4-3 Attachment Joseki

For lessons, as well as threads about specific moves, and anything else worth studying.
Kirby
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4-3 Attachment Joseki

Post by Kirby »

Here's a textbook opening position:
Click Here To Show Diagram Code
[go]$$cm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Now, white has several options for reducing the top right. One of them is this:
Click Here To Show Diagram Code
[go]$$cm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . . . . . W . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
A standard sequence is as follows:
Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 7 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X . . . |
$$ | . . . . . . . . . . . . . . . 6 . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Would black really be in that bad of shape to play this way?
Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 6 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Sure, there is aji around the black stone on the right, but what can white really do to make as good of a result as in the joseki?

For example:
Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . X 6 . |
$$ | . . O . . X . . X . . X . . O O X 5 . |
$$ | . . . O . . . . . , . . . . O X 1 3 . |
$$ | . . . . . . . . . . . . . . . 2 . 4 . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
White clearly can't do this.

Maybe this?
Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . X . . |
$$ | . . O . . X . . X . . X . . O O X . . |
$$ | . . . O . . . . . , . . . . O X 2 . . |
$$ | . . . . . . . . . . . . . . . 1 . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
What now? This?
Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . X . . |
$$ | . . O . . X . . X . . X . . O O X . . |
$$ | . . . O . . . . . , . . . . O X 2 . . |
$$ | . . . . . . . . . . . . . . . 1 . . . |
$$ | . . O . . . . . . . . . . . . 3 X . . |
$$ | . . . . . . . . . . . . . . . . 4 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Black's just making territory, and white's stones seem not worth as much as in the joseki.

What am I missing here?
be immersed
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EdLee
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Post by EdLee »

Variations:
Click Here To Show Diagram Code
[go]$$W Variaton A
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 7 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X . . . |
$$ | . . . . . . . . . . . . . . . 6 . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ----------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$W Variation B
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 6 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X 8 . . |
$$ | . . . . . . . . . . . . . . . 7 . . . |
$$ | . . O . . . . . . . . . . 9 . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
The :b6: reply in Variation A has its value (it's OK to allow W to extend to :w7:);
it's difficult to say if it's better or worse than blocking with :b6: in Variation B.
How about :w5: instead of the turn?
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 5 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 6 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
Kirby
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Re: 4-3 Attachment Joseki

Post by Kirby »

Thanks for the comments, EdLee.
Regarding the variations, I prefer Variation B to the examples I provided - the shape seems much more flexible, and doesn't push black into getting territory on the third line.

However, perhaps in line with your conclusion, it's not clear to me if this is better for white than Variation A.

Regarding the alternate :w5:, I studied this area a little bit, and the two space extension is common when black plays solidly, as follows:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . 5 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . . X 4 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
I think this is considered even, because though black is more over-concentrated here, in the future, he can play this:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . O . . O O X . . |
$$ | . . . O . . . . . , . . . . B X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
If white answers passively, black is still looking overconcentrated, but the exchange got black some influence toward the center:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . O . W O O X . . |
$$ | . . . O . . . . . , . . . . X X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
On the other hand, if white answers with hane, black can play this way:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . O . . O O X . . |
$$ | . . . O . . . . . , . . 2 1 X X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
If white pushes back, black can attack the entire group:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O . . X . . X . . O 4 . O O X . . |
$$ | . . . O . . . . . , . . 2 1 X X X . . |
$$ | . . . . . . . . . . . . . 3 . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
In the current position, with the diagram you proposed, I wonder if black can still do this to white:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . X . . |
$$ | . . O . . X . . X . . O 4 . O O X . . |
$$ | . . . O . . . . . , . . 2 1 B B C . . |
$$ | . . . . . . . . . . . . . 3 . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
In this case, though, black's shape isn't quite as strong, so maybe it's not going to work... Black's two stones could potentially be utilized, for example, in some way.

