Weak-Square Complex
(1 of 2)

Point Count Chess, NO.93A to NO.93C, p133-134
Teichmann v. Allies, 1902

In this example, White forces Black to leave two sets of Weak-Square Complexes (clusters of same-colored Holes), to target Black's King, in his Stronghold on the Kingside.

The first cluster of Holes (a "Dark" Complex of Weak-Squares) is forced to occur primarily in the Center of the board, which White occupies with Queen and Knight, respectively.

The second cluster of Holes (a "Light" Complex of Weak-Squares) is forced to occur within the Black King's Stronghold, just in front of Black's King. White aims to exploit this with his King, which will be brought up to support White's intended Mating attack.

Beneath the ChessFlash viewer, you'll find my analysis of the three positions featured in Point Count Chess:
1. PCC, p.133, No.93A, before 1.Nd4
2. PCC, p.133, No.93B, after 3.Qxd4
3. PCC, p.133, No.93C, after 8...f6
4. Result of the Weak-Square Complex (1 of 2).
5. Summary of the Weak-Square Complex (1 of 2).
6. PGN

Weak-Square Complex (1 of 2)
My Analysis

Position #1, My Analysis
PCC, p.133, No.93A, before 1.Nd4

Before: 1.Nd4
 Weak-Square Complex (1 of 2), Before 1.Nd4 Before 1.Nd4, H&M-S say: "At first glance, the positions seem to be equal, or perhaps slightly in Black's favor because of the bishop." In the diagram (left), I've matched up like-for-like Pieces, and you can see Black's light-Bishop (Be6) on the board with an Open Center (which generally suits Bishops), against one of White's Knights (I've just picked on the Ng3, for the sake of the diagram).
 Weak-Square Complex (1 of 2), Before 1.Nd4 However, it's the position of Black's Queen, compared to White's Queen, that apparently gives White an opportunity. H&M-S say: "...when we note the inferior position of the Black queen as compared with the White, we realize that Black is in some difficulty." H&M-S don't exactly explain why White's Queen is more advantageous than Black's Queen ...

At first (as seen in the diagram, above), having compared the position of the two Queens, I assumed it most likely to come down to the ability of White's Queen to take up a post in the Center of the board (e4), whereas Black's Queen can only move to one of two flank squares (f6 or g6), which gives Black's Queen less overall scope across the board (thus inferior), than White's Queen can get with that potential move to e4.

 Weak-Square Complex (1 of 2), Before 1.Nd4 But, after H&M-S continued and said: "White proceeds to aggravate it by forcing the following exchanges", and after having played through the entire sequence a few times, it seems much more likely that the Black Queen's "inferior position" is due to her lack of coordination with the other Black Pieces (Nc6 & Rd8), against the d4-square, compared with that of White's Queen, which coordinates with both White's Rd1 & Nf3.

With H&M-S's information about White's option to force exchanges to aggravate Black's supposed predicament, you can now see (above) that White's Queen (Qa4) is the surplus Piece that allows White to force the exchange of Black's Knight (Nc6) and Rook (Rd8), with White's Queen left over, to remain on the board, in a superior position (in the Center, at d4), after completing the series of exchanges.

While all that's going on, Black's Queen must watch the swaps take place, unable to join in, because she's not currently in direct line of sight of the d4-square. And, because it's now White's turn to move, Black doesn't have the time to move his Queen into position to help (e.g. to f6). So that, I believe, is why H&M-S consider Black's Queen to have the "inferior position."

Position #2, My Analysis
PCC, p.133, No.93B, after 3.Qxd4

After: 1.Nd4 Nxd4 2.Rxd4 Rxd4 3.Qxd4

After: 3.Qxd4

1. The first part of White's invasion plan forces Black to leave a "Dark" Complex of Weak-Squares, primarily through the Center of the board.

