zaterdag 25 oktober 2008

Calculation and patterns

How much deeper do you have to calculate, and visualize to improve 100 rating points? What patterns do you have to master to do the same? Can you gain a significant number of ratingpoints without improving in both at the same time?

These were and are crucial questions in my own search for improvement and in my teaching. In my quest for an answer to there questions, I have used the stepsmethod. From my own experience I can make some estimations about the relationship between rating and mastering the steps. And I have come to the following conclusions:

Step 1:
Calculation level: 1 to 3 ply
Patterns: mate, capture, defend, promotion

At this level the immediate capture of a undefended piece, an immediate mate, and defending an attaked piece or square are mastered. Most exercises are 1 or two ply deep, sometimes three. I cannot give an rating assessment because I have never had a student at this level who played competitive chess in rated tournaments.

Step 2:
Calculation level: 2 to 4 ply
Patterns: Mate in two moves, fork, double attack, pin, mating with king and rook, discovered
attack, eliminating defense, defending against mate.

When he has mastered step 2, the student is able to use standard techniques to attack or defend. He is capable to coordinate piece action (mating with king and rook, double attack). If he has mastered these skills he should be able to reach a 1000/1100 rating.

Step 3:
Caculation level: 3 to 6 ply
Patterns: stalemate, mobility, eliminating defense, luring, discovered attacks.

Step three builds on the foundations of step 2. It is not as much that new techniques are added. The basics are expanded by the game setting. The position have more pieces, and more distractions. Also the solutions require more calculation because exchanges or other forcing moves are part of the solution. After mastering step 3 the student should be able to reach a level of 1200/1300.

Step 4:
Calculation level: 5 to 8 ply
Patterns: attacking kingside, 7th rank; pawnendgame (key squares), rook endgames (passed pawn).

Now that the student has reached a level that he is able to avoid 3 ply deep blunders, he can expect to reach the endgame in some of his games. So the basic endgame's are introduced in this step.. The 8 ply deep calculations are only necessary in very forced positions with no sidelines. The student should be able to reach a 1400/1500 level after mastering step 4.

Step 5:
calculation level: 7 to 10 ply
Patterns: Pawn race, seventh rank, rook endgames (Philidor and Lucena position) open files, drawing techniques (fortress), strong squares, Zugzwang, uncastled king, king side attack, small plan, Pin, discovered attack.

In step 5 the average solution is about 5/7 ply deep, but especially in the forced sequences the student has to be able to calculate up to 10 ply deep. These occur mainly in endgames (pawnrace). Mastering step 5 should get the average student to a 1700/1800 rating.

Step 6:
Calculation level: 9 to 13 ply deep
Patterns: mobility, drawing techniques, zugzwang, imbalances (bishop vs night), strategy (small plan), kingside attack (intermediate moves, adding pieces after sacrifice)

I am doing this step now. I score about 80% on average. So this step is fairly challenging for me (current dutch rating over 2050). The main difference with step 5 is that it is harder to recognize the patterns, and in many of the exercises there is more emphasis on preparatory and intermediate moves. About 60% of the exercises are endgame positions and themes. Mastering this step should lift you over 2000.The main conclusion I draw from this excursion is that the ability to calculate and visualize 13 ply deep is enough to reach a 2000 level. But only if you have mastered the required patterns. Mastered them so well that you can implement them in all of your (slow time control) games.

This survey confirms my suspicion that I calculate not as easy and as well than most of the players that have a comparable rating to me. More than I would like to admit, I notice in a post mortem that a player I just beat, out calculates me. The main reason that I can compete and level with those players, is that I have mastered more patterns than they have.

20 opmerkingen:

Anoniem zei

Do you also used the extra and the plus workbooks? Is it worthwhile to use them as well as the cd?
Alastair

Phaedrus zei

Hello Alastair,

I have also used step 5 "extra" and "+" myself. they were challenging enough to keep me motivated to work them through completely.

I think that the extra en + books are a very good addition. especially to bridge step 3 to 4 and 5 to 6.

Somehow I always felt that there were gaps between those steps. Though the really talented players I had never experienced any problems, the average students did.

Temposchlucker zei

This survey confirms my suspicion that I calculate not as easy and as well than most of the players that have a comparable rating to me. More than I would like to admit, I notice in a post mortem that a player I just beat, out calculates me. The main reason that I can compete and level with those players, is that I have mastered more patterns than they have

At this, we should have a closer look. According to my hypothesis, calculation, pattern recognition, speed and visualisation have a 1:1 relationship. I know I failed to convince you of this. A recognized pattern is a chunk that your mind can work with. No chunksmeans no visualisation, no calculation and no speed. Besides this, there are two other parameters that play a role: quality of the pattern and frequency of the pattern. The quality of a pattern I define as the impact of it on the outcome of the game. The frequency of a pattern is how often it occurs in a game. If my hypothesis is right, the difference between you and your opponents of equal level must lie in those two parameters: quality and frequency of the recognized patterns. In the notion of your opponents you must be able to calculate real fast, but other things than they are able to calculate. It even hints to that there is no such thing as calculation. It might be only a presumption of what happens in the mind of others to explain why they have results in an area where we don't. Our opponents presume the same magic to happen in our minds.

chesstiger zei

I think that calculation isn't on first spot. Visualization is because without correct visualization your calculation probably at some point in the line will be bogus because you dont see the position clear enough.

