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.
PART I:
ReplyDeleteFEN: r1b1r1k1/pppq3p/5Bp1/b2pP2Q/2nP4/3B3P/PP3PP1/RN3RK1 w - - 0 1
Humans vs. Computers: How Thinking in Chess Has Evolved | Watch
The given position is taken from a video by The Chess Nerd, illustrating the difference between a human approach and a computer approach to a specific position. I’ll first give the transcript of the video, then some comments, and then the analysis by GM Stockfish after the suggested first move 1. Bxg6.
Transcript:
What’s up everyone, I’m the Chess Nerd and today I’m going to show you the difference between a human thinking and chess and a computer playing chess. This is a game, I play it against myself in a random position that I found in a book and just to see how your attack fixates on a particular concept compared to a computer thinking outside the box and how we should all think outside the box.
So yeah, this is the game. So this is the position in which White is clearly attacking the king. Here you can see the black squares around the king are pretty weak and we have a nice bishop pair acts fixated on the king’s castle. And obviously we take on g6 here [1. Bxg6] and sacrifice. Now with this sacrifice comes a lot of potential [1… hxg6] in attacking, so queen takes g6 [2. Qxg6+] here check. And now the king has to move to f8 only square. Now after king f8 [2… Kf8], white can’t play queen g7 checkmate because of the queen defending the 7th row, that queen on e7. So instead we opt for another plan for white. We have to think hard and long about this and think how to trap the king.
So you look at the candidate moves and one of those moves is 3. Qh6+ which gives the black pieces two choices, one of which is 3… Kg8 and that gets there, and the other of which is 3… Kf7; both give the same thing.
3… Kg8 4. Qh8 Kf7 does not leave time to play 5. f4 because of 5… Rxh8.
3… Kf7 4. Qg7+ is followed by 4… Ke6, and then you know white would love to push 5. f4 then 6. f5# checkmate here. But, unfortunately, white does not have time because of 5… Qxg7.
And so that makes it complicated for white because you can’t just play twice in a row with the same pieces. So you have to use a tempo to play 5. f4 here, but that is incorrect because of 5… Qh7 saving the black pieces.
[He resets to the position following 2. Qxg6+ Kf8 without any dialog.]
So 3. f4 directly here. What about that? Now we’re threatening 4. Qh6+ Kf7 (or 4… Kg8) 5. Qh8+ Kf7 6. Qg7+ Ke6 7. f5#, which is, it’s a reasonable threat. And, you know, moves like a rook lift with Rf3 are possible.
[The commentary gets muddled compared to what he is doing shifting the pieces around.]
But here black have a clear defense move. So after 3. f4 Re7 here staring down on the 7th row again, and well, let’s see what it gives for the black pieces as a defense mechanism. 4. Qh6+. 4… Kg8 does not work because of 5. Qh8+ Kf7 6. Qg7+ Ke8 (6… Ke6 7. f5#) 7. Qg8#. The specialty that black now has is the defense move with the rook: 3. f4 Re7 4. Qh6+ Rg7, well, it’s pretty well defended. I mean, white can’t give up their bishop for the exchange because the attack has run out.
“After 3. f4 Qe6 as” — [he does not continue with this line immediately, but switches back to repeating the previous line. The reason may be that he saw 4. Qh6+ Kf7 (or 4… Kg8 5. Qh8+ Kf7) 5. Qg7#.]
PART II:
ReplyDeleteSo white have to think of a special plan here to get it to win. And so 4. f5 a6 comes here with the idea which threatens 5. e6 [attacking the black queen] and now the white black queen has no possible defense for her rook on g7. And [after 5… Qd6] the white pieces just win very easily with 6. Qxg7+ Ke8 7. Qf7# (or 7. Qg8+ Qf8 8. Qg6+ Qf7 9. Qxf7#) there, as you can see.
