Two against one, what is the right intuition?

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kvasir
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Two against one, what is the right intuition?

Post by kvasir »

Fighting with two groups separated by one group occurs frequently in Go. It is common in joseki and in the middle game.

Here is an example from a bookish joseki :study:
Click Here To Show Diagram Code
[go] $$B
$$ ----------------------+
$$ . . . . . . . . . . .|
$$ . . . . . . . . . . .|
$$ . 0 . . . O . 7 5 . .|
$$ . , . . 8 . . X 4 . .|
$$ . . . . . . . . 6 . .|
$$ . . . . 9 . 3 1 O . .|
$$ . . . . . . . 2 . . .|
$$ . . . . . . . . . . .|
$$ . . . . . . . . . . .|
$$ . , . . . . . , . . .|
$$ . . . . . . . . . . .|
[/go]
Click Here To Show Diagram Code
[go] $$Bm11
$$ ----------------------+
$$ . . . . . . . . . . .|
$$ . . . . . . . . . . .|
$$ . O . . . O . X X . .|
$$ . , . . O . . X O . .|
$$ . . . . . . . . O . .|
$$ . . . . X . X X O . .|
$$ . . . . . 3 2 O . . .|
$$ . . . . . . . . 4 . .|
$$ . . . . . 5 . 1 . . .|
$$ . , . . . . . , . 6 .|
$$ . . . . . . . . . . .|
[/go]
I find this somewhat unexpected that two groups can fight equally with one group. You can, after all, only play one move at a time in Go. On account of this it would seem to be a huge advantage to only have one group to take care of. This is the case in many situations, for example in capturing races, it is easier for the side with the single group to win a capturing race than it is for the side with two groups. I think this is because the side with the single group only has one concern and can use the one and only move that they are allowed on their own turn to address this concern; the other side has multiple concerns and is forced to choose among them. Still, it is the case that two groups can fight with one group in the middle game and in joseki.

Why is that? Which side is better in principle and what is the right intuition? If you just glanced at a fighting position with two against one, what is it that you would say is what is most important to look for?

I can offer this really bad example of such a position (which I completely made up) for anyone wishing to elicit on these question but any example is welcome.
Click Here To Show Diagram Code
[go] $$B Maybe black could play a or b next.
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . X O . . . O . O . . X X X . . .|
$$ | . . X , O . . . . , . . . . O O X X .|
$$ | . . . . . . . . . . . . . . . . O . .|
$$ | . . X . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . O . .|
$$ | . . . . . . . . . . . . . . . b . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . a . , X . .|
$$ | . . O . . . . . . . . . . . . 7 . . .|
$$ | . . . . . . . . . . . . 0 . 6 5 . . .|
$$ | . . . . . . . . . . . . . . 4 1 . . .|
$$ | . . O . . . . . . . . . . 8 3 2 O . .|
$$ | . . . . . . . . . . . . . . 9 . . . .|
$$ | . . O O . . . . . X . . . X X X O . .|
$$ | . . O X . X . . . . . . . X O O O . .|
$$ | . . X . X . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . ..|
$$ +--------------------------------------+
[/go]
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