## Monday, November 24, 2008

### A global game plan?

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I realize quite well that my previous post is hard to read since my thoughts are still brewing. I hope somebody will take the effort to formulate some answer to the question at the end of the post though. The idea of a closer study of the parameters that decide the game is very tempting. But take a look at the following three positions:

diagram 1

=/=
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White to move: draw
Black to move: draw

diagram 2

+/=
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White to move: wins for white
Black to move: draw

diagram 3

=/-
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White to move: draw
Black to move: forced loss for black

This all looks rather esotherical.
Nunn wrote a book of 320 pages solely devoted to the KRp vs KR ending. His book makes it seem as if there are 3 levels of endgame knowledge:
• The totally ignorant patzer, among which I reackon myself
• The one-eyed king, who wins drawn endings against ignorant patzers
• The endgame tablebase assisted computer which draws lost games and wins clear draws
If I am going to study the parameters by working my way through Nunns book, I basically try to jump from level one to level three. Somehow I think that might not work.

But maybe it is possible to develop a global game plan for the moment. My previous posts seem to suggest that from all endings the ones with minor pieces are the most likely to have an outcome that is not according the tablebases. Where a one-eyed king can win from the total ignorant. So when I don't know what to do in a game, I follow my endgame maxims (see my sidebar) and head for a minor piece ending. Just for study purposes.

1. I have Nunn's book--you actually were the one to tell me about it! I doubt I will ever read it cover to cover. If you know 200 rook endings by heart you know as much as GMs! Nunn's 750 R+P vs R positions serve more as a reference or a spiritual journey than a way to improve. Maybe knowing 30-50 positions is enough at the expert level and below to get a leg up on the average opponent.

2. I still have a hope that it should be possible to formulate the laws behind such endgames, so memorizing individual positions isn't necessary. But Nunn did a rather poor job on this. Maybe indicating that it is too difficult for mortal men. Which makes it all the harder to resist to have a look for myself.

3. "I still have a hope that it should be possible to formulate the laws behind such endgames, so memorizing individual positions isn't necessary."

None of the mainstream rook ending authors advocate learning every position, and they all advocate learning at least some.

Pandolfini, Silman, and Seirawan reveal tens of positions. Minev, Ward, Dvoretsky, and Mueller show 100-200. And Nunn nearly 1000.

If you aim to master them without memorizing any precise positions, you're blazing a unique path. But why? Humans recall pictures better than words (provably), and there are sayings in our language like, "A picture is worth 1000 words."

"Nunn did a rather poor job on this"

His goal of explaining every possible R+P vs R ending was quite ambitious. If you are content to explain practical endings then you have many authors to choose from who have that aim and so do a better job, including all the ones I named before.

4. If you know the Pythagorean theorem, there is no longer need to memorize hundreds of special instances of A, B and C which obey to this law.

There are about 640 million instances of the KRp vs KR ending. How is the choice made which instances to memorize? How do I know how I must treat a concrete position which I haven't memorized? Must I treat it as a position that I do have memorized? But which one?

5. "How is the choice made which instances to memorize?"

Authors try to identify the most practical points and demonstrate them using basic and/or worst case examples. How many and in how much depth is ideal depends on the playing strength of the audience.

"How do I know how I must treat a concrete position which I haven't memorized?"

Minev (my favorite rook ending author) spends 50 pages on general tactics & strategy, and then 60 pages on specific positions.

First, maybe you recognize it.

Second, if you don't, you often know what small change will make it into a position you recognize. That helps you put up an optimal offense or defense and swindle yourself some half-points.

Third, if those fail you can fall back on the general principles.

110 pages of Minev is enough to handle the vast majority of rook endings--but sometimes it's not, and you have to lament that you do not have time to memorize Nunn. Then again, neither does Kasparov!

"But which one?"

C'mon now, usually books explain when the given position / principle / technique / evaluation applies and when it doesn't. Eg:

"This threat is absent from analogous positions with a knight pawn (b- or g-pawn), when the stronger side cannot win."

