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If white tenukis thrice after the 3-3 invasion, and answers Q18 with R18, then white kills with S19:

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But what if white plays Q19 instead?

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Can black still kill unconditionally, or ko is the best one can achieve?

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2 Answers 2

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4

I know this is a textbook situation, but I do not practice tsumego, so I had to read through this. It was quite tricky and took some time to, hopefully, get right.

The strongest (i.e. hardest to correctly answer) resistance I found is this:

$$ ------------------
$$ . X 3 5 2 . . . |
$$ . X O O 1 . 4 . |
$$ . X X X O O O . |
$$ . . . . X X O . |
$$ . . . . . . X . |
$$ . . . . . X . . |

After 5, white has nothing left.

I'll grant you that looks strange, so let's see why other moves are worse.

$$ ------------------
$$ . X 3 . 2 . 5 . |
$$ . X O O 1 4 . . |
$$ . X X X O O O . |
$$ . . . . X X O . |
$$ . . . . . . X . |
$$ . . . . . X . . |

If 4 captures, black kills with 5.

$$ ------------------
$$ . X X a O b 1 . |
$$ . X O O . O . c |
$$ . X X X O O O . |
$$ . . . . X X O d |
$$ . . . . . . X . |
$$ . . . . . X . . |

a and b are miai, and c and d, too - if white takes or prevents one, black always takes the other.

$$ ------------------
$$ . X X 3 O . 1 . |
$$ . X O O . O 2 5 |
$$ . X X X O O O . |
$$ . . . . X X O 4 |
$$ . . . . . . X . |
$$ . . . . . X . . |

White's strongest attempt is probably trying to trick black into mistakenly not playing at 3. If black replies correctly, it leads to temporary seki. White cannot play inside without creating a dead shape, and black cannot capture white directly.

However, at the end of the game this shape is dead: It is "reducible to bent-4 in the corner". Situations like this are actually quite complicated and even lead to arguments at the highest level of professional play.

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

If 4 at 2-1, then black 5 kills. If white 4 at the other 1-2 point, black 5 kills, too.

$$ ------------------
$$ . X . . 2 . 3 . |
$$ . X O O 1 . 4 . |
$$ . X X X O O O . |
$$ . . . . X X O . |
$$ . . . . . . X . |
$$ . . . . . X . . |

If black plays 3 here, as I was initially sure is the answer, it is in fact a mistake and white punishes with 4. Black's strongest attempt is easily foiled:

$$ ------------------
$$ . X 1 . O 2 X 4 |
$$ . X O O X . O . |
$$ . X X X O O O . |
$$ . . . . X X O 3 |
$$ . . . . . . X . |
$$ . . . . . X . . |

White 2 is important. If white instead captures, she dies:

$$ ------------------
$$ . X 1 3 O . X . |
$$ . X O O X 2 O 5 |
$$ . X X X O O O . |
$$ . . . . X X O 4 |
$$ . . . . . . X . |
$$ . . . . . X . . |

This shape is the same seen earlier.

To sum it up: White's other atari is the same result.

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2
  • In your 2nd diagram after black 5, white plays 6 at S19 (2-2 point). 7 R19 by black puts itself in Atari.. Black playing 7 T18 instead leads to white playing connection at 8 P19(5-1) forming eyes for white. Am I missing something?
    – David Siegel
    Jan 9, 2021 at 1:09
  • @DavidSiegel I've added some more diagrams on this complicated situation. Does this answer the question?
    – mafu
    Jan 10, 2021 at 18:48
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The black stone at Q18 is in a ladder, albeit a short one. If black pushes this, with R18, black will eventually be killed and white will live. R18 is a strong KO-threat, however, because if it is not answered black can kill the white group.

If black plays P29 white must capture at R18. If black pushes at O19 the capture is again forced and white will eventually have to connect at Q18. losing 1-2 points of potential territory. This also is a significant ko-threat for black, although not as large as R18.

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2
  • Thanks! Do I presume correctly that white's best move after black's S19 (following second picture) is just R19?
    – corey979
    Jan 7, 2021 at 23:28
  • If after the 2nd picture, black plays S19, I think white should play R18, capturing and explicitly forming eyes. But white might pass or play elsewhere, potentially gaining a point and the initiative. It is hard to see how black van make life eve with one unanswered move, so S19 is perhaps not even a good KO-threat. R19 or T18 are stronger threats, and I think S18 has the best chance at life if unanswered. But really there is no chance at life for black here unless white leaves a move unanswered so any such move is useful only as a KO-threat.
    – David Siegel
    Jan 7, 2021 at 23:42

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