A practical approach
Yesterday, the book of Averbakh arrived. It contains a treatise of corresponding squares. It is not really a theory. It is more a set of findings of the endgame composer M. Zinar, with an attempt to categorise those and to distill a few rules from it.
These are my conclusions:
- My attempt to simplify matters was way too optimistic. Almost ridiculous, actually.
- The shallow approach of corresponding squares by Dvoretsky is exactly what I need.
- The book provides exactly what I need to understand the videos about correspondence squares of NM Caleb Denby
For all practical intents and purposes, the work of Dvoretsky is enough to understand corresponding squares for tournament play at my level + 500 (<2200). The video is useful above 2200, I guess.
The following three videos make a lot more sense (to ME) than the NM Caleb Denby video. I could clearly SEE the ideas based on the simpler positions. I list them in the order that I viewed them; that may not be optimal for learning the nuances.
ReplyDelete(1) https://www.youtube.com/live/vXH5NJZfbFs
(2) https://www.youtube.com/live/s88rXp4W9H8
(3) https://www.youtube.com/live/3kmqYMJ2fWM
HTH.
The Euwe/Hooper method for visualizing distant (indirect) opposition is helpful (to ME) for visualizing the correspondence squares without having recourse to colored circles and arrows. YMMV.
I like the concept of corresponding squares very much. The problem is that I cannot estimate how often I can get this on the board. Grigoriev cs. are known for their freak positions. But somewhere between the freak position and the triangulation there are positions that I guess are possible to see without much calculation.
DeleteIf I was sure I can get that type of positions often on the board, for sure I would put in the effort. But if it is only once per two years, I can spent my time better, I guess.
I’ve been thinking about why there seems to be a disconnect between middlegame concepts and endgame concepts. Perhaps it is caused by the different terminology that endgame teachers use in an attempt to isolate the fundamental features from everything else. I asked Claude.ai to provide a description while changing the terminology.
ReplyDeleteI asked Claude:
Explain the chess concepts of key squares and corresponding squares in terms of invasion squares and defense against invasion.
Edit
In chess endgames, key squares and corresponding squares form a critical tactical concept that determines whether one side can successfully invade the opponent's position or whether the defender can maintain the fortress.
Key Squares (Invasion Squares)
Key squares are specific squares that, when occupied by the attacking king or piece, guarantee a breakthrough into the opponent's position. These squares are "key" because controlling them forces a winning advantage, typically by:
Allowing the attacking king to penetrate the enemy position
Supporting the advance of passed pawns
Creating unstoppable threats
Breaking down the opponent's defensive structure
For example, in a king and pawn endgame, if your king can reach certain squares in front of or beside the opponent's defensive setup, you can force your way through regardless of how the opponent responds.
Corresponding Squares (Defensive Coordination)
Corresponding squares represent the defensive counterpart to this concept. These are squares where the defending king must be positioned to prevent the attacker from reaching the key squares. The relationship works like this:
For each key square the attacker wants to reach, there's a corresponding square where the defender must maintain their king.
If the defender's king is forced off its corresponding square, the attacker gains access to the key square.
This creates a zugzwang situation where being forced to move first becomes a disadvantage.
The Dynamic Relationship
The interplay between these concepts creates a strategic dance:
Opposition and Triangulation: Players maneuver to gain the move advantage, forcing the opponent into positions where they can no longer maintain the correspondence between squares.
Breakthrough Preparation: The attacker probes the defensive setup, looking for moments when the defender cannot maintain proper square correspondence, then strikes toward the key squares.
Defensive Vigilance: The defender must constantly calculate which squares maintain the defensive relationship and avoid being outmaneuvered through tempo play.
This concept appears frequently in pawn endgames, rook endgames with passed pawns, and positions where one side seeks to improve their king's position while the other tries to maintain a defensive barrier. Mastering this relationship between invasion and defense is essential for precise endgame play.
[End of answer]
By using the simple linguistic “trick” of changing the terminology to resemble that used in the phases prior to the endgame, perhaps we can gain a more holistic view of the chess game. The idea of invasion applies to the opening, the middlegame and the endgame. It takes a different technical form, but is still (in essence) the same idea.
I’ve often found that analogies between different domains are much easier to SEE if a common terminology is used for both domains. It really does not matter which domain terminology is adopted (IE, describing A in terms of B or vice versa), or even if a new common terminology is used. It enhances the ability to SEE similarities and differences.
Once a common terminology is adopted, I think it highly likely that you will become aware that these common types of position are occurring more frequently in your games (much more frequently than once every two years or so), although in different phases of the game.
You noticed well that the discovery of invasion in the endgame is a different animal than the mindless rules we are flooded with. And your intuition that the invasion has a lot of brothers and sisters waiting to be discovered is correct too.
DeleteThe more I think about it, the more I realize that I must study pawn endings to the bone. Since all endings can convert into a pawn ending, potentially. And the only way to judge whether that is a good idea or not, is to study pawn endings thoroughly.
I don't know whether the thorough study of corresponding squares will pay off. But I sense the brothers and sisters, and I can only judge how useful they are by discovering them.
One entry point is the freak positions of endgame composers. Usually when you translate these positions to the middle of the board, they become more general and less freaky. That way you can see the effect of diminishing possibilities by shifting these positions closer to the rim.
ReplyDeleteFurthermore, there is a lot of beauty and surprise in these positions. What doesn't dismiss us from staying practical. Don't get carried away. First the tables of multiplication, then calculus.
ReplyDeleteFurthermore, I get the impression that the pawn ending is the perfect weapon. Invisible for those who haven't absorbed the patterns.
ReplyDelete