John Fairbairn wrote:Bill
The earliest discussion in depth I have seen of the value of thickness [atsumi] is that by Yamazaki Masuo in Kido 1959. However, he does not discuss numerical values. Rather he is concerned with whether we can count it at all and what factors might go into it. I give a short excerpt below (NOT to be copied elsewhere) so that others know what we are talking about. Yamazaki was a pro but also an intellectual, hence the style.
Many thanks, John!
This is great. Yamazaki is very interesting.
John Fairbairn wrote:As to the point of previous researchers coming up with different estimates and maybe underestimates, I always had the impression (no more than that) that Takagawa evaluated thickness rather more generously than others, and what was distinctive about his approach was that he was concerned not with an "external" value but an "internal" one based on tewari.
I think we can say that Fujisawa Hideyuki also evaluated thickness highly. Both he and Takagawa were considered masters of fuseki.
I may have more to say about Yamazaki's thoughts, but let me respond to his opening statement.
Yamazaki Masuo wrote:The value of thickness, however, is extremely vague, and in the form in which it constitutes itself it does not have a value in the (absolute) sense that applies for territory.
There is also a vagueness in the estimation or assessment of territory, which should also be addressed. For instance, suppose that a joseki leaves behind a simple ko in a corner which has a swing of 27 points between winning and losing the ko. Everyone who understands evaluation agrees on the estimate for the corner territory. However, they also know that at the end of the game the actual corner territory will differ from the estimate by 9 points or 18 points, depending on who wins the ko.
This possible difference of 18 points in the corner territory does not bother them, because they also know that, when the ko is fought, there will almost certainly be many plays of approximately the same size as the ko on the board, so that whoever loses the ko will come out even, or almost even, by taking one or two of those plays. There will be a tradeoff between potential territory in the corner and territory elsewhere on the board.
That is not so different from the tradeoff between the influence of a wall and territory elsewhere, although the mechanisms of the different tradeoffs differ. But there is a different kind of uncertainty associated with walls. Nobody knows how to evaluate them in the first place. (Whereas, we have known for more than 200 years how to evaluate simple kos.
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That is not to say that it is impossible to come up with good evaluation methods for influence, even though no consensus method has emerged yet. But once we do, I think that the ordinary uncertainty associated with thickness will be less than the +/- 9 pts. of the example ko, perhaps on the order of +/- 5 points, perhaps less.
Even now, my guess is that in Robert's initial diagram (assuming an otherwise empty board) White has an advantage of 5 - 10 points, though those are not hard limits.
