Translation
The book of Dvoretsky contains many compositions. Compositions are often some kind of freak positions that happen only once in every two lives. That doesn't mean that we need to dismiss them beforehand. The mechanisms that are at play in pawn endings are finite. It is important to study these mechanisms whenever we can. By translating the positions by a few files and/or ranks, we get a clearer picture on how these mechanisms actually work. Have a look at this position:
8/1k6/1p6/1K6/P1P5/8/8/8 b - - 0 1
What white has done:
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| Diagram 1.Black to move |
8/1k6/1p6/1K6/P1P5/8/8/8 b - - 0 1
Only one move draws. White to move draws. It is not immediately clear why.
Let's translate this position over two files.
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| Diagram 2. Black to move |
8/3k4/3p4/3K4/2P1P3/8/8/8 b - - 0 1
Black to move loses.
White to move is a draw.
Black to move
Black must stay in contact with his pawn. So the only feasible moves are 1. ... Ke7 and 1. ... Kc7
The mechanism that white uses is to sac the pawn opposite the black king. Black has to take, and the white king can take back while seizing the opposition. Like:
- 1. ... Ke7
- 2. e5 dxe5
- 3. Kxe5
From there it is an easy win for white.
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| Diagram 3. Black to move |
- sacrificed a pawn to get the black pawn out of the way
- seized that pawn back while grabbing the opposition. Thus keeping the black king at bay.
Notice how universal these mechanisms are. You will find that time and again. There are a finite amount of mechanisms that can be combined in a zillion ways.
It is easy to see how the position from diagram 2 can be mirrored when black plays 1. ... Kc7
White can try a different approach. After 1. ... Ke7
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| Black to move |
- 1. ... Ke7
- 2.Kc6
Black must grab the opposition with
- 2. ... Ke6
White to move
What is the mechanism to draw when white is to move in diagram 2 (=5)?
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| Diagram 5. White to move |
When white sacs a pawn in order to free the path to promotion for the other pawn, the problem is that black maintains the opposition. So white cannot promote his pawn.
If white plays 1.Kd4, he doesn't make progress. The only thing black has to do is to occupy d7 when the white king returns to d5. Thus seizing the opposition.
Conclusion.
Dvoretsky has a penchant for freak positions every now and then. From a didactical point of view that complicates matters unnecessary. By generalizing the position first (translate it to the middle), you can come to grips with the general mechanisms. From there you can better understand how the exceptions work.
Now you can deem what is necessary in order to absorb pawn endings. It is not rocket science, there is a finite amount of mechanisms, and it takes time to learn to see them instead of calculating them. But when you manage to do so, it will be a formidable weapon.
Furthermore, without my learning method it is close to impossible to get the job done. People will waste their time by trying to find the solutions on their own, thus losing the energy to complete the task of absorbing them. When they can calculate it, they will think they are ready.
One of my 'sins' while trying to study endgames has been dismissing ‘freak’ positions (studies; compositions) without any study whatsoever. If it seems likely to NOT occur within two lifetimes, I lose all interest. As a consequence, I never really studied corresponding squares very deeply. I did study opposition (direct and distant), outflanking and triangulation (especially the Trébuchet!) and picked up 'tricks' like the rule of the square.
ReplyDeleteI’ve come to appreciate the importance of the idea of “two weaknesses,” embodied in the reality of there being more than one key square. The ‘trick’ is often to force the defender to choose one or the other of the key squares to defend, allowing the attacker to head for the other key square. This principle is applicable throughout the entire game. Capablanca in particular was very fond of attacking a weakness on one side of the board, drawing the defenders to that side, and then switching to a second weakness on the opposite side of the board.
While studying corresponding squares (thanks to your blog posts), I realized that there are several shortcuts that simplify the process somewhat.
The first task is to mark the key squares. It seems to help to use a special symbol for the key squares, such as Ø. (Hopefully, this character will be displayed by Blogger.)
The second task is to connect the key squares with a shortest path. It does not matter which direction along the path is taken during marking. It may help to mark the connecting squares for the attacking side with capital letters and the corresponding squares for the defending side with lower case letters, rather than using numbers. This insures that the critical connecting path is clearly distinguished from the remaining corresponding squares. I count the number of squares on the connecting path and then choose a letter so that the end of the connecting path is always ‘Z’. For example, if the connecting path is 4 squares long, I start with ‘W’; if 6 squares long, I start with ‘U’.
At this point, numbering of the corresponding squares begins. The numbers used are not important. However, it is very important to avoid confusing the corresponding square numbers with ‘number of moves’ in any context. Start with the squares adjoining the first key square. Mark the attacking square(s) and the corresponding defending squares with the same number.
If there is a possibility of promoting, then the defensive king is constrained to the square of the passed pawn. Any corresponding squares outside of the square can be left unmarked.
The edge of the board may limit the defending side’s possibilities.
The goal is always to maneuver toward the key squares AND the squares on the connecting path as required to break (for the attacker) or maintain) for the defender) correspondence. The attacking side strives to find a sequence of moves that (eventually) causes the defending king to occupy a defensive square from which it cannot reach the one of the corresponding squares. When this occurs, the attacking side (in essence) outflanks by taking that square. The next sequence of moves repeats this idea until either a key square is reached (with the opposition) OR one of the squares on the connecting path is reached which forces the defending king to choose which side he will defend, leaving the other side undefended.
Throughout the marking process, as well as in the actual move process, it helps to be alert for simplifications. After all, some of these solutions appear to be random without the marked squares. Anything that can be done to simplify the marking process (the most elaborate and most difficult to calculate over the board) is very helpful in reducing the mental load.
I’m still studying examples to determine if there are other simplifications that can be made.
Another extension that helps simplify the marking is to simply copy the square numbers (vertically, horizontally and diagonally) to every other square to the edge of the board. Or, mentally visualize them, while only marking the squares adjoining the key squares and the connecting path squares. ALWAYS REMEMBER: the numbers (symbols) used for marking are irrelevant; only the fact that there is a correspondence between attacking and defending squares is important.
ReplyDeleteThe first step is to connect the key squares with the shortest path between two invasion squares.
ReplyDeleteUsing numbers to identify the squares along the shortest path is not ideal. I asked Claude to advise which program to use for diagrams. He came up with Scid. Alas that can only produce digits.
From the Averbakh book I got the impression that simplification might be within reach by assuming that the path from the king to the shortest path (from invasion square to invasion square) is governed by distant opposition. I haven't checked that yet.
I think that for practical play it suffices to draw two "rings" or "chains". The first one is the shortest path, the second is all the squares adjacent to that. But then again, I haven't tested that idea yet.
On another note, I had a peek into the future by watching the 8 hours of video about rook endings that accompany the Dvoretsky endgame course on Chessable.
ReplyDeleteI think that I can weaponize pawn endings because there are a lot of invisible things going on. When I absorb that, it will give me an edge.
I wanted to investigate whether the same is true for rook endings. I think it is, but it is a lot of work. I'm going to start with it after the pawn endings.
"Capablanca in particular was very fond of attacking a weakness on one side of the board, drawing the defenders to that side, and then switching to a second weakness on the opposite side of the board."
ReplyDeleteI was skimming through all kind of videos lately in search for middlegame plans. This is it. Invasion on two sides of the board. I saw Karpov doing it.
Karpov middlegame plan
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