 Weak-Square Complex (1 of 2), After 1.Nd4 Nxd4 2.Rxd4 After 1.Nd4 Nxd4 2.Rxd4, as mentioned above, starting with the lowest-valued Piece, White's Nf3 leads the first series of exchanges, on d4 (1.Nf3-d4 Nc6xd4), ending with White's Rd1 completing the Knight swap, on d4 (2.Rd1xd4).
 Weak-Square Complex (1 of 2), After 2...Rxd4 3.Qxd4 After 2...Rxd4 3.Qxd4, the Rook swap takes place (2...Rd8xd4), completed by by White's Queen (3.Qa4xd4). Note: this series of exchanges that White initiated, leaves White's Queen attacking Black's undefended a7-Pawn, and it's this attack that begins the process of forcing Black's Queenside Pawns forward, in order to create the Complex of Weak-Squares (Holes, specifically, at c7, d6 & e7) for White's Queen and Knight to invade (the Knight will coordinate with White's Queen, against the vulnerable f7-square of the Black King's Stronghold).
 Weak-Square Complex (1 of 2), After 3...b6 After 3...b6, Black advances his b-Pawn (3...b7-b6) into Chain formation, to defend his a7-Pawn, against the direct attack from White's Queen (Qd4). However, the move leaves Black's c7-Pawn in a vulnerable, Backward position. At present, there is only one square in Black's territory that could probably be considered a Hole (e7). But, it needs a cluster of same-colored squares, for a Weak-Square Complex to be declared (this will be achieved at c7 & d6, if Black's c7-Pawn can be "persuaded" to leave its current post, where it occupies c7, and guards d6).
 Weak-Square Complex (1 of 2), After 4.Qe5 c5 After 4.Qe5 c5, White completes the first part of his invasion plan, which leaves Black with a "Dark" Complex of Weak-Squares (Holes), at c7, d6 & e7. White achieves this by attacking Black's Backward c7-Pawn, with his Queen (4.Qd4-e5), forcing Black's c-Pawn to seek refuge at the head of Black's Queenside Chain (4...c7-c5). But this leaves Black with a cluster of dark squares, which are neither defended, nor occupied by Black Pawns: a Weak-Square Complex (of dark squares).

Position #3, My Analysis
PCC, p.133, No.93C, after 8...f6

After: 3...b6 4.Qe5 c5 5.f4 Bc8 6.f5 Bb7 7.Qe7 Qc6 8.Re2 f6

After: 8...f6

2. The second part of White's invasion plan forces Black to leave a "Light" Complex of Weak-Squares, in front of the Black King's Stronghold, on the Kingside.

 Weak-Square Complex (1 of 2), After 5.f4 to 6...Bb7 After 5.f4 to 6...Bb7, White begins his plan to cause Black to move his Kingside Pawns onto dark-squares, which will leave a "Light" Complex of Weak-Squares (Holes, at f7, g6 & h7), for the eventual invasion, by White's King. In successive moves, White's f-Pawn is advanced towards Black's f-Pawn (5.f2-f4 » 6.f4-f5), with the intended aim of forcing Black's f7-Pawn to step forwards, taking it off the light-square and onto the dark-square ...

... in order to prevent White's f-Pawn from breaking through the Black King's Stronghold, at g7 (whether White's f-Pawn captures it, or Black's g-Pawn captures White's f-Pawn, at the expense of becoming Doubled on the f-file).

Due to its higher vulnerability against the less-valuable Pawn (White's f-Pawn), Black is forced to relocate his light-Bishop (5...Be6-c8 » 6...Bc8-b7), choosing to bring it to the Fianchettoed position, targeting White's g2-Pawn. However, it's at the expense of opening the path along the e-file, for White's Queen, which will be moved up to e7, with support coming from White's Re1.

 Weak-Square Complex (1 of 2), After 7.Qe7 to 8...f6 After 7.Qe7 to 8...f6, White has successfully forced Black's f-Pawn off its light-square (f7) and onto the dark-square (f6), in order to form a defensive Chain formation, to prevent White's f5-Pawn advancing to attack Black's g7-Pawn. The first Hole appears (f7). White's Queen is moved up the e-file, to the dark-square (f7), on the 7th Rank (7.Qe5-e7), supported by the Re1.

Black has the wrong-colored Bishop, which is unable to attack White's Queen; and Black's Rf8 COULD NOT move to e8, to attack White's Queen, as Black's King was vulnerable to a Back Rank Mate. And so, Black was forced to move his Queen to the a8-h1 diagonal, in Battery formation with the Bb7, threatening to Checkmate White's King (...Qc6xg2#), in a desperate attempt to dissuade White from continuing his assault on the position of Black's King.

White's Rook steps onto the 2nd Rank (8.Re1-e2), maintaining its defence of White's Qe7, while simultaneously guarding White's g2-Pawn, effectively snuffing out Black's Mating Attack (losing Queen and Bishop, to gain a Pawn and a Rook, is a bad trade!).

At this point, Black appears to have no other viable options, and is forced to put his f-Pawn onto the dark-square (8...f7-f6).

 Weak-Square Complex (1 of 2), After 9.Ne4 Qd5 10.Nd6 After 9.Ne4 Qd5 10.Nd6, White brings his Knight up to the "Dark" Complex of Weak-Squares (9.Ng3-e4 » 10.Ne4-d6), to increase pressure against what will become the "Light" Complex of Weak-Squares (Nd6 attacks the f7-square). I assume the move by Black's Queen (9...Qc6-d5) is an attempt to halt the threat of White's Queen going to f7, at some point.
So, what we see is the "Dark" Complex of Weak-Squares, is the base from which White will be able to attack the "Light" Complex of Weak-Squares, in front of the Black King's Stronghold, over on the Kingside.
 Weak-Square Complex (1 of 2), After 10...Bc6 to 12.c3 After 10...Bc6 to 12.c3, Black does his best to counter White's attacking threat on the Kingside, with an Queenside offensive. However, the advance of his c-Pawn (11...c5-c4) is brought to a halt as White's c-Pawn comes out (12.c2-c3) to blockade any further advance. Once more, Black's Bishop can move wherever it wants (10...Bb7-c6), but it poses little threat to White's Queenside Pawns, that are on dark-squares (b2 & c3).

