PeterPeter wrote:
Can you explain that to a beginner? How can a wall in the centre help a stone some way off to the side?
In essence, the strength of the black wall and the n15 connection and o17 stone separating the white corner from the top side group means that the white corner is weak and must be careful of its eyespace, so black can make benefecial exchanges to threaten this group and build elsewhere. In detail:
Say I played my other move on the left. First let's look at a bad move for black, trying to make territory next to his wall with something like

. In terms of local shape, it's a nice enough move (2 space jump from 3 stone wall, though could go further with the extension of the wall to the right of the 3 stones) and if black's wall ever got weak and needed to make some eyeshape it could be ok, but now black's wall is perfectly strong and this is a passive move which makes just half a dozen points and allows white to make a lot more on the side.
- Click Here To Show Diagram Code
[go]$$Bcm29
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . B B B O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . O . O . . . . 1 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . 2 . . . |
$$ | . . O O O . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
So for black's good move, if white ignores black gets to seal white in the corner and now you can see his wall working well to develop a large area in the centre. White needs to spend a move in the corner now or is in real danger of dying (and even then it is a miserable small life) so then black can expand his moyo along the right side. It's not territory yet, but even if he only gets half of it that's a lot of points.
- Click Here To Show Diagram Code
[go]$$Bcm29
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 4 . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . O . O . . . . . . . . . 3 . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 7 . 5 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . 2 . . . . . . . 6 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
To prevent getting sealed in and black having such a huge centre potential, white should come out and separate black. This move also threatens to press black down low if black tenukis. White would build his own influence now which negates black's thickness on the top side.
- Click Here To Show Diagram Code
[go]$$Bcm29
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . O . O . . . . . . . . . 2 . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . X . . . . . . . . . . . 4 5 . . |
$$ | . . O O O . . . . , . . . . . 6 7 . . |
$$ | . . . . . . . . . . . . . . . 8 . . . |
$$ | . . X . X . . . . . . . . . . . 9 . . |
$$ | . . . . . . . . . . . . . . 0 . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . 3 . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
So black should help his side stone to stop it getting pressed down low and develop his own position on the side. In terms of territory, white's kosumi didn't make any, whilst black's knight's move on the side is likely making some points there. This is all thanks to that imposing black wall above scaring white into having to be defensive. Black is using his wall at the top to make territory on the right side.
- Click Here To Show Diagram Code
[go]$$Bcm29
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . O . O . . . . . . . a . 2 . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . 3 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
White now faces a choice. He could keep running into the centre but this doesn't really affect black much, doesn't make any territory or eyes. So probably it's best to make some eyes and territory in the corner to make his group safe. The following is one such sequence. White lives with around a dozen points in the corner and can also aim at later linking up at
a, black can aim at
b himself to prevent this in maybe sente (timing of this is hard)
- Click Here To Show Diagram Code
[go]$$Wcm32
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . a b 5 . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O 3 . . |
$$ | . . O . O . . . . . . . . . O . 2 . . |
$$ | . . . . . . . . . . . . . . . 1 X . . |
$$ | . . . X . . . . . . . . . . . 4 . . . |
$$ | . . O O O . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
Black now has sente so can approach the lower right corner to develop his right side territory.
- Click Here To Show Diagram Code
[go]$$Wcm32
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O O . . |
$$ | . . O . O . . . . . . . . . O . X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . O O O . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . a . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 6 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . b . . . . . . . 7 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
The right side is not totally safe yet (e.g. there is still an invasion point at
a to consider) but as black I would probably play at b in the lower left now, but for the sake of argument let's say black completes his territory there:
- Click Here To Show Diagram Code
[go]$$Wcm32
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . O . O . O O O . X . . . . . |
$$ | . . . X . . . . X X X O . . . O . . . |
$$ | . . X . . . X . . . . X X X . . . . . |
$$ | . . . . . . . . . . . . . . . O O . . |
$$ | . . O . O . . . . . . . . . O . X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . O O O . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 0 . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . 8 . |
$$ | . . . . . . . . . . . . . O . . 9 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
Black's now made around 20 points on the right side. This was thanks to the power of his wall on the top letting him attack white's corner and in the process develop the side. But don't just think of this as what black's made, also think about white could have made here but didn't. If white made 20 points here then the difference is 40 points! (Of course white has also made some points in the top left and bottom left corner too). That's why using the wall to make points on the side is efficient, it's a big swing from white points to black points. If you make a few points in the centre as in the first diagram you just make a few points, it's not like white was going to make any there anyway.