Phaedrus zei

Temposchlucker,

You are right! We disagree. I think that visualisation and calculation are related to patterns, but that there is a big difference in the chess players ability to visualize and calculate.

A grandmaster recently told me that after a team game he and his teammates would analyse the games during dinner, of course without a board at hand (blindfold). I do not have that capacity and probably never will have it. But I can compensate it a little bit by making sure that I recognise as many patterns as possible within my visualisation and calculation horizon.

I do agree however that there is a strong relationship between patterns and chunks. To me, a pattern is a sequence of moves that changes the evaluation of a position favorably, or prevents it from changing unfavorably. Some of these patterns occur more frequently than others. And some have more impact on the evaluation than others.

So the most important patterns to master are those that occur the most and have the most impact. But in either case it is of the utmost importance not to minimize the number of patterns you miss in a game.

This is what a computer makes so strong. He sees all patterns within his horizon. His weakness is the horizon and his failure to see or estimate what lies beyond.

Phaedrus zei

Chesstiger,

Calculation and visualisation are so closely related that I can hardly distiguish them. I guess visualisation is more like a photograph and calculation more like a film. The first is more static than the other. To evalutate the strenght of a move, one needs both.

chesstiger zei

I agree that calculation and visualisation are closely connected. No doubt that one needs both to come up with good moves.

My point however was that if your visualisation is bad your calculation will suffer aswell since you have no idea how the position on the board will look like after a few moves further in your calculations.

To summarize, visualization and calculation are closely connected but if visualisation is bad calculation will suffer aswell (when playing an official game! During analyse one may move the pieces so then visualization isn't that big of a deal).

Blue Devil Knight zei

Very interesting post, great overview!

On the discussion with Tempo, Chapter 6 of Rowson has some relevant stuff. I'll be summarizing it someday in the next couple of weeks. He discusses chunking, patterns, and the exponential jungle of chess.

likesforests zei
Deze reactie is verwijderd door de auteur.
likesforests zei

I disagree with the hypothesis that patterns, calculation, and visualization are one and the same.

Pattern recognition is obviously a key to chess strength. It helps us to spot blunders and informs & speeds up our calculations.

But while playing and studying chess, we are able to slowly solve new positions with some accuracy. This points to there being more to tactics than pattern recognition.

Medical studies of chess players list them as different skills.

Additionally, many coaches like Dvoretsky, Pandolfini, Heisman, Rowson, Aagaard, Stoyko, etc. advocate training your calculation and/or visualization skills.

The tough question:

Should we spend 20 minutes/day on Stoyko exercises or is that time better spent another way?

Coaches and the medical profession seem at odds on this issue; there is the argument that new patterns have a bigger effect on depth of calculation than sheer speed, and that we already get practice with calculation during games and while studying new material.

Temposchlucker zei

LF,

I disagree with the hypothesis that patterns, calculation, and visualization are one and the same.

That's not what I said. I said

According to my hypothesis, calculation, pattern recognition, speed and visualisation have a 1:1 relationship

Meaning that you can't change one of them without changing the other.

Probabably I'm talking semantics when I talk about visualisation. Maybe "notion" is a better word. Prof. de Groot said that grandmasters don't "see" the board when they are playing blindfold, but they have a notion of the important parts of the board. It is actually more a form of "knowing that it's there". Much the same as a tennisplayer hits a ball that he doesn't actually sees.

When I talk about visualisation, I have this kind of "knowing what's there without seeing" in mind. Which is of course confusing when I forget to tell you that. Sorry for that.

Phaedrus zei

CT
I have to agree with Temposchlucker if he says that it is hardly possible to calculate well without visualizing. So it is hard to say that one can do well in one of those without doing well in the other.

Temposchlucker
I will give some example in my next post in which I personally have experienced the difference between pattern recognition and calculation/visualization, and in which I am sure that I succeeded of failed because of my ability to recognize many patterns, as well as my inability to calculate and visualize very well.

likesforests zei

Phaedrus -

Isn't playing over a game without a board primarily visualization, and using an analysis board during correspondence chess primarily taxing your calculation?

Tempo -

"That's not what I said"

Sorry about that! It's this darn communication medium. ;)

"Meaning that you can't change one of them without changing the other."

