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I've seen that in the diagram below, the two black stones can connect by attaching to the white stone, but I can't work out the sequence. How does black play to connect her stones?

$$cm1

$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
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2 Answers

up vote 12 down vote accepted

The 3 space extension is vaguely connected, but compared to the more solid 2 space extension, it can be split a lot easier.

$$cm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . a O b . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

If the opponent invades and there are no other relevant circumstances (nearby stones of either player), the moves to think about are a and b.

Attach on top

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . 1 O . . |
$$ . . . . . 3 2 . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

If black attaches on top and white plays bad shape at 2 (bumping her head), black will nobi at 3 and a short fight will ensue, however, black should be able to stay connected.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . 3 5 . . |
$$ . . . . 4 X O . . |
$$ . . . . . 1 2 . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

So instead, white will hane at 1. If black cuts at 2, white 3 is the only move (anything else dies). Next, black could think about extending at 4, allowing white to connect at 5. The marked black stone is damaged and black is split. Also, white 1 is not captured yet. This should be very good for white.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . 1 4 a . |
$$ . . . . 3 X O 2 . |
$$ . . . . . O X . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

It is a better idea to counter-atari at 2, forcing white to capture. Next, black usually connects solidly at 4, sometimes at a, or plays tenuki. If white plays 3 at 4, black happily connects solidly at a and white still has to capture at 3.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . O X . . |
$$ . . . . O . O X . |
$$ . . . . . O X . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

In this result, black is connected and pretty strong, but white got a good shape in the center. Usually, this is considered slightly bad for black. On the other hand, it may be the best way to try to get this result, if white is strong nearby and black would really hate to be split.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . O 2 1 . |
$$ . . . . O a O X . |
$$ . . . . . O X 3 . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

If black tenukis, white can start a ko, so black should be careful.

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . 1 O 3 . |
$$ . . . . . 2 . . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

It is also possible to play at 3 directly, but this leaves more options to white than the way previously shown.

Attach below

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . . 2 . |
$$ . . . . . . O 1 . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

The attachment below is far more common. The goal is not to connect, but to get a good result, usually outside influence. White naturally hanes. Which side to hane on depends on the environment, especially nearby corners. This is a very large topic so I won't go into it, just keep in mind that hoshi stones in the corner allow for easy invasions, thus it is more difficult to attack very strongly.

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . . 4 2 . |
$$ . . . . . . O 1 . |
$$ . . . . . . . 3 . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

Drawing back at 3 leads to large damage to the marked stone and is rarely a good idea.

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . 1 O . |
$$ . . . . . a O X . |
$$ . . . . . . . 2 . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

Practically always, black will cut at 1 and white will capture the single stone at 2 (very rarely white will nobi to a instead, this is a special plan).

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . X O . |
$$ . . . . . 1 O X 2 |
$$ . . . . . a 3 O . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

Next, black 1 is the only move. If white captures at 2, black will probably play at 3 or at 3 and white is in trouble.

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X b . |
$$ . . . . . . X O . |
$$ . . . . . 1 O X . |
$$ . . . . . 3 2 O . |
$$ . . . . . 4 X a . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

Thus, white will extend to 2 and black must cover at 3. Depending on the board white might crawl at a or b, allowing black to fix his outside. But far more often, white will cut at 4, splitting the single stone.

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . X O . |
$$ . . . . . X O X . |
$$ . . . . . X O O . |
$$ . . . . . O X a . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

This resulting shape massively depends on nearby corners, and it's difficult to tell the best variation without a complete board.

As mentioned earlier, black will use the aji in the position (mainly the atari at a) to either fix his outside and get thick, or to jump down the side, usually into a corner.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . 4 . . |
$$ . . . . . . 8 7 . |
$$ . . . . . 0 5 6 . |
$$ . . . . . . . 9 . |
$$ . . . . . . 2 . . |
$$ . . . . 3 , . . . |
$$ . . . . . 1 . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ -------------------

This is a common situation featuring a kosumi in the corner.

$$Wcm1
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . X . . |
$$ . . . . . . X O . |
$$ . . . . . X O X 5 |
$$ . . . . . 2 1 O 7 |
$$ . . . . . 3 X 4 6 |
$$ . . . . O . . . . |
$$ . . . . . O . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ -------------------

Black sacrifices more stones by playing 4 and 6...

$$Bcm1
$$ . . . . . . . . . |
$$ . . . . . . . . b |
$$ . . . . . . X 3 a |
$$ . . . . . . X O . |
$$ . . . . . X O . O |
$$ . . . . . X O O O |
$$ . . . 5 1 O X X X |
$$ . . . . O 2 4 . . |
$$ . . . . . O . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ -------------------

... only to get to play 1 and 3 in sente (the order of 1 and 3 depends on the board, it is almost no difference). Later, a or b are sente, too. 5 finally fixes the shape, and black got a somewhat thick shape while white got a mediocre corner. This is a joseki.

$$Bcm1
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . X . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . 6 8 9 . X . . . |
$$| . . . . . . . . . O 4 1 7 O . a . . . |
$$| . . . . . . . . . b 3 2 5 0 . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Another common shape that involves a hoshi corner. This time, white plays 10 and aims at attaching at a to live in the corner. The idea is to force black to crawl at b. I am not familiar with the joseki involved here so I can't tell sequences.

Conclusion

The 3 space extension is not very solid, but if you treat it right, it is pretty flexible. Connections can usually be enforced, but it is often a better idea to sacrifice for a better result. Nearby corners play an important role.

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Well, you can't completely connect. That's why the two-space extension or three space knight's move are more common on the third line.

Attaching on top fails:

$$cm1

$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . 4 6 . . |
$$ . . . . 5 1 O . . |
$$ . . . . . 2 3 . . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

Attaching underneath gets closer, but you still have two cutting points:

$$cm1

$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . 7 6 4 . |
$$ . . . . . 5 O 1 . |
$$ . . . . . . 3 2 . |
$$ . . . . . . B . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

With the three-space knight's move, it's easier to stay connected:

$$cm1

$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . 6 4 7 . |
$$ . . . . . O 1 5 . |
$$ . . . . . 3 2 . . |
$$ . . . . . B . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |

White can't play 6 at 7 because Black at 6 is atari, and then two stones will be captured. This depends on what is nearby, though.

If white invades on the third line, you stay more or less connected. White usually has to worry about his stones, so you have time to fix up one of your cutting points.

$$cm1

$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . B . . |
$$ . . . . . 5 . . . |
$$ . . . . . 1 O . . |
$$ . . . . 3 2 4 . . |
$$ . . . . . B 6 . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
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I think the second diagram is what I was thinking of. Thanks for the extra info. –  Max Jun 26 '12 at 11:45
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