And so 4. f5 looks like a good move here to defend and threaten 5. e6. So now black have to respond with a very good move. And that move is 4… Kg8. And so, on that move, there’s 5. e6. But then, the superb move 5… Rxg2+ 6. Kxg2 saves the black pieces in an incredible fashion with the substitute move 6… Qh7 after that sacrifice, and the white black pieces are somewhat saved in this crazy position after 7. Qg5+ Kf8. [Taps the BBc8.] And you know, white still have an attack here, but it’s way less, it’s delayed and it’s not winning anytime soon. As you can see, the black pieces are pretty weak. I mean you still have an undefended king for the black pieces, your bishop can’t really move, and your two pieces on the queen side are kind of out of play, right? But still, this is a good defense for the black pieces and it doesn’t look like it’s enough for the white pieces to win here.
[Resets the position to after 1. Bxg6 hxg6 2. Qxg6+ Kf8.]
Now let’s look at what the machine, the chess computer says right here, directly right here goes against all of our thinking of centuries and plays 3. e6 here. WHAT?!? This looks like a crazy move! Even there you see my head bopping just like—what is THAT? This is a sacrificial move and obviously the queen can’t take 3… Qxe6 4. Qg7#.
And now let’s see what happens if the rook takes 3… Rxe6 because that’s the most interesting. Again, this is not, I did not think of 3. e6 on the spot. This is when I looked at Stockfish on chess.com and it suggested this move. 4. Qh6+ Kg8 (4…. Kf7 5. Qg7+ Ke8 6. Qg8#) 5. Qh8 Kf7 5. Qg7+ Ke8 6. Qg8# and now we have this checkmate that we always wanted that was never available. And obviously 4… Qg7 5. Qxg7+ doesn’t work here because simply it gives the queen. The magic of 3. e6 here is that it takes the black queen off of the 7th row and stops it from
protecting the g6 g7 square if it moves. And so the black pieces have to take the pawn or do something about it to evade the immediate threat.
And so that’s how a computer thinks compared to just a simple human thinking of a logical plan. It goes against all logic and computers. This is the change that computers have put on the world. And, you know, obviously we’re excited to see that computers are better than humans and they’ve brought something new to the chess world. But it’s not always it takes you off guard. That’s what I’m trying to say. Anyways, thank you so much for watching and see you next time.
END Transcript:
Where "white black" occurs, the word "white" had a "strikethrough" in my original text (before copying it to the blog). I was trying to indicate that Zack had voiced "white" rather than the correct "black" a couple of times. Sorry for any confusion.
DeletePART III:
ReplyDeleteZack (Zachary Saine), also known as The Chess Nerd on YouTube, currently has a FIDE rating of about 2079 in standard chess, 2031 in rapid, and 2065 in blitz.
One of the most obvious “facts” about this video is that Kotov’s logical thinking process (nor any other logical step-by-step process) was NOT used, in spite of a reference to finding “candidate moves” at one point. Instead, it is fairly obvious that Zack’s “thinking process” was much more characteristic of Tisdall’s “variation processing” (effectively an application of Klein’s Recognition-Primed Decision model). He also backtracked multiple times, returning to an earlier point and trying something different from that point, in essence using the Tisdall “stepping stones” approach.
The most significant thing (to ME) was that he made no attempt to evaluate or summarize the various “clues” in the position before diving right in. There was an “obvious” opportunity to sacrifice on the g6-square destroying the black kingside pawn cover, and he jumped right into it, and began traveling down an “interesting” variation.
A first glance at the position shows that White has a significant advantage on the kingside. Most of Black’s pieces are over on the queenside, not doing anything whatsoever to defend the king. Black has no pathway to quickly bringing those pieces back to help the defense. White had a local superiority [3:2] of pieces aimed for the attack. The “three-piece rule” comes to mind: one piece to break open the king position (destroying the pawn cover), and one piece to defend the checkmating piece so it can get “up close and personal.”
