7

Let's stay one player has a corner of the board totally enclosed, but with no stones in it, like this:

$$ ------------------
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | X X X X X X X .
$$ | . . . . . . . .

How big does this space have do be before the other player can successfully invade it? Successfully invade here means build an alive structure despite the owner of the territory defending it move-for-move with expert play on both sides. The defender's surrounding stones should be assumed immortal.

It seems obvious that 4x4 and smaller is not invadable, and I strongly suspect a 5x5 space isn't invadable either.

This page on Sensei's Library suggests that a 6x6 space is not invadable under optimal play, but there is some dispute. Is that true? How about 6x7 or 7x7?

4
  • Am I right to think you mean the invader has to create a pass-alive shape, while the defender’s stones are presumed immortal?
    – PJTraill
    Dec 19