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Your width and depth pages are very nice. Now I see the picture. If one has sufficient knowledge of the concepts listed on the BeginnerExercises problems,then the depth and width given are all that should be needed. Put another way, if one can't see the solution after searching the specified width and depth then one needs work in the listed concept areas. Nice how it all hangs together!
By the way, your examples on the width and depth page are concrete illustrations of what I had said on my page (Gronk), namely that for some level of problem, one need not look at a solution to know one had solved it. It is only a matter of finding the right level of problem such that this can be done in reasonable time (I suggest 10 minutes) and with reasonable tree search (given by your depth and width).
Very good metrics!
Bob McGuigan: Nice exposition of some often overlooked ideas about reading. Of course it is the combination of width and depth that makes for difficulties. If you concentrate you can read out one of Mr. Nakayama's 100+ move ladder problems in your head in a few minutes (great depth) because there is almost no branching (little width). On the other hand, at the very beginning of the game there is tremendous width. Perhaps that's why weaker players have trouble with the opening. The use of learned patterns to control width has relevance for go-playing computer programs, too.
I'm not familiar with Mr. Nakayama's problems but I wonder if the depth dieter might give one is really the full number of moves (which might be called "capture-depth" or something). That is, if one can skip the explicit reading of many of the moves (due to some pattern that continues until you bump up to something that requires change to the pattern) then maybe those moves don't count as part of depth as dieter has defined it (which is more "obvious-it-is-solved-depth", or something).
If this is so,then maybe it is quite rare to have very large "obvious-it-is-solved-depth" with very small width.
I suppose if one knows how to count liberties then many capture race problems have a "obvious-it-is-solved-depth" of zero!
I think that the exercises are aimed towards people who have some basic knowledge about eyes. That's what I call a beginner. Those who don't are novices and should get some basic L&D tutoring before starting any kind of beginner exercise with more complexity than atari - cover.
Maybe I shouldn' add these criteria to the series: it's subjective.
Maybe I shouldn' add these criteria to the series: it's subjective.
Which criteria? The depth and width? Or the related concepts? I rather like all of this as it suggests (to a reader who understands what they mean) how to evaluate whether they need more work in an area. It also suggests the difficulty of the problem.
But yes, they are subjective. I don't think they could be otherwise without being silly (like width = all possible variatons and depth = max length of all variations). A pinch of subjectivity adds a heap of utility. That's my opinion on this anyway. I'm sure it is not universally shared.
I removed them from the Beginner Exercises a while ago. Imo they are more a concept for discussing positions instead of putting it right in the middle of Beginner Exercises (which I found pretty confusing). They are a bad measure for difficulty, too. (Each learned technique would change the numbers completely.)