“One piece to blind them (the sacrificial lamb), one piece to bind them (the protector of the mating piece) and in the darkness (of “SEEing” ahead), one piece to kill the king (checkmate).” Or something like that (with apologies to the legacy of J R R Tolkien).
At critical points in his “analysis,” he did not explore every possible alternative/opportunity, especially for the defense. This is how he overlooked the possibility of 3. e6. I don’t think that move was “outside the box” or a move that only a computer could find. Instead, I think he overlooked it because it was not protected, and he had already focused on getting the f2-pawn to f5.
This demonstrates the importance of being aware of the convergence of piece action (the “auras” of the pieces AND the pawns) on various squares. Zack focused almost exclusively on increasing the activity of his own pieces, without taking into consideration that a central pawn could also be considered an “attacking piece” and used to deflect a crucial defender. Deflection/diversion is an elementary tactical theme/device. The problem is that if we jump into the “tunnel” and ignore everything that wasn’t obviously part of the initial attacking group of pieces, we MAY forget to bring ALL of the pieces (including pawns) into consideration at critical points.
PART IV:
ReplyDeleteHere’s GM Stockfish’s analysis after 1. Bxg6. Note that 1… hxg6 is 7th down on the list of possible replies—none of the higher priority moves were considered at all. The fact that Black is objectively lost in all variations does not excuse the failure to even consider possible alternatives.
23:49:54 1...Re7 (1/38) Nodes: 1967.31 M (676.97 kn/s)
Stockfish
# Lines: 10
D41 -6.95 1...Re7 2.Bc2 Rg7 3.e6 Qxe6 4.Bxg7 Kxg7 5.Qxh7+ Kf8 6.Nc3 Qf6 7.b4 Bb6 8.Nxd5 Qg7 9.Qxg7+ Kxg7 10.Rae1 Nd6 11.Re7+ Kf8 12.Bb3 Bf5 13.g4 c6 14.Nxb6 axb6 15.Rfe1 Bd3 16.R1e3 Bc4 17.Rd7 Bxb3 18.axb3 Nb5 19.Kg2 Rc8 20.g5 Rc7 21.Rc3
D41 -7.72 1...Re6 2.Nc3 Qg7 3.Bxg7 Rxg6 4.Bh6 c6 5.Ne2 Bf5 6.Nf4 Bd8 7.Nxg6 hxg6 8.Qf3 Be7 9.Kh1 Re8 10.Qc3 a5 11.Qc1 a4 12.b3 Na3 13.bxa4 Nc2 14.Qb2 c5 15.Rad1 Nxd4 16.Rxd4 cxd4 17.Qxb7 Kh7 18.Bg5 Bd3
D41 -8.61 1...Nd6 2.Qg5 Kf8 3.exd6 hxg6 4.Qh6+ Kf7 5.Qg7+ Ke6 6.Be7 Qxd6 7.Qf6+ Kd7 8.Bxd6 cxd6 9.Kh1 b5 10.Qxg6 Bb7 11.Rc1 Rac8 12.Nc3 Bxc3 13.Qf5+ Kd8 14.Rxc3 Rxc3 15.bxc3 Bc8 16.Qxd5 Bd7 17.Qxd6 Re2 18.Qb8+ Ke7 19.d5 b4 20.d6+ Kf7 21.Qb7 bxc3 22.Kh2 Kg6
