the center (e5) with possible weakening of the Black center, since d5 is no longer protectable by a Pawn.

    IMHO, there is no possibility of determining the proper strategy to pursue without a knowledge of White’s corresponding Pawn structure and the overall piece placement of both players.


    1. I saw a position in one of the videos which contained EXACTLY the position I wanted to show you. But I couldn't find it within a reasonable time. I was reluctant to place the pieces myself in the position, since usually that leads to an unintended alternative solution which distracts from what I wanted to share. So I took a picture from another video. Which is of course confusing, since the highlighted squares play no role in my story. Sorry for that. In the original position there was a black bishop on f8 and a white pawn on a5. So 1.a6 put up the pressure on b7.

      The last stage before a working tactic, is often an invasion. Remember the focal squares of Vukovic. When blacks white squared bishop is off the board or outside the chain, then chances are there that you can outnumber black on the white squares on the queenside. IF you manage to force the b7 pawn to move. Of course you need to know where ALL the pieces are to make up the balance for each white square on the queenside.

      So you need a disbalance on the white squares AND an enemy pawn that forsakes its duty on the white squares (b7). Then your opponent has a weak color complex. Via which you can invade the queenside.

      The natural invaders are the white squared bishop, the knights and the queen. The rook is a bit too vulnerable and has often too little mobility in the middlegame to invade.

      Not all invaders are the same. The white squared bishop only attacks the white squares. The knights though, attack the DARK squares when invading on the white squares. While the queen attacks both colors when invading.

      Sorry for the confusion.

    2. I am not convinced of GM Bangiev method. I wonder if it ever detects anything you cant see the traditional way anyway?

      Robert said:"My understanding of a weak color complex is that the “weak squares” reside on the color OPPOSITE to the color that the Pawns are fixed on."

      Weak color complex = missing bishop and/or color of squares of pawns and/or color of squares of knights

    3. If the Pawns are all on one color (perhaps in a local area, such as the kingside), then those Pawns are also only “attacking” squares of the SAME color. Thus, pieces must be used to control and protect the squares of the OPPOSITE color. The classical example is Black Pawns at e6-f7-g6-h7 with the Black King on g8. If White can exchange the dark-square Black Bishop, then there is a weak color complex on the dark squares. A weak color complex can occur anywhere on the board, and is not limited to the immediate area around a King.

      GM Sam Shankland has an excellent lecture video on YouTube:


      Attacking a Color Complex:

      Grandmaster Sam Shankland presents a game between Alexander Grischuk and Boris Gelfand from 2010 Linares in which he analyzes attacking a color complex.

  2. (Sorry about the deleted comment - MS Word got hung up and there was garbage verbiage in the comment.)

    Thanks for the explanation!

    The basic position you gave is located here (I think):

    LINK: Chess Lesson : Square strategy theory - the control zone

    Start at minute 2:53; goes to the end of the video.

    I note that the suggested White piece placement is WBb5-WNc5-WQb2-WRc1. Operations are taking place on the c-file (outpost at c5, with the Rook supporting the outpost). I find WQb2 to be somewhat odd: I think that (normally, if there is such a thing in chess) WHite would have a Pawn on b2 or b3, which negates the LoA of the White Queen toward b7, unless it's in front of the b-Pawn. I would expect to "see" the WQB2 supporting a White Bishop on the a1-h8 diagonal, applying pressure against the (eventual) Black King castled position. I'm fairly certain that Black would NOT be contemplating queenside castling, given this structure, unless there is a dire emergency on the kingside. I'm not sure how Bangiev's method might be superior to Nimzovich's analysis regarding outposts and operations on open or half-open files. Perhaps a combination of methods might work - or not.

    . . . Time passes. . .

    I just watched the rest of the video (again), all the way to the end. White placed his Queen on b3, in front of the WPb2, so there is no half-open b-file. I have a "feeling" that Black wasn't particularly effective in countering White's obvious plan. At a quick glance: as Black, I would have given up the idea of castling kingside, moving the Black King to e7 and connecting the Rooks as quickly as possible, while keeping the Black Bishop on d6 (to cover the dark squares, particularly c5). This allows a6 as an option, because capturing the BNd7 no longer comes with check; the Black Queen would be "hanging" but Black has time to capture on b3 before recapturing on d7. White needs three tempi to get the White Rook to the c-file. Surely there is something more productive that Black could have done in the interim, rather than putting the BRa8 on c8 and (especially) putting the BBd6 on b8!

    Of course, it is entirely likely that I'm missing all kinds of alternatives; I have not used a computer engine to take a look at each step of the illustrative game to see what alternative(s) GM Stockfish might suggest. I'll try to do that when I get some more time.

