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]
xela
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Re: Two against one, what is the right intuition?

Post by xela »

kvasir wrote: Sun Mar 15, 2026 12:26 pm 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.
Right. But on the other hand, the single group is normally the one in the middle. The two groups are compromised because they don't get to play one stone per turn per group. The single group is compromised because it's floating: there isn't an easy option for making a base at the edge of the board.
kvasir
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Re: Two against one, what is the right intuition?

Post by kvasir »

xela wrote: Mon Mar 16, 2026 3:16 pm Right. But on the other hand, the single group is normally the one in the middle. The two groups are compromised because they don't get to play one stone per turn per group. The single group is compromised because it's floating: there isn't an easy option for making a base at the edge of the board.
That is a really good insight.

Here is an example from the Kisei match, Shibano was black and Ichiriki was white. Maybe it could be said that it is two vs. two but the fourth group is less involved, for now. Black has cut and in my eyes has one group against white's two. White does appear to gain advantage in the fight that follows.

I especially like :w12: and I think at that moment it could be said that white is the one attacking. Moves like his are said to be called ears in Japanese. The stone at :w4: would be the other ear and the nose is :b3:. I saw the ear thing in the incredibly ambitious 90s book called Utilizing Outward Influence by Jin Jiang and Zhao Zheng. This so called ear move is frequently seen in high level games.
Click Here To Show Diagram Code
[go] $$B
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . O . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . X . . .|
$$ | . . . . . . . . . . . . . 4 . . . . .|
$$ | . . O . . . . . . . . 3 . . . . . . .|
$$ | . . . . . . . . . . . . . 2 . . . . .|
$$ | . . . . . . . . . . . 1 5 6 . . . . .|
$$ | . . . . . . . . . . . . . O . . . . .|
$$ | . . . , . . . O . , . X . . . X . . .|
$$ | . . . . . X . . . . . X O . O X . . .|
$$ | . . . . . . . O 7 . O X O . O X . . .|
$$ | . . X O . X . . . O . O X . O X . . .|
$$ | . . X O . . . X . . . O X . O . . . .|
$$ | . . . O . . . . . X . X . X O . . X .|
$$ | . . X O . . . X . X . X . . O , X . .|
$$ | . . X O . X X O O O O . X . . O O X .|
$$ | . . X X O O O . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ +--------------------------------------+
[/go]
Click Here To Show Diagram Code
[go] $$Wm8
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . O . . . . . . . . . 7 . . . . .|
$$ | . . . , . . . . . , . 6 . . . X . . .|
$$ | . . . . . . . . . . . . . O . . . . .|
$$ | . . O . . . . . 5 . . X . . . . . . .|
$$ | . . . . . . . . . . . . . O . . . . .|
$$ | . . . . . . . . . . . X X O . . . . .|
$$ | . . . . . . . . . . . . . O . . . . .|
$$ | . . . , . . . O . , . X . . . X . . .|
$$ | . . . . . X . . 1 3 . X O . O X . . .|
$$ | . . . . . . 4 O X . O X O . O X . . .|
$$ | . . X O . X . 2 . O . O X . O X . . .|
$$ | . . X O . . . X . . . O X . O . . . .|
$$ | . . . O . . . . . X . X . X O . . X .|
$$ | . . X O . . . X . X . X . . O , X . .|
$$ | . . X O . X X O O O O . X . . O O X .|
$$ | . . X X O O O . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ +--------------------------------------+
[/go]
xela
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Re: Two against one, what is the right intuition?

Post by xela »

Nice example! Earlier in the same game:
Click Here To Show Diagram Code
[go]$$Wc1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 0 . . . |
$$ | . . . . . . . . . . . . . . 7 . . . . |
$$ | . . . O . . . . . . . . . 8 9 . . 4 . |
$$ | . . X O . . . . . . . X . . O . X . . |
$$ | . . X O . X . . . 5 . . 6 . . 3 1 2 . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+ [/go]
:w1: is the move that the old joseki books tell us not to play! And indeed, a few moves later, the five white stones at lower right look horribly weak in a two-groups-against-one fight. Yet white is able to get a good position out of it.
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