The convergence pattern
Plans are based on moves that are irreversible: a pawn move or a piece trade. Whenever a piece is exchanged or a pawn is moved, you have to reconsider your plan.
The motivation for a pawn move lies in changing the piece activity. Piece activity comes in two flavors:
- Increasing the activity of your own pieces
- Restricting your opponents' pieces
In order to get the hang of pawn moves, you must develop an eye for convergence squares. A convergence square is a square which can act as a pivot point for pieces.
 |
| White to move |
r3k2r/ppq1n1pp/2nbbp2/2p5/2PpPP1N/3P4/PP1N2BP/R1BQ1RK1 w kq - 0 12
- e4 is a convergence square for the white pieces (bishop and knight)
- e5 is a convergence square for the black pieces (bishop, knight, queen)
Both squares are currently blocked. The manoeuver 1.e5 fxe5 2.f5 clears e4 while blocking e5 permanently. The cost is a pawn, but it takes black 4 tempi to redeploy his pieces to active squares. I read somewhere the rule of thumb that a pawn is worth 3 tempi. Stockfish deems this as +2.83.
See how the scope of the pieces on both sides has changed!
 |
| After 2. ... Bf7. White to move |
Nice to see you are still at it. I plan on catching up. Jim
ReplyDeleteI don't rest before 2000.
DeletePART I
ReplyDeleteFrom Chess Tempo’s Training → Tactical Motifs
[EXCERPT]
Removing the Guard. Distraction. Luring the Defender.
Luring the Defender is a tactical theme that occurs when you distract a defensive unit from its duties by luring it to another square, for example by creating a threat that the piece must move to respond to. Note that while distraction by luring contrasts with distraction by attacking, the lured away defender may actually be attacked. The key idea in luring is that the movement of the defender to another square occurs in order to perform another duty on that square, such as recapturing a piece that was captured by the opponent or blocking an attack, rather than moving away simply to flee an attack. Indeed the lured piece may continue to be under attack on its new square.
FEN: 2Q3nk/1rq3rp/2p3p1/2P1p1P1/1PBpP3/3K1P2/7R/7R w - - 0 1
1...Qc7 White is attacking the knight on g8 twice, and would like to mate on that square, however black is currently defending the knight with the black king and rook. 2.Rxh7+ Checking the king, black now has no option but to take the checking piece with the black rook that was helping protect the knight on g8. Note that while the rook is actually attacked, this is seen as a luring of the rook away from the defense in order to protect its king rather than forcing it to flee, so is of the luring not the attack subtype of distraction. 2...Rxh7 Lured away to block the check 3.Qxg8# and now with the rook no longer guarding g8, white is able to mate.
[END EXCERPT]
The majority of tactical “motifs” are descriptive rather than prescriptive. A fork, for example, involves two (or more) attacking “prongs”, but the description gives no prescription as to how to recognize and utilize a fork. Besides, sometimes a knife can be used for the same function as a fork; it takes more skill to eat peas with a knife. The most appropriate tool depends on the context.
I question whether descriptions are really helpful in recognizing potential tactical sequences.
PART II
ReplyDeleteGary Klein uses two terms to describe “convergence” points: leverage points and choke points. A leverage point facilitates a favorable action. A choke point inhibits a favorable action.
Looking at the example position, it is not difficult to “SEE” that there are two squares which are directly defended by the same Black defensive pieces.
The White Queen and Bishop “converge” on the g8 square. The two White Rooks “converge” on the h7 square.
The Black King (h8) and Black Rook (g7) directly defend both of these squares. The g8-square is B.A.D. However, the h7-square is not “formally” B.A.D.: it is also “defended” [2:4] by the Black Queen and Black Rook (b7). The practical question is: Is h7 actually B.A.D.?
As noted previously, the King cannot engage in a multi-piece exchange sequence on a given square except as the last capture.
Less obvious is that the Black Rook on g7 prevents the Black Queen and other Black Rook from directly defending h7. It effectively “chokes” off the line of attack of the additional defending pieces.
These two defenders are overloaded by their defensive functions and the limitations of formal chess rules.
The tactical question is: Can White take advantage of this situation?
Given a defensive overload situation, there MUST be a way to take advantage of it. The “clue” involves forcing the Black Rook to move so as to maintain the “choke” on h7, preventing the Black Queen and other Black Rook from intervening in the defense of the Black King.
The solution is to take on h7 first with check, forcing the Black Rook to recapture (because the Black King cannot recapture first because there are two White Rooks involved in the attack).
It is important when playing to “SEE” all of these considerations without working through a process using step-by-step System 2 logic. By all means, train this “convergence” recognition using System 2, to the degree that the background considerations are burned into System 1.