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I've noticed that with some annotations, videos, etc that I run across where a GM will say, and ____ isn't even worth looking at as black is clearly better and even after setting it up to look at it I don't understand why.

As long as the coach had been playing for a long time... lets say 10 years, I would be happy with them at "only" 200-300 points stronger.

WARNING: This is going to be wordy- you have hit a topic that I am very interested in

I can relate to this. In some ways; however, (I am sorry, I do not mean to keep making references to math education but they are so dang similar I cannot help it) it reminds me of two schools of thought you see in math regarding upper division textbooks- and teaching styles.

1) Some textbooks give you an abundance of information, examples, explaination of concepts, etc... The idea here is that you provide all of these ideas to the sudent so that he/she can assimilate them well. (Much like the chess coach carefully walking you through a variation, explaining each step- then asking you to practice and assimilate it)

2) Others, such as texts by people like Walter Rudin or John Milnor, take the approach- give the student all of the main- essential ideas and do it in a very straitforward, direct, but rigourous way, but leave the rest out (with these style books, you see a lot of- "a straitfordward calculation will show..." and "the student can verify..." when in all truth these things are not trivial at all and take several hours worth of work to verify). The idea here is that the student gets the big picture and knows which ideas are important, but has to work for the rest and develop the theory on their own.(Much like the GM telling you that "variation X is not worth looking at because ...(some vauge reason)")

Each student has a personal preference as to which style they like. Both approachs work- but for different people (and in different situations).

The first approach (in math), has the advantage that it is less tiresome for the student, he/she can begin to discover results fairly quickly. The downside is that it takes longer (depending on the teaching style of the prof.), and sometimes it can be hard for the student to see what the essential important points are(again, some of this depends on the prof.).

The second approach has the advantage that the prof. needs to deliver less information and the student has a chance to discover the depth for him/her self. (When such books are written properly- such as Walter Rudin's "Principles of Mathematical Analysis" hands down my favorite undergraduate analysis book of all time- beautifully written math book) the ideas, and techniques required to understand the book tend to build upon each other very well. In a nutshell- the student gets to own the theory for him/her self. The downside- MUCH harder to learn this way! Not everyone makes it(First time I tried to learn from Rudin, I failed miserably- of course I was doing this on my own which did not help much). It is really easy to miss a subtle point (rather than a big picture point)- which can often times be more deadly in math than big picture points. Also, these books are usually aimed at a higher caliber students (Like UC Berkeley or Ivy leauge material). The trade off (in my personal experience), is that you learn the material very very well (if you learn it at all of course- for my Analysis qualifying exam I studied almost exclusively out of Rudin- I pulled an unusually high score because of it- I had like half the faculty in the office building comment about it when I walked down the halls- especially since Analysis was my weak subject in math at the time- now it is one of my best! Undergraduate analysis is almost easy for me now because of that book).

Anyway, I did not mean to ramble. I just wanted to mention that because it parallels very well this discussion. The nice thing about learning from someone who has mastered the material is that although they may seem confusing- they usually have a clear idea of how to think about things properly- it is just a matter of trying to figure out what they are thinking. Then again, you could learn how to interpret what that master is talking about by meeting their level half way (ie by learning from an IM or FM).

I see plausibility with both arguments.

Very interesting discusion- keep it coming! This has all given me a lot to think about.

Although a GMs evaluation about a position in chess is far from the final word as I imagine it would be for the author of a math textbook, I can see what you mean.

I had a strong expert evaluate a game for me, and there was a certain move of mine he criticized above the others as being fundamentally wrong in the given position and told me to spend a lot of time with the game.  After I analysed it for about a week, I discovered the move I played was actually correct and his suggestion was slightly weaker.  (The correct evaluation wasn't obvious until the game unfolded another 10 moves or so when it turned out black was at the same time not better than white, and also his play couldn't be meaningfully improved).  But rather than scoff at the analysis he did in an hour or two, I looked at the original position and asked myself why he would say that and tried to learn that much more... this relates back to a mysterious evaluation "and we can see white is better."  Yes I think it's valuable to try to understand why they would say so even if later your analysis doesn't agree (I've been told strong players like to try to disprove the annotations).  Although obviously the chances of this happening with a GM are much less.

The danger though is similar to your example that it depends upon the proff.  If they did this with the right kind of positions, then I agree the student could learn a lot.  But if they did this as if talking to another GM and the reasons are simply too complex for an aspiring player... well as you said the student either learns a lot or doesn't learn at all.

I suppose what I've just described says that some players will take the step by step explanations, and then challenge them to see if they're true much in the way you would take a big picture example and work the details for yourself.  In this case it's up to the student how much he/she is willing to work and learn.

The math analogies are interesting to me... if you think of any more don't hesitate to point them out.  Heh, and if I switch to a math major I'll be sure to check out Rudin's "Principles of Mathematical Analysis"

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