  3. PART I:

    1. d4 d5
    2. c4 c6
    3. e3 (34.8%/45.7%/19.5%)

    White begins to leave the main lines (3. Nc3; 3. Nf3). 3. cxd5 is very drawish [symmetrical Pawn structure].

    3. … Nf6 (35.2%/45.9%/19%)
    4. Nf3 (34.5%/45.9%/19.7%)

    Transposing back to a main line.

    4. … Bf5 (31.1%/45.5%/22.4%)

    Most popular choice. 4. … e6 is a close second choice.

    5. cxd5 (29.3%/46.2%/24.5%)

    Definitely moving off the beaten path: 5. Nc3 is much more popular.

    5. … cxd5 (27.9%/46.8%/25.3%)

    Again, the most popular response.

    6. Nc3 (30.8%/37.8%/31.4%)

    The immediate 6. Qb3 (26.4%/51.5%/22.2%) is twice as popular.

    6. … e6 (30.1%/39.8%/30.1%)

    The most popular response. I turned on the engines for analysis at this point, with the number of moves to analyze set at 10.

    7. Ne5 (28%/37.8%/34.1%) (+0.15)

    The most popular move (82 games), but not one of the top 5 choices by GM Stockfish (after running for at least 2 hours). GM Stockfish oscillated back and forth between the various alternatives, before settling on 7. Nh4 or 7. Qb3 as best (+0.01), with 7. Be2 (-0.12), 7. Bd3 (-0.15), 7. Qa4+ (=-0.16), 7. Bb5+ (-0.17) and 7. Ne5 (Eval=-0.20) following.

    GM Komodo had a different assessment of the alternatives: 7. Ne5 (-0.05), 7. Nh4 (-0.06), 7. Bb5+ (-0.11), 7. Bd3 (-0.13), 7. Qb3 (-0.14), 7. Be2 (-0.14), 7. Qa4+ (-0.14). I didn’t let GM Komodo analyze as long as GM Stockfish, so that may be on why the scores are different. From a human perspective, such small differences don’t seem significant.

    The move 7. Nh4 does not seem to be following the Bangiev squares strategy, but rather a plan of gaining the two Bishops and/or weakening the Black central Pawn structure, even if it costs some tempi.

  4. PART II:

    The interesting thing is that neither GM considers White to have (in essence) a forced tactical winning line at this point, whatever the basis of strategy.

    7. … Bd6(?!) (50%//50% - 4 games) (-0.17)

    GM Stockfish prefers 7. … Nfd7 (+0.18), immediately challenging the WNe5 and opening up the possibility of ejecting the WNe5 with f7. GM Komodo agrees with the priority of candidate moves, with 7. … Nfd7 +0.11) and then 7. … Bd6 (+0.01).

    8. Qb3(?!) (50%//50% - 2 games) (-0.72)

    GM Stockfish considers 8. Bd2 (+0.12) or 8. g4 (+0.22) to be much better than the game move, ranked below #20. GM Komodo gives the game move a score of (-0.38).

    8. … Qb6(?) (100%//0% - 1 game 1926: Kmoch v. Nagy) (-0.57)

    GM Stockfish prefers 8. … Nc6 (+0.89), 8. … Nbd7 (0.0), 8. … Qe7 (0.00) or 8. … Qc8 (+0.00). GM Komodo prefers 8. … Nc6 (+0.36), 8. … Qc8 (+0.05) or 8. … Qe7 (0.00).

    9. Bb5+(?!) (100%//0% - 1 game 1926: Kmoch v. Nagy) (-0.04)

    GM Stockfish prefers 9. Qxb6 axb6 10. Nb5 Bb4+ 11. Bd2 Bxd2+ 12. Kxd2 Ke7 (+0.26). Alternatives are 9. Bb5+ (0.00), 9. f3 (0.00) and 9. Bd2 (0.00). GM Komodo prefers 9. Qxb6 (+0.25) or 9. Bd2 (+0.06).

    9. … Nfd7(?) (-0.33)

    GM Stockfish prefers prefers 9. … Nc6 (+0.00) or 9. … Ke7 (-0.03). GM Komodo prefers 9. … Nc6 (0.00) or 9. … Ke7 (-0.04).

    10. Nxd7 (+0.09)

    GM Stockfish prefers 10. f4 (+0.13). GM Komodo prefers the game move (+0.17) to 10. f4 (0.00) or 10. g4 (0.00).

    10. … Nxd7 (-0.05)

    GM Stockfish believes everything else loses badly. GM Komodo rates the game move (-0.12); everything else loses badly.

    11. Bd2 (+0.08)

    GM Komodo is slightly more optimistic, scoring this move (+0.32).

