Life In 19x19

I think a wall can have many different applications depending on the overall game position

- Creating territory nearby via an extension stone
- Harrassing opponent's stones and thereby creating territory elsewhere
- Killing opponent's stones (by denying them a big fraction of their angular escaping space)
- Breaking ladders
- Enabling invasions into opponent's moyo
- Connecting two own weak groups thereby making them strong (this saves time and thus enables big plays elsewhere)
- I guess that there are many more possible applications which are too subtle for me to recognize

The approximation formula for the "value" of a wall (or: influence stones) discussed here seem only relevant for the first application I mentioned. Thus I think the value of a wall depends on what actually can be achieved with it in the actual game position. If a wall just results from being chased out of an opponent's framework, it can be pretty useless. A numerical formula like n(n+1)/2 may give an approximate idea for the nearby territory potential (first mentioned application) but should be IMHO strongly misleading in all other cases.

schawipp, the influence stone difference is not always sufficient, but can be used, e.g., for these purposes:

- joseki evaluation if stones in the neighbourhood do not dominate the local situation
- center control if the influence stones have similar center access and are similarly stable (the center will be pretty neutral if the influence stone difference is about 0; the (sufficiently big) center will be valuable for the player have a great favourable influence stone difference)
- domination of a fighting region (the attacker has a great influence stone difference)

For other considerations, influence stone difference might be insufficient. Then other aspects of influence might have to be judged for representative intersections in or near a sphere of influence: degrees of connection, life and territory.

Robert, this definition of local excess territory makes sense, though I share mitsun's worry.

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. )

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.

Thank you very much for this excerpt John, very nice. I really like the "happy" or "unhappy" feeling.

I'm to weak so that my feeling could be trust, but it is really how i think in a game: cool, i'm strong and have free hands; damn, he's to thick and i have to play small otherwise i get in trouble; wow, no way you get my solid 25 points with this stupid wall; argh, i'll miss points...

Than a good part of trying to improve, in my case, is "correcting" these intuitions with comments from stronger players and review of pros games. Somehow i cannot imagine myself using some mathematical formulas during a game to evaluate things (maybe it is a weakness of mine?)

Anyway, it was interesting to read, thank you

gasana, most formulas applied in a game are simple sums, differences, multiplications, divisions or comparisons of two values. Iterative application can make this more complicated, e.g., during endgame value calculation. Some formulas combine two basic calculation steps.

Bill, walls can be evaluated in principle, but in practice the necessary calculation in combination with reading can become too complex.