So maybe the variation you provided is good for :w5:... :scratch:

Hard for me to say.
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Re: 4-3 Attachment Joseki

Post by moyoaji »

I think the better question is: why is black descending? Is it simply for better endgame? Does he just want to more strongly defend the corner? Or is he trying to undercut white as well?
Click Here To Show Diagram Code
[go]$$Wcm1 Black descends
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . . . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
It looks like black is trying to undercut white - in fact, I think that's probably the primary reason for this move. For this reason I think black would be happy if white just made a base here. He may not get any eyes from it because black can remove them pretty easily. So perhaps 5 is almost an asking move. Saying "If I can't make a base here could I get out toward the center?" White may be seeing forcing his way out as almost equivalent to making a base because he can't have any guaranteed eyes there anyway so he may as well run.

DailyJoseki has a similar sequence to black playing 'b'. There is only one position for this in the database and it looks like black is trying to split up white by taking away the potential base. White's response in this position is, in fact, the atari. Here is the DailyJoseki position.
Click Here To Show Diagram Code
[go]$$Wcm1 'a' and 'b' miai?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . b . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X . . . |
$$ | . . . . . . . . . . . . . . . a . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
So white asks if he can get out and black says "Nah, I'd prefer if you try to live here rather than coming out to the center." And since white has no way to forcibly get out to the center, but black also can't seal him in with one move, and white has now strengthened himself locally, white takes the base.
Click Here To Show Diagram Code
[go]$$Wcm1 White has an undercut group but can't be sealed in
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . 4 . . |
$$ | . . O . . X . . X . . 7 . . 3 1 2 . . |
$$ | . . . O . . . . . , . . . . 5 X . . . |
$$ | . . . . . . . . . . . . . . . 6 . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."

-Kageyama Toshiro on proper moves
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Re: 4-3 Attachment Joseki

Post by John Fairbairn »

I obviously can't know if I'm right, but if anyone is interested in my thought processes, I had two instant thoughts when I saw the initial position.

One was that the White move shown is an invasion, not a reducing move. I think it is worth maintaining the traditional distinction because it makes it easier to talk about strategy - see below.

The more important thought was that this can't possibly be a textbook position. It is just a conglomeration of textbook sub-positions. The reason it can't be a textbook position is that it is surely bad for Black. He has a position at the top which invites invasion, but whether he encloses the invader and makes thickness or chases it out to the centre, there is nothing Black can gain because White has solid positions to left and right of Black's upper shape. Therefore Black must have done something wrong earlier on.

To confirm this, I did a Kombilo search. The position has never appeared in pro play. Taking the position in the bottom half only, that has appeared 17 times in actual play (out of 78,000 games; interestingly, five of those examples were by Cho Hun-hyeon). Taking only the top half of the position, it has appeared just 14 times. Taking both the left and right half-positions, each has appeared just once. Furthermore, in the 17 games that matched the lower half, I could find no examples where the upper half remotely matched the upper half of the OP.

I therefore feel justified in saying this is not textbook play, and if that is correct then it tells us something about what White's strategy should be. It is highly unlikely that there is one correct answer, but in my impatient amateur way I would say that one strategy to consider strongly is to punish Black for his poor play by making him overconcentrated, and this can be done by playing a traditional reducing move such as K15 and K16 (leaving horrible aji for Black at the 3-3 point in the upper right), and then using sente to expand White's moyo prospects on the lower side.

Invasion of the upper side by White will also take away points from Black, of course, but like all invasions it runs a very high risk of ending in gote, which would give Black the chance to negate White's potential on the lower side.

However, there is a third option, which is the one apparently most favoured by pros, and that is to leave Black's position to stew in its own juices (he can't finish it off in one move anyway). Of the fourteen games where the upper half appeared, White entered this area in this position only three times - in each case at the mole invasion point of Q18. Every other time White either blocked Black's position on the left or right sides or played in the lower half until Black had added a move at the top (two examples of which were P17 and K15).
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Re: 4-3 Attachment Joseki

Post by macelee »

Click Here To Show Diagram Code
[go]$$Wcm1 Black: 0 White: 0
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . X . . |
$$ | . . O . . X . . # . . X . . O O X . . |
$$ | . . . O . . . . . , . . c . O X 2 . . |
$$ | . . . . . . . . . . . . . . . 1 . a . |
$$ | . . O . . . . . . . . . . b . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 3 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Territory-oriented players will find the :w1: / :b2: exchange unbearable. Not only the territory in the corner is reduced, but also some aji can be exploited later. For example, :w3: is a large move, leaving further reduction at 'a'. So in my opinion black actually loses many points here.