    11. … Rc8 (+0.00)

    GM Komodo is slightly more optimistic, scoring this move (-0.07).

    12. O-O (+0.02)

    Other ideas are 12. Qa4 (0.00), 12. h3 (0.00), 12. h4 (0.00) and 12. g3 (0.00).

    12. … Bb8?? (-1.62)

    GM Stockfish gives 12. … Qd8 (+0.00).

    13. f4 (+1.64)

    GM Stockfish gives 12. Na4 (+1.77), with 6 other moves also being to White’s advantage. It’s clear that White is in the driver’s seat now.


    Black made several tactical mistakes before White obtained an advantage due to his “square strategy.” I submit that this example does NOT show the superiority of GM Bangiev’s method. (It’s an open question as to the efficacy of that method.)

    It also validates my “feeling” that Black messed up long before losing a Pawn for no compensation. I may not be the strongest player commenting here, but (sometimes) even a blind squirrel occasionally finds a nut.

    1. I don't think the B-method is intended to give you the best moves. It might make think you about the best targets, though. Since other grandmasters have other definitions for weaknesses, we still need to do the hard work ourselves. What do WE consider as "viable" targets? ;)

  5. I think it is time to devise a concoction of my own. After all, I must use it myself. From the Bangiev method, I don't understand the difference between the e4 and the d4 strategy (the strategy question), and the direction question seems rather trivial.

    What I get out of this all, is the importance of the pawns. Positional progress can only be measured by health of the pawns. So the focus on the weakest base pawn is enlightening.

    Putting pressure on the weakest pawn binds the defenders. Which gives you more room to wriggle. The pawn under attack must be restraint first. Movement of the pawn under pressure leaves weakened squares in its wake.

    Those are the ingredients I never thought about before. It is another way of looking at matters. With this I gathered the first few ingredients for my homemade brewing.

  6. Weak squares and outposts (

    LINK: Weak Squares and Outposts Part 1 - Alexander Alekhine

    LINK: Weak Squares and Outposts Part 2 - Optimal Utilization

    LINK: Weak Squares and Outposts Part 3 - Judit Polgar

    LINK: Weak Squares and Outposts Part 4 - Mikhail Botvinnik

    There may be more to come in this series of blog posts. The last line of Part 4 reads:

    The following is an Example in which Grandmaster Adrian Mikhalchishin took the page right out of Botvinnik's score book and glued it into his own.

    There is no following example.

  7. "https://" is not allowed using the "<a href..." HTML, so I removed it. Precede the links above with that in your browser. The links would not directly connect. Sorry about that.

  8. I just read this post, which is another example of chess synchronicity in study. In the game I just analyzed for my annotated games series, a key feature of it was the weakness of a6 and c6 after the b7-b6 pawn advance, which led to (what should have been) a winning tactic.

    This is also a good illustration of how one should be constantly evaluating the best targets (weakest places) in your opponent's camp, then finding ways to pressure them. Soltis among others has cited this as a defining characteristic of master play. As you mention, it's not just a question of finding a single weak point, it's the fact that pressuring it will normally lead to other weaknesses and create other problems for your opponent. This is also the idea behind the principle of two weaknesses, where the attack being switched over to the second weakness is really the purpose of the strategy.

  9. @ ChessAdmin:

    I presume you are referring to Annotated Game #234. After 15. ... b6, Black has two immediate obvious weaknesses: (1) the weak color complex on the queenside and (2) the isolated Queen Pawn at d5. As a result of these weaknesses, Black will experience difficulties in coordinating his pieces (particularly the Rooks) so as to hold everything together (due to lack of maneuvering space). White also has good chances of gaining control of the c-file, so (perhaps) that's a 3rd weakness. The important thing is to NOT allow Black to exchange off all the Rooks along the c-file.

    Once a weakness has been identified, we MUST (in Lasker's view of strategy) attack the weakness, or risk losing whatever advantage we might have. As Silman has noted, we have to identify the imbalance(s) and enhance our own imbalance(s) while preventing (if possible) the opponent from enhancing his imbalance(s).

    I know how disappointing it must have been to gain such an advantage and then lose the thread of the game: this is one of my worst failings. I get to a position against a stronger player that I KNOW should be winning, and then can't figure out how to increase the pressure without letting the opponent use his counter-chances to get back in the game and then win. I continue to study PoPLoAFun in order to increase my tactical awareness (technique). Identification of B.A.D. (Barely Adequately Defended) squares/pieces is an integral part of that technique.

    "The hardest game to win is a won game.
    - Emanuel Lasker

    If you continue to play this way, it’s only a matter of time until you collect that Master’s scalp!

    Good luck!