D41 -11.22 1...Qg7 2.Bxe8 Nd6 3.Bxg7 Nxe8 4.Bh6 Be6 5.Nc3 Bb4 6.Qg5+ Kh8 7.Kh1 b5 8.Ne2 Rb8 9.Rg1 Rb6 10.Nf4 a6 11.Rad1 Rc6 12.a3 Bxh3 13.Nxh3 Rg6 14.axb4 Rxg5 15.Bxg5
D41 -11.80 1...Bb4 2.Bxe8 Bf8 3.Bxd7 Bxd7 4.Qg5+ Kf7 5.Nc3 c6 6.Kh1 Be6 7.Rg1 Ke8 8.Qh5+ Kd7 9.Qxh7+ Kc8 10.Be7 Bxe7 11.Qxe7 Bf5 12.Qf7 Bg4 13.e6 a6 14.e7 Kb8 15.e8=R+ Ka7 16.Rxa8+ Kxa8 17.Qg8+ Ka7 18.Qxg4 c5 19.dxc5 Nxb2 20.Qh4 Nd3 21.Kh2 d4 22.Ne2 Kb8 23.Qd8+ Ka7 24.Qxd4 Nxf2 25.Qxf2 b6 26.Qh4 bxc5 27.Nf4 Kb7
D41 -12.67 1...Rf8 2.e6 Rxf6 3.exd7 Bxd7 4.Qxh7+ Kf8 5.Qh8+ Ke7 6.Qg7+ Rf7 7.Qxf7+ Kd6 8.Qf6+ Be6 9.Bf7 Kc6 10.Qxe6+ Nd6 11.Qxd5+ Kd7 12.Qxa5 Rf8 13.Be6+ Kxe6 14.Qxc7 Nf7 15.Nc3 Kf6 16.Qg3 Rd8 17.Rfe1 Rxd4 18.h4 b5 19.h5 Rg4 20.Qxg4 Ne5 21.Qf4+ Kg7 22.Qxe5+ Kf8
D41 -14.04 1...hxg6 2.Qxg6+ Kf8 3.e6 Rxe6 4.Qh6+ Qg7 5.Qxg7+ Ke8 6.Nc3 Bxc3 7.bxc3 a5 8.Rfe1 Ra6 9.Bg5 Ne5 10.Qg8+ Kd7 11.Qd8+ Kc6 12.Qxc8 b6 13.Qxe6+ Kb7 14.Rxe5 Ra7 15.Qxd5+ Ka6 16.Qb5+ Kb7 17.Re7 Ka8 18.Qd5+ Rb7 19.Re8+ Ka7 20.Qd8 Rb8 21.Qxc7+ Ka6 22.Qxb8
D41 -16.10 1...Rxe5 2.dxe5 Nd6 3.e6 Qg7 4.Bxg7 Kxg7 5.Qxh7+ Kf6 6.Nc3 Bxc3 7.bxc3 a5 8.Rfe1 c6 9.Qh6 Ne4 10.Bxe4+ Ke7 11.Bf3 Ra6 12.Qg5+ Kd6 13.Qd8+ Kc5 14.Qxc8 Ra7 15.e7 Kc4 16.e8=Q d4 17.Qg4 Kxc3
D41 Mate -10 1...Nxe5 2.Bxh7+ Kf8 3.Qh6+ Kf7 4.dxe5 Qg4 5.hxg4 d4 6.Qg6+ Ke6 7.Qxe8+ Kd5 8.Qb5+ c5 9.Bg8+ Ke4 10.Qe2+ Kf4 11.g3#
D41 Mate -8 1...Kf8 2.Qh6+ Kg8 3.Bxe8 Qf7 4.Bxf7+ Kxf7 5.Qxh7+ Ke6 6.f4 Ne3 7.g4 Bb4 8.f5+ Nxf5 9.gxf5#
Well, I eat sacrifices around the king each day before breakfast. When I saw that the most straightforward mate failed, I started to look immediately at e6 as the most logical move. Luring away the queen from the 7th rank. So it is a very human move which took me a minute or two.
ReplyDeleteThe author typically demonstrates that a mindless trial and error is going to bring you nowhere in a complex position.
I see that a lot of titled players on Youtube are advocating the CCT method in order to find "candidate moves". Which is in essence advocating the trial and error method.
ReplyDeleteWhat they don't realize is that they are using the underlying chess logic themselves automatically. Hence they forget to tell you that.