If white needs to settle down first, instead of 'b' suggested by Edlee, 'c' is also a good move. Black's position :bs: is low so it doesn't matter to make the black group even stronger. So shoulder-hit is a good move.
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Re: 4-3 Attachment Joseki

Post by ez4u »

I wouldn't want to claim that one of the authors of my favorite database did not look closely enough but surely the position below would fit the picture fairly well. :blackeye:
Click Here To Show Diagram Code
[go]$$Wc Cho Hun-hyeon (White) - Ch'oe Myeong-hun; 5th Kiseong League 1993-05-04
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . 3 1 4 5 . |
$$ | . . O . . X . . X . . 7 . . . 2 6 . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 8 . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . 0 O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . O , . . . . . X . O . |
$$ | . . X O O X . . . . . O . X . . X 9 . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
More to the point in terms of the OP is that the attachment at the 4-3 point is extremely rare. The position below with a Black stone on the side occurs about 1,000 times in GoGoD. White played :w1: only three times. In contrast "a" was played 203 times and "b" 55 times. In fact White did not rush to the corner in any case. And by the way, Black answered on the outside at :b2: in all three games. In general the outside play occurs in actual practice much more often than the inside play.
Click Here To Show Diagram Code
[go]$$Wc Continuations
$$- - - - - - - - - - - - - +
$$. . . . . . . . . . . . . |
$$. . . . . . . . a b . . . |
$$. . X . . . . . 2 1 . . . |
$$. . . , . . . . . X . . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . X . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . . . . |
$$. . . , . . . . . , . . . |
$$[/go]
Dave Sigaty
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Re: 4-3 Attachment Joseki

Post by Kirby »

John Fairbairn wrote: One was that the White move shown is an invasion, not a reducing move. I think it is worth maintaining the traditional distinction because it makes it easier to talk about strategy - see below.
Sure, let's call it an invasion.
John Fairbairn wrote:
The more important thought was that this can't possibly be a textbook position. It is just a conglomeration of textbook sub-positions. The reason it can't be a textbook position is that it is surely bad for Black. He has a position at the top which invites invasion, but whether he encloses the invader and makes thickness or chases it out to the centre, there is nothing Black can gain because White has solid positions to left and right of Black's upper shape. Therefore Black must have done something wrong earlier on.
While off-topic to the question I (now, somewhat regrettably) posted, I disagree with your assessment. Black's play, while uncreative, has solidly gained points, and the top side cannot be said to be black's points, anyway - it's just the next big area to play in the opening.

If black were trying to profit from a moyo on top, you might be correct, but black's choice of joseki in the top left is clearly a territorial choice. Black has already made profit from the solid points he has made.

If black has made a mistake earlier on, what was it?

John Fairbairn wrote: To confirm this, I did a Kombilo search. The position has never appeared in pro play. Taking the position in the bottom half only, that has appeared 17 times in actual play (out of 78,000 games; interestingly, five of those examples were by Cho Hun-hyeon).
From a whole board perspective, this is close to meaningless. The number of variations in the game make it unlikely for a given player to even play the same game twice. When people do these database searches of positions, later in the opening, the pattern results are always just a handful (10 or 20, or in some cases, maybe 2 or 3 matching positions).

Pattern searching can be useful for local positions, but it starts to lose power in whole board positions. As a test, take the next pro tournament from any country, and pick an upcoming game. I can bet that the game diverges from game databases before the middle game starts. It doesn't mean that the game is bad - it just means that the combinations of moves are great, and it's unlikely to get exactly the same game twice.

This being said, I feel both black and white's play lack creativity - they are playing basic josekis, but I don't see where any player has played poorly to fall behind.

