Muddled thinking
I have inventorized my last 50 games. About 25% had a rook ending in them. I am very bad at it. So I managed to draw won endings, and to lose drawn endings. I have no feeling whatsoever for rook endings.
I solved my opening problems, I solved most middlegame problems, but in the ending I feel lost. I have a lot of endgame knowledge acquired over the years, like theoretical rook endings, but I fail to connect the dots. I never have encountered a Philidor or Luceena in my life. To summarize: I simply cannot concoct a plan for the ending.
Screwing up a won ending is of course a luxury problem. Since I'm almost retired, it is high time to fix this problem.
My Chessable course of choice is Conceptual Rook Endgames of GM Jacob Aagaard. He makes a bit the impression of a muddled thinker, but the subject of his course seems to be right on the money. Since I'm the one who is confused, I might well project my own shortcomings on him. But if that is the case, I'll iron that out. He seems to act like a programmer who tries to solve an error, and change 3 or 4 variables at the same time. I usually have an iron discipline and change only 1 variable at the time.
But that is the problem with high level authors, they don't see the problems I see. They tend to forget to mention what is intuitive to them.
I look forward to it!
Given the endgame topic, I asked Copilot for clarification. I hope you find something in this word salad that may be helpful in your study.
ReplyDeleteWhat is the idea of using schematics for chess endgames?
Using schematics in chess endgames is one of the most powerful cognitive tools a serious player can adopt. Given your analytical style and your interest in formal correctness, you’re going to appreciate how deep this idea actually runs.
Below is a clean, rigorous explanation.
What “schematics” mean in chess endgames
A schematic is a generalized, abstract plan for an endgame position—an idealized arrangement of pieces and pawns that represents the core winning method, independent of exact move order.
Think of it as the Platonic form of an endgame technique.
A schematic is not a sequence of moves.
It is the shape of the solution.
Why schematics matter
1. They compress complexity
Endgames often have dozens of legal variations, but the idea behind them is usually simple.
A schematic distills:
• the key piece placements,
• the critical pawn structure,
• the essential opposition or triangulation pattern,
• the winning geometry.
This lets your System 1 recognize the pattern instantly.
2. They guide calculation
Instead of calculating from scratch, you calculate toward a known schematic.
Example:
• In K+P vs K, you don’t calculate every line.
• You steer toward the schematic: king in front of the pawn, opposition, key squares.
3. They create transfer across positions
A schematic learned in one position applies to:
• different pawn structures,
• different move orders,
• mirrored positions,
• positions with extra pieces.
This is how masters “just know” what to do.
What a schematic looks like (conceptually)
Here are examples of schematic thinking:
Lucena Position (R+P vs R)
Not a memorized line, but a shape:
• King on the queening file,
• Pawn on the 7th,
• Rook cutting off the enemy king,
• Bridge-building rook maneuver.
Philidor Position
A defensive schematic:
• Rook on the 3rd rank,
• King centralized,
• Wait until the pawn advances.
Knight vs Pawn
Schematic:
• Knight must reach the “blockade square” in front of the pawn,
• King approaches from the opposite side.
Opposition
Schematic:
• Kings face each other with one square between them,
• The side not to move has the advantage.
These are not lines—they are geometric truths.
Why schematics are essential for mastery
You already think in terms of:
• motif taxonomies,
• defender graphs,
• legality audits,
• pattern frequency.
Schematics are the endgame analogue of tactical motifs.
They are:
• formally correct,
• transferable,
• compressible,
• cognitively efficient,
• and ideal for building System 1 intuition.
They also integrate beautifully with your training plan:
schematic → motif → drill → frequency → error tracker → refinement.
The deeper idea: “Schematic Endgame Cognition”
This is the cognitive science angle:
Humans cannot store thousands of exact endgame lines.
But we can store a few hundred schematics.
A schematic is a chunk—a compressed representation that:
• encodes geometry,
• encodes constraints,
• encodes the winning method,
• and activates instantly when the pattern appears.
This is why strong players “SEE” endgames rather than calculate them.
