Kirby wrote:I read a bit about this reduction sequence:
I doubt it. In GoGoD the diagrammed array of White stones occurs only five times and Black never plays the shoulder hit next. So I am guessing that you actually studied a different position.
Kirby wrote:$$Bc
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$$ | . . . O . . . . . . . . . . . . . . . |
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$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . . . . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
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[go]$$Bc
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$$ | . . . O . . . . . . . . . . . . . . . |
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$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . . . . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
This is said to be the best sequence for both (for this invasion shape, ignoring the rest of the board).
It is almost impossible to ignore the rest of the board in evaluating this postion. For example, assume there is a two-space extension along the bottom (the reason Black does not approach along the bottom or invade a wider extension). Immediately when White answers

with

the shape becomes over concentrated. The higher White pushes, the most wasteful the marked stone becomes. Meanwhile, the further Black extends up the greater the threat to invade the left side becomes.
$$Bc White extension on the bottom
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . W . . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$Bc White extension on the bottom
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$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . W . . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Alternatively, consider what happens if the marked stone is Black. White pushing up suffers from a similar problem. It is not over concentrated, but it is ineffective if White doesn't have a good follow up on the right.
$$Bc Black blocker on the bottom
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$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . B . . . |
$$ | . . . O . . . . O . . . B . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$Bc Black blocker on the bottom
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$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 5 7 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . B . . . |
$$ | . . . O . . . . O . . . B . . . . . . |
$$ | . . . . . . 6 . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Kirby wrote:I wonder why white has to come back and play

. It seemed OK to keep going:
$$Bc
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$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . C . . . . . . . . . . . |
$$ | . . . . . . . 5 6 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$Bc
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . C . . . . . . . . . . . |
$$ | . . . . . . . 5 6 . . . . . . . . . . |
$$ | . . O . . . . 3 4 . . . . . . . . . . |
$$ | . . . , . . . 1 2 , . . . . . , . . . |
$$ | . . . O . . . . O . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
I guess black might play the marked intersection next... Maybe this isn't as good for white because it's "pushing from behind"?
It just seems that black's shape is so nice with

in the first diagram.
Anyone have ideas on this?
Naturally there will be some positions where it is good for White to keep pushing with

in your diagram. Guess what? Black won't choose to play the shoulder hit in that case!