This position came from a go lecture, and I feel it is a reasonable opening for both sides.

If you find a pro player who says this position is bad for black, then I will consider the argument, but I will still be wondering why they feel that way. A database search, on the other hand, is not convincing to me from this whole board position, this late in the game.
John Fairbairn wrote:
...this can be done by playing a traditional reducing move such as K15 and K16 (leaving horrible aji for Black at the 3-3 point in the upper right), and then using sente to expand White's moyo prospects on the lower side.

Invasion of the upper side by White will also take away points from Black, of course, but like all invasions it runs a very high risk of ending in gote, which would give Black the chance to negate White's potential on the lower side.
Interesting idea to try to get sente. In my opinion, the invasion will probably get more points for white locally, but depending on the board position, it might be good to give this up to achieve sente.
John Fairbairn wrote: However, there is a third option, which is the one apparently most favoured by pros...
If you are going to be trusting the database search, and you don't feel this is a "textbook position", then how is it possible for you to make conclusions here on the option "most favoured by pros"? If this position doesn't appear in your pattern search, then how do you know where most pros will play here? Perhaps you are comparing to similar positions, but is this analysis possible with a "non-textbook" position? Maybe the top half of the board is the same, but this says nothing conclusive about the quality of the position here.
John Fairbairn wrote:in each case at the mole invasion point of Q18.
I agree that Q18 is a good option, and I use it sometimes in games.

To be clear, I don't care about the board position here as much as I wanted to set up a feasible example of the sequence in question. Maybe I shouldn't have used the word "textbook" - my point was just to set up a position for illustration.

I appreciate that you've given some alternative options to making the invasion in the first place, but I feel more like the intention of your post was to attack the choice of wording that I used.

While I have some disagreements even in this critique, as described above, it doesn't matter to me strongly if this position is a "textbook" position. I saw it on a lecture, and the lecture was discussing various invasions in the top right area. I agree that the invasion in question may not always be best, but all I am curious about is the invasion, itself, which others have kindly commented on.

If it makes more sense, let's refer to this board position as a "mickey mouse" position, rather than a textbook position - it makes little difference to me. I simply wanted to ask about alternative followups to a choice of invasion from this mickey mouse board position.
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Re: 4-3 Attachment Joseki

Post by Kirby »

@John:
And, I apologize if my last post is somewhat negative in tone, but if I am frank, the reason is because your response hurt my feelings a little bit.

Whether or not this is a "textbook position", it wasn't my intention to debate about this. I only had a question about the local position, really, and I felt like my choice of wording was being attacked.

I admit that I am sometimes casual with the selection of terms that I use, and I apologize if this is confusing. But my intention here wasn't to argue, but to ask about this 4-3 invasion. I hope you understand.

Maybe I am being too sensitive here.

In any case, I do still appreciate the contextual comments you've provided, particularly, the idea about using a reduction to get sente, even if you might not gain as much as an invasion. This wasn't what my question was about, but it was useful information, nonetheless.
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Re: 4-3 Attachment Joseki

Post by Kirby »

ez4u wrote:
More to the point in terms of the OP is that the attachment at the 4-3 point is extremely rare. The position below with a Black stone on the side occurs about 1,000 times in GoGoD. White played :w1: only three times. In contrast "a" was played 203 times and "b" 55 times. In fact White did not rush to the corner in any case. And by the way, Black answered on the outside at :b2: in all three games. In general the outside play occurs in actual practice much more often than the inside play.
Click Here To Show Diagram Code
[go]$$Wc Continuations
$$- - - - - - - - - - - - - +
$$. . . . . . . . . . . . . |
$$. . . . . . . . a b . . . |
$$. . X . . . . . 2 1 . . . |
$$. . . , . . . . . X . . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . X . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . . . . |
$$. . . , . . . . . , . . . |
$$[/go]
Thanks, Dave. Yes, I agree that the alternatives posed in your last diagram may be better here. Still, I was mainly curious about the 4-3 option in general, and I just needed a board position to set it up on.