I agree then, that when trying to memorize new tactical patterns you have to visualize and calculate... and that doing Stoyko exercises uses and adds to your store of patterns, chunks, and principles.

Certain exercises tax one of these attributes more than the others. For example, blindfold chess = visualization, using an analysis board = calculation, and memorizing basic tactics = patterns. Although each one touches every skill just a bit.

My educated guess is that Stoyko exercises are more effective for an OTB player than blindfold chess or an analysis board because it uses both skills simultaneously as you would in an OTB game. And that Stoyko exercises become more relevant after one has developed a large pattern database of tactics, strategic, endgame, and opening positions.

Temposchlucker zei

Ok, I look forward to your next post.

Let's do an experiment.

Close your eyes.
Imagine before your minds eye a bishop that goes from c1 to a7. "See" the square where he changes direction.

Now do the same with a rook that is going from d1 to a7.

It is much easier to see the path of the rook than the path of the bishop. The reason for that is that we are much more familiar with rows and columns than with diagonals. This familiarity results in:

1. A better visualisation.
2. You accomplish the task faster.
3. You will be better in performing calculations with rooks than in calculations with bishops.

likesforests zei

"3. You will be better in performing calculations with rooks than in calculations with bishops."

Yikes! I instantly saw the rook path. The bishop path took me almost 10 seconds to visualize.

Phaedrus zei

LF
I do not believe it makes any sense to train visualization without calculation. For this reason I do not make a big point of distinguishing these two. But I like your metaphor's. They describe the difference pretty much as I see them. And what, pray tell, is a Stoyko exercise?

likesforests zei

FM Steve Stoyko suggested that one good way to improve is to find a rich middlegame position and spend 45-120 minutes analyzing it. Heisman also calls it by this name, although clearly Stoyko isn't the only or even the first to recommend such exercises.

Rowson recommends a shorter interval of 20 minutes (this book targets roughly 2100+ players).

I think Stoyko exercises timed to be as long as you would have at max in a regular game are better than blindfold or correspondence since it trains your calculation and visualization skills in equal proportion as in a real game.

But, I think neither is necessary for me at this point because there are still so many patterns for me to learn (#patterns known aid deep calculation more than speed). And besides, I get lots of calculation practice as I go through books like My System trying to acquire new knowledge (patterns and principles).

Anoniem zei

Hi Phaedrus

Have you read this article?

http://www.sciam.com/article.cfm?id=the-expert-mind

This quotation seems to support your notions about the advantage of pattern recognition over calculation:

the expert relies not so much on an intrinsically stronger power of analysis as on a store of structured knowledge. When confronted with a difficult position, a weaker player may
calculate for half an hour, often looking many moves ahead, yet miss the right continuation, whereas a grandmaster sees the move immediately, without consciously analyzing anything at all. page 2

And this quotation suggests, to me at any rate, a way to enhance the Steps books (by including information about the salient positional features of each puzzle; cf your advice to ChessLoser earlier this year:

A grandmaster, however, may see one part of the position as "fianchettoed bishop in the
castled kingside," together with a "blockaded king's-Indian-style pawn chain," and thereby
cram the entire position into perhaps five or six chunks. page 3

Alastair

transformation zei

all you guys are great. i will be back in touch. big news, to tell my chessBlog community, but most of my close friends (most of you here!), already know.

great blog, great post. thank you.

still not up for air here, but slowly seeing the work of my good friends in the blogosphere.

warmest, dk

transformation zei

'Step 6:
Calculation level: 9 to 13 ply deep
Patterns: mobility, drawing techniques, zugzwang, imbalances (bishop vs night), strategy (small plan), kingside attack (intermediate moves, adding pieces after sacrifice)

I am doing this step now. I score about 80% on average. So this step is fairly challenging for me (current dutch rating over 2050). The main difference with step 5 is that it is harder to recognize the patterns, and in many of the exercises there is more emphasis on preparatory and intermediate moves. About 60% of the exercises are endgame positions and themes. Mastering this step should lift you over 2000.The main conclusion I draw from this excursion is that the ability to calculate and visualize 13 ply deep is enough to reach a 2000 level. But only if you have mastered the required patterns. Mastered them so well that you can implement them in all of your (slow time control) games.

This survey confirms my suspicion that I calculate not as easy and as well than most of the players that have a comparable rating to me. More than I would like to admit, I notice in a post mortem that a player I just beat, out calculates me. The main reason that I can compete and level with those players, is that I have mastered more patterns than they have.'

phaedrus, to me, this is the really meet and potatos of this post, which i finally got to reread calmly. excellent.

what you clearly say, is you can calculate deeply, but if you dont HAVE all the patterns, you wont see what you are calculating.

or conversely, what if you could see all this, but couldnt carry it on long or deep enough?

with all of us, its a little bit (or LOT!) of both.

warmest, dk