Extension From a Wall
For extensions from a wall, or extensions in general, the following rule of thumb applies:
It is also embodied in the following proverb:
- From one, two. From two, three.
This rule can be applied to walls of heights one to four, and in rare occasions, five. Extensions of more than six spaces are very rare because an invasion is likely to succeed.
Here we can see examples of such ideal extensions in their abstract form. At the top, we see a two space extension from a single stone, at the right a three space extension from a two stone wall, at the bottom a four space extension from a three stone wall. In practice, nearby stones affect the rule of thumb. Mostly we talk about extensions happening on the third line, but it can also apply to extensions on the fourth line.
For the analysis as to why these extensions are ideal, we refer to the specific pages about these extensions. Basically, they are the farthest extensions on the third line which cannot be broken without the support of nearby stones.
Any closer extension suffers from overconcentration, any farther extension suffers from thinness. Again, on higher lines, such as the fourth or fifth, and with nearby stones, the rule of thumb must be inspected with caution or disregarded altogether.
Let's provide one example, on two common extensions.
The only way Black can prevent being separated is by granting White a powerful ponnuki on the third line.
Note: The usual response to is , not .
With the marked stone, separation is not possible at all, neither gets White a good result. Of course, White stones in the area will influence the position.
There's an interesting quantitative point here: if the area of the framework defined by wall plus proper extension from it really goes up quadratically with the height of the wall, we have various possible conclusions, such as
- the influence of the extra stones in the wall is greater
- the framework is less securely held, but this is still correct because to get value for the wall you should fight
- come on, this must break down for walls of height ten and probably well before.
Actually there is no reason to think any of these statements is completely misleading - all perhaps aspects of the truth.