Perhaps the one I selected wasn't the best example.
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Re: 4-3 Attachment Joseki

Post by macelee »

ez4u has raised a good point that black can choose to play outside. A possible sequence is the following. I like :b10: because it leaves a good point at 'a'.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . 6 . 5 . . |
$$ | . . O . . X . . X . . . . . 2 1 . 9 . |
$$ | . . . O . . . . . , . . . . . X 3 . . |
$$ | . . . . . 0 . . . . . . . . . 4 . 7 . |
$$ | . . O . . . . . . . . . . . . . X 8 . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . a . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . X . O . |
$$ | . . X O O X . O . . O . . X . . X . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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Re: 4-3 Attachment Joseki

Post by SmoothOper »

Kirby wrote:
John Fairbairn wrote: One was that the White move shown is an invasion, not a reducing move. I think it is worth maintaining the traditional distinction because it makes it easier to talk about strategy - see below.
Sure, let's call it an invasion.
John Fairbairn wrote:
The more important thought was that this can't possibly be a textbook position. It is just a conglomeration of textbook sub-positions. The reason it can't be a textbook position is that it is surely bad for Black. He has a position at the top which invites invasion, but whether he encloses the invader and makes thickness or chases it out to the centre, there is nothing Black can gain because White has solid positions to left and right of Black's upper shape. Therefore Black must have done something wrong earlier on.
While off-topic to the question I (now, somewhat regrettably) posted, I disagree with your assessment. Black's play, while uncreative, has solidly gained points, and the top side cannot be said to be black's points, anyway - it's just the next big area to play in the opening.

If black were trying to profit from a moyo on top, you might be correct, but black's choice of joseki in the top left is clearly a territorial choice. Black has already made profit from the solid points he has made.

If black has made a mistake earlier on, what was it?

John Fairbairn wrote: To confirm this, I did a Kombilo search. The position has never appeared in pro play. Taking the position in the bottom half only, that has appeared 17 times in actual play (out of 78,000 games; interestingly, five of those examples were by Cho Hun-hyeon).
From a whole board perspective, this is close to meaningless. The number of variations in the game make it unlikely for a given player to even play the same game twice. When people do these database searches of positions, later in the opening, the pattern results are always just a handful (10 or 20, or in some cases, maybe 2 or 3 matching positions).

Pattern searching can be useful for local positions, but it starts to lose power in whole board positions. As a test, take the next pro tournament from any country, and pick an upcoming game. I can bet that the game diverges from game databases before the middle game starts. It doesn't mean that the game is bad - it just means that the combinations of moves are great, and it's unlikely to get exactly the same game twice.

This being said, I feel both black and white's play lack creativity - they are playing basic josekis, but I don't see where any player has played poorly to fall behind.

This position came from a go lecture, and I feel it is a reasonable opening for both sides.

If you find a pro player who says this position is bad for black, then I will consider the argument, but I will still be wondering why they feel that way. A database search, on the other hand, is not convincing to me from this whole board position, this late in the game.
John Fairbairn wrote:
...this can be done by playing a traditional reducing move such as K15 and K16 (leaving horrible aji for Black at the 3-3 point in the upper right), and then using sente to expand White's moyo prospects on the lower side.

Invasion of the upper side by White will also take away points from Black, of course, but like all invasions it runs a very high risk of ending in gote, which would give Black the chance to negate White's potential on the lower side.
Interesting idea to try to get sente. In my opinion, the invasion will probably get more points for white locally, but depending on the board position, it might be good to give this up to achieve sente.
John Fairbairn wrote: However, there is a third option, which is the one apparently most favoured by pros...
If you are going to be trusting the database search, and you don't feel this is a "textbook position", then how is it possible for you to make conclusions here on the option "most favoured by pros"? If this position doesn't appear in your pattern search, then how do you know where most pros will play here? Perhaps you are comparing to similar positions, but is this analysis possible with a "non-textbook" position? Maybe the top half of the board is the same, but this says nothing conclusive about the quality of the position here.
John Fairbairn wrote:in each case at the mole invasion point of Q18.
I agree that Q18 is a good option, and I use it sometimes in games.