I use CCT (and PoPLoAFun) only for my opponents' moves. In order to find defensive (PoPLoAFun, how can he interact with the LoA) or counter attacking (CCT) resources.
I hypothesize that the top of the bell rating curve is correlated with how deep you can calculate with trial and error as the main mechanism.
ReplyDeleteIt seems to me that most chess (indeed, almost all areas of) instructional material is biased toward "received wisdom" (sometimes going back hundreds of years) instead of being based on personal experience. Perhaps it is caused by a desire to avoid the "heresy" of disagreeing with the established authorities. After all, if I were an “authority” I would have a master rating, n’est-ce pas?
ReplyDeleteAn example would be the many logic-based (System 2) "thinking processes" that have been proposed as THE way to figure out what's happening in a given position and what should be played as a result of that in-depth analysis, beginning with a complete set of ‘candidate moves’. That approach is of value for any novice with no idea what to do or how to do it. That approach is abandoned as skill improves. Experts, beginning around the 1700-1800 Elo rating, do not follow a logical step-by-step thinking process. Instead, they subconsciously follow something similar to Tisdall's "variation processing," which is merely a description of what happens without being prescriptive. Either you acquire that approach by osmosis or you don't—and if you don’t, you won’t progress much above that level.
Why is that true?
Given the constraint of limited time to make moves, System 2 cannot work through all possibilities of the combinatorial explosion to find the correct solution move-by-move. Only System 1 has the massive parallel processing capability to rapidly recognize useful patterns and trigger a sequence of plausible moves. That does not mean that the first pattern recognized should be played. It just means that the move investigation as it drills deeper is guided by patterns, not logical syllogisms. Ergo, there is a necessity to acquire a broad set of patterns in order to play at a higher level.
The received wisdom is that you just have to play through a set of 50-100 tactical problems focused on each specific tactical theme/device in order to embed the chunks needed for pattern recognition. My personal experience (buttressed by others’ experience) contradicts that assumption. For example, I’ve gained more skill for playing pawn endgames by studying the Trébuchet [oh no: not THAT again!] in every possible variation of structure rather than a general exposure to hundreds of various pawn endgames.
Another very useful pattern is the piece relationships associated with the Epaullete and Dovetail checkmates. I first noticed a pattern of a queen and the necessity of covering the two squares (at a knight’s distance from the queen) in order to cover all squares for a mate. That progressed into “SEEing” that when the king is protecting a piece diagonally, with two pawns on either side of that diagonal (at a right angle), that the king can be attacked with a lower value piece, forcing it to abandon the defense. It is a specific variation of the broader, more abstract theme of diversion or distraction, but it occurs frequently, especially in situations where a fianchetto has occurred and the bishop has been exchanged with the king in its place. In that specific case, the abstract description does not capture the actual usable pattern; the abstraction is at a high level that is too broad.
In each unique special case, there is a corresponding mini-skill in recognizing the pattern and what to do when that pattern occurs.
It is the collection of mini-skills that enables SKILL in general.
Just as “a picture is worth a thousand words,” a specific mini-skill is worth at least a collection of a thousand tactical puzzles on a specific theme that have been selected at random and cursorily ‘studied’.
We have logic (system 2) aplenty. Furthermore, we are very skilled in recognizing patterns (system 1). The only problem is that the two systems don't talk to each other. System 2 is too busy with its slow word salads (it talks too much) while system 1 is busy to play a speed game with irrelevant patterns.
ReplyDeleteOnly attention can force the two systems to look at the cutting edge between logic and patterns. Because system 1 and system 2 look over the shoulder of attention. Where logic and patterns connect. We must guide our attention along the relationship between patterns and logic. At a slow pace, otherwise system 2 can't follow.
Indeed I found the move e6 by trial and error. Since that is the best way to find moves with speed. But I could do that because I had absorbed the right logical patterns.
ReplyDeleteTrial and error in the tournament hall, slow deliberation in the study room.