Meanwhile, over the Kingside, the advance of White's h-Pawn (11.h2-h3) opens a path on the dark-squares, so that White's King will be able to begin the journey up toward Black's besieged King.

 Weak-Square Complex (1 of 2), After 12...h6 After 12...h6, White achieves the second part of his invasion plan, which leaves Black with a "Light" Complex of Weak-Squares (Holes), at f7, g6 & h7. Perhaps fearing the genuine threat of White's h-Pawn coming all the way up to attack Black's g7-Pawn, Black's h-Pawn is advanced (12...h7-h6) into a defensive Chain formation, supported by the g7-Pawn (which has now become a Backward Pawn).

However, the downside of Black's h-Pawn advance is it leaves the g6-square unguarded, and the h7-square is no longer occupied by a Pawn. Both these squares have become Holes, to add to the Hole at f7, and it's this cluster of Holes, of the same colour ("Light" squares), that signals another Weak-Square Complex, in Black's position. This one is probably more severe than Black's "Dark" Complex of Weak-Squares, because it gives White diagonal avenues into the Black King's Stronghold.

The Result of the Weak-Square Complex (1 of 2)...

 (RESULT) Weak-Square Complex (1 of 2), After 13.Kh2 After 13.Kh2, White's King is mobilized, and will be sent up to Black's "Light" Complex of Weak-Squares, on the Kingside, where it will extra support to assist with White's Mating attack.
 (RESULT) Weak-Square Complex (1 of 2), After 13.Kh2 This entire sequence shows how two opposite color Complexes of Weak-Squares (clusters of Holes) can be forced upon the enemy, then exploited as part a plan to get at the enemy King. In this case, with Black's King Castled on the Kingside, White forced the creation of a "Dark" cluster of Holes, which White's Queen and Knight used, as a base from which to force the creation of a "Light" cluster of Holes in the Black King's Stronghold, and which White will exploit to win the game (either Checkmate, or through forcing Black to resign).

Summary of the Weak-Square Complex (1 of 2)...

1. The first part of White's invasion plan forces Black to leave a "Dark" Complex of Weak-Squares, primarily through the Center of the board. White invades with Queen (7.Qe5-e7) and his last remaining Knight (9.Ng3-e4 » 10.Ne4-d6), to coordinate against the f7-square within the region of the Black King's Stronghold, over on the Kingside.

2. The second part of White's invasion plan forces Black to leave a "Light" Complex of Weak-Squares, in front of the Black King's Stronghold, on the Kingside. With White's Queen (Qe7) and Knight (Nd6) coordinating their attack from the "Dark" Complex of Holes, and White's Kingside Pawns beginning their trek up the board (towards the Black King's Stronghold), Black resorts to shifting his Stronghold Pawns all onto dark-squares, into a defensive Reverse-Salient formation, which create the "Light" Complex of Weak-Squares (Holes). White then mobilizes his King, bringing it up to the cluster Holes on the Kingside, to take part in the Mating attack, against Black's besieged King.

3. One of Black's key material weaknesses appears to be retaining just a single Bishop, of the wrong color (the light-Bishop, in this case) which is unable to help attack, and thus remove White's Queen (Qe7) and Knight (Nd6) from their key vantage points, within Black's "Dark" Complex of Weak-Squares.

PGN

[Event "PCC, p133 Diagram NO. 93A to NO. 93C"]
[Site "?"]
[Date "1902.??.??"]
[Round "?"]
[White "Teichmann"]
[Black "Allies"]
[Result "*"]
[SetUp "1"]
[FEN "3r1rk1/ppp2ppp/2n1b2q/8/Q7/5NN1/PPP2PPP/3RR1K1 w - - 0 0"]
[PlyCount "25"]

{PCC, p133 Diagram NO.93A} 1. Nd4 Nxd4 2. Rxd4 Rxd4 3. Qxd4 {PCC, p133 Diagram NO.93B} b6 4. Qe5 c5 5. f4 Bc8 6. f5 Bb7 7. Qe7 Qc6 8. Re2 f6 {PCC, p133 Diagram NO.93C} 9. Ne4 Qd5 10. Nd6 Bc6 11. h3 c4 12. c3 h6 13. Kh2 *

End.