John Fairbairn wrote:You can't count influence
When you wrote this in 2010, a good influence definition was not published yet. In 2011, I published it. So, now, one can assess influence numerically.
You can count the type of thickness known as atsumi.
In 2011, I published a general definition of thickness. Therefore, each type of thickness can be assessed numerically.
There are different type of thickness, though they all denote a degree of strength.
No. Each of them denotes THREE degrees of strength! Namely the degrees of n-connection, p-alive and t-territory.
To qualify for the name, the outward facing strength called atsumi - the initial sort that often results from josekis - has to be strong enough to be able to turn into the type of really solid thickness called atsusa. That means it has to have no defects, or otherwise not be attackable.
Such a thickness description can be part of a reasonable informal rough characterisation. However, one must not slavishly exclude all defects; rather the degrees of connection and of life imply a possibility of (preferably non-existing or else marginal) aji.
There are two common ways of bolstering such a conglomeration to turn it into atsumi. One is to play a local move that defends the weaknesses and so makes it (for the moment) unattackable. This type of atsumi is hard to count.
It is easy to count by simply counting the number of successive plays to get a desired degree of, say, *-connection, 1-connection or at least 0-connection.
Two usual processes would either be (a) to do a tewari analysis and, if you are satisfied that all the moves have been efficient, assume that the thickness is worth the size of the other side's corner,
Tewari is a hopeless overkill for the purpose. Specifying a desired degree of n-connection implies the search for the MINIMALLY necessary number of additional plays to reach that degree and hence implies efficiency WITHOUT EXTRA EVALUATION EFFORT.
or (b) to use a QARTS type evaluation and say something like:
QARTS and other symbolic number models are hopelessly unsystematic and imprecise. Such kind of theory is for historians. Now, my theory allows to abandon earlier alchemy and get precise assessments.
The other way of making an outside shape thick is to play an extension from the wall, i.e. giving it a base for strength.
This increases the degree of connection of a wall's stones slightly, can increase their life degree significantly and usually increases their territory degree. This is more accurate than saying "making thick".
It is still best treated by the third method mentioned above.
Not any longer. Now, t-territory is the choice of evaluation.
The basic heuristic of this method is (relying on my memory!) to take the height or length of a sound wall, in stones, as N and calculate (N x (N+1)) / 2.
Alchemy. - The proper way is to identify, for each intersection, the t degree of t-territory. Optionally, a sum can be formed: 0-territory (aka "current territory") counting 100% and 1-territory 50%. (2-territory tends to be overkill.)
The resulting value is not meant to represent the territory you will get locally, but a territory-equivalent value over the whole game
Now, it is easier to assess the current estimate of local territory. (For the other kind of territory estimate, one would want to determine per-move values, but in practice this is too tough during the middle game, except for specialised application such a average value of a particular unsettled group).
The beauty of this method, mostly associated with Abe Yoshiteru though other pros have variations on it, is that you can use it for walls that go round corners, or kinky walls.
There is no beauty in flawed, imprecise theory!!! Replace it (and the professionals should also replace it) by my theory!
There are some modifications to it. For example if you can guarantee certain extra moves you can count them in the size of your wall. It seems also that stones on the first line are not counted. If you have a residual weakness, or an element of overconcentration, you have to reduce the size of the wall. Also some reduction is needed when two walls face each other - I forget the details but basically it's just excluding the overlapped area. There are some other fine points, too.
Note that in this method, you can count the atsumi thickness even if there is no extension from the wall. But there must still be room to make a sensible extension (or to attack an enemy group that dares to come too close).
Luckily, my much mightier theory does not need such exceptions related to shapes or position relative to the edge.
Abe stresses very much the need to have no defects. Even a peep can ruin the value of a wall.
He is wrong. It is not a necessity - rather it is an aspect of degree. Typically, a wall allowing a peep is 0-connected and not *-connected. After the peep, the influence on nearby intersections is worse than before for the wall's player and improved for the peep's player. However, "ruin" the value of a wall is an exaggeration. As a better description, the values decrease. This can have significant impact, but not to the extent of necessity in general.
You will know if your atsumi has been used well because it will turn into atsusa - you will be unattackable -
Instead of continuing usage of such rough terms, it is more meaningful to speak of 1-connection or *-connection instead of 0-connection (similar for life). Your stones are pretty much unattackable if they are at least 1-connected and 1-alive and even less attackable for higher degrees.
and you will pick up point after point either in a moyo or in the endgame while the opponent is busy remedying his
Correct.
defects.
It is not just aji. Rather the opponent can also be busy defending his stones with too small degrees of connection or life.
eventually we will reach a stage atsumi has become atsusa and the boundary plays can start.
Boundary plays need not start at a particular moment of the game; a few are best played early.