To be clear, I don't care about the board position here as much as I wanted to set up a feasible example of the sequence in question. Maybe I shouldn't have used the word "textbook" - my point was just to set up a position for illustration.

I appreciate that you've given some alternative options to making the invasion in the first place, but I feel more like the intention of your post was to attack the choice of wording that I used.

While I have some disagreements even in this critique, as described above, it doesn't matter to me strongly if this position is a "textbook" position. I saw it on a lecture, and the lecture was discussing various invasions in the top right area. I agree that the invasion in question may not always be best, but all I am curious about is the invasion, itself, which others have kindly commented on.

If it makes more sense, let's refer to this board position as a "mickey mouse" position, rather than a textbook position - it makes little difference to me. I simply wanted to ask about alternative followups to a choice of invasion from this mickey mouse board position.
While I agree that blacks position is somewhat defective and I look for and find invasions such as that all the time in kyu play, however I think Fairburn's notion of textbook's relation to professional play is pretty far off base, in the sense that I look for and find invasions like that in kyu play all the time. It's like saying a programming example isn't textbook, because Zuckerberg or Gates didn't write it.

The 3-4 attachment under the 4-4 3-6 enclosure with hane on the outside leads to the carpenter's square and a ko.
Bill Spight
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Re: 4-3 Attachment Joseki

Post by Bill Spight »

The 4-3 attachment is much more applied to the position after the large knight's extension from the 4-4 stone, and the inside hane is also more frequent in that case. Besides the same issue comes up, in a slightly different form.
Click Here To Show Diagram Code
[go]$$Wc Joseki with same question
$$- - - - - - - - - - - - - +
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . 4 . . |
$$. . X . . 7 . . 3 1 2 . . |
$$. . . , . . . . . X . . . |
$$. . . . . . . 5 . 6 . . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . X . . |
$$. . . . . . . . . . . . . |
$$. . . . . . . . . . . . . |
$$. . . , . . . . . , . . . |
$$[/go]
Why not :b6: at 7?
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Re: 4-3 Attachment Joseki

Post by Boidhre »

An example board from real play for you:

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . O . . O X X . X . |
$$ | . . . O . . . . . , . . O . O X X O . |
$$ | . . . . . . . . . . . O X O X O O . . |
$$ | . . O . . . . . . . . O X X X . . X . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . O . . O X . X . |
$$ | . . . . . . . . . . . . . . O X X . . |
$$ | . . . , . . . . . , . . . . O O X . . |
$$ | . . . . . . . . . . . . . . . X O O . |
$$ | . . . . . . . . . . . . . . . X X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X . . . . . . . . . . . . |
$$ | . . O , X . X . . , . . . . . , . . . |
$$ | . . . O O X . . . . . . . . . X . . . |
$$ | . . . . . O O . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
The game itself:
Attachments
Example.sgf
(1.25 KiB) Downloaded 818 times
macelee
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Re: 4-3 Attachment Joseki

Post by macelee »

Good example. However I am quite puzzled why white allowed black to run out.I would let black live inside the corner (BTW there's still a ko in the corner). After :w9: I can get either 'a' (a big side) or 'b' (a big moyo).
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 4 2 5 . . . . . . . . . . . . . |
$$ | . . . X 1 . . . . . O . . O X X . X . |
$$ | . 8 6 O 3 . . . . , . . O . O X X O . |
$$ | . . 7 . . . . . . . . O X O X O O . . |
$$ | . . O . . . . . . . . O X X X . . X . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . O . . O X . X . |
$$ | . . . . . . . . . . . . . . O X X . . |
$$ | . . . 9 . . . . , . . . . O O X . . |
$$ | . . . . . . b . . . . . . . . X O O . |
$$ | . . . . . . . . . . . . . . . X X . . |
$$ | . . . a . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X . . . . . . . . . . . . |
$$ | . . O , X . X . . , . . . . . , . . . |
$$ | . . . O O X . . . . . . . . . X . . . |
$$ | . . . . . O O . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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