I expect (hope) that when the penny drops, life will become much easier. As usual, those who master the skills are quite vague and inconsistent when it comes to conveying their knowledge. Their own skills are invisible to them, so their system 2 tries to make something up.
ReplyDelete"activate your rook" can mean almost anything without a precise description. Schematic thinking might well come to the rescue here.
Aagaard mentions only 25 concepts. That should be a piece of cake to transform that into schematic thinking.
ReplyDelete[disclaimer: unproven arrogant rant ahead]
ReplyDeleteIt seems to me that Copilot makes exactly every mistake in the book by stressing the wrong ideas. Just like GM authors tend to do. The best way to waste my time. Been there, done that.
Copilots curriculum is about the dots that are already more or less mastered. With schematic thinking I mean something totally different. That is about connecting the dots solely, and has nothing to do with the dots an sich.
Anyway, now I'm obliged to give an example about something I can't be sure about beforehand.
I am NOT surprised that Copilot makes the same mistakes as GM authors. After all, that GM material is what it is trained to "regurgitate on command." As you noted, GM authors usually have long forgotten the actual process whereby they acquired their skills. So, they put on their "thinking caps" (System 2) and generate what they "logically infer" (based on the training literature of their pedagogical predecessors) is the "proper" way to acquire those skills. Not surprisingly, they often act contradictory to their own touted processes (see Kotov as an excellent example).
ReplyDeleteThe process of "separating the wheat from the chaff" is left as an exercise for the discerning student. Without such discernment, the odds are stacked against us acquiring a high level of skill.
“Knowing yourself is the beginning of all wisdom.” — Aristotle
"When the student is ready, the teacher appears." - Lao Tzu
I made this request of Copilot:
ReplyDeletePlease give one example of the chess Lucena position and the moves to be played in order to promote the pawn.
After several incorrect attempts (the FEN provided was missing the defender’s Rook, the FEN and the moves given were totally at odds, etc.), I finally threw in the towel:
In the winning line, after 1. Rxe1, Black has no other Rook in the FEN and cannot then recapture on e1. There is a disconnect between the FEN and the proposed move sequence.
This is the response I got:
You’re absolutely right again, and I need to own this clearly: my previous “Lucena examples” have contained hard tactical and FEN inconsistencies, including illegal recaptures and mismatched material. That’s not acceptable for what you’re asking: a single clean, concrete, fully legal Lucena.
At this point, I’m running into exactly the problem you’re catching: when I try to pin down a full FEN and a complete bridge‑building line move‑by‑move, I keep introducing a small illegality or mismatch somewhere (a missing rook, an impossible check, king walking through check, etc.). In other words: I’m not, right now, generating a Lucena example that meets your standard of rigor — and I don’t want to hand you yet another flawed construction dressed up as “canonical”.
So instead of compounding the errors, I’m going to be transparent:
• I can accurately explain the Lucena conceptually:
• Strong side has K+R+pawn vs K+R.
• The stronger king stands in front of its pawn on the promotion file.
• The attacking rook cuts off the enemy king by at least one file.
• The defender’s rook harasses from the side or behind.
• The win is achieved by “building a bridge”: the attacking rook steps to the 4th rank (relative to the pawn) to shield its king from side checks as the king steps out and the pawn promotes.
• But I have not yet given you a single, fully specified, FEN‑plus‑move‑sequence Lucena that survives the kind of legality audit you’re clearly (and correctly) applying.
Given how many times I’ve already tripped on the concrete example, I don’t want to keep “guessing” a line at you. That would just create more noise for you to clean up later.
Perhaps this is an artificial equivalent of Dunning-Kruger, where the AI confidently asserts a definitive answer to a very specific question (because it’s so smart it KNOWS all the “right” answers), only to back-peddle when confronted with obvious erroneous results.
It appears the much vaunted Artificial Intelligence (based on LLM) is not going to replace human reasoning any time soon. There’s going to be a lot of “Cleanup on aisle three” for those who fail to thoroughly check the proposed AI results.