6. A note on the Pythagorean thoerem:

Even that is not so simple. It only works for right triangles, so after learning if they teach you how to decompose other shapes (such as isosceles triangles, equalateral triangles, and trapezoids) into right triangles so you can apply Pythagoras using helper rules such as, "Parallel lines, cut by a trans, opposite interior angles are equal".

7. life is much better to know men such as temposchlucker, BDK, and likeforests, the triumphate of post-Knights Errant Blogging.

im slowly making my way back here, out and about, after what was it, a year underwater holding my breath?

i scannned ALL your recent visible posts, and much of great merrit produced by you... i have the utmost respect for you, and your efforts.

here? lots of analysis and viewing of high level GM games, much play at both FICS and ICC, and in the next year, now, a real possibility to play OBC, rated, face to face, finally.

it is wonderful to see you still growing.

love dk

{PS: saw Polly in person for tea last night for a few hours, what a gem}

8. Great blog here! I've looked at some of the "Knights errants" blogs as an interested bystander and OTB player.

I've thought about systematizing the Nunn Rook Endings material myself, because many Rook Ending books treat these positions so briefly I have trouble remembering them (If I don't understand something to a certain depth I easily forget it).

A few guidelines I've developed for my own work:

- Ignore at first all positions with pawn on the 2nd and 3rd ranks (100 pages!), since they are extremely rare in practice. If I ever reach one I will just try to calculate to a winning "4th rank" positon.

- Start with the 7th rank, then work backwards (since a pawn can always move forward)

- Make use of known position types like Lucena, Philidor/3rd rank defence, Last rank defence, Passive defence against the a- and b-pawn, Rook stuck in front of pawn, King stuck in fron of pawn, etc. as mnemonic help.

- For positions where defending king is cut off from the pawn, take Chéron's "Rule of five"* as a guideline, and determine in which ways it must be changed.

* "Add the number of the rank of the pawn to the number of files the defender's king is cut off. If the sum is more than five it's a win". - from Soltis: GM Secrets: Endings.

My studies so far indicate that "sum 5" is indeed often a borderline case where some positions are won and some are drawn, while "sum 6" is usually won. With an a-pawn (much harder to win) it seems like "sum 8" is the borderline case. This "rule" is most useful for pawns on the 3rd, 4th and 5th ranks.

9. "If you know the Pythagorean theorem, there is no longer need to memorize hundreds of special instances of A, B and C which obey to this law."

A better analogy, I think, is: knowing the details of the proof of the four-color theorem is of no help whatever in coloring any particular map.

10. Also, "How is the choice made which instances to memorize? How do I know how I must treat a concrete position which I haven't memorized?"

Typically, you would memorize a few typical instances that show the procedures used to win or draw (for example, Lucena and Philidor); some "edge" cases (where the result depends on whose move it is), and some generalized "rules" (heuristics; "checking distance", for example, or how far the King has to be cut off for a pawn on each rank to win).

You treat concrete instances you haven't memorized by seeing if any of the heuristics apply (e.g. "how far is the defending King cut off?"), or if they are in the same class as one of the typical examples (e.g., "is it in the Phildor class?").

I wish I had enough time to write this more clearly.

11. Stig,
thanks for the maxims, I will have a close look at it.

There will certainly come a moment I cannot longer resist to dive deep in Nunns book. Usually such expeditions lead to nothing, chesswise that is. But I enjoy it so much.

12. Ed,
I know what you mean. My whining is about that I memorized positions like the Lucena and the Philidor, but that I tend toforget them easily since I don't have a clue how they fit in the rest of the game. I haven't build any cues for retrieving them.

Probably now it is different. Hansens book helps me to see the relation between an ending and the rest of the game. I really need that, otherwise I simply forget everything. In stead of being hypnotized by the individual variations I start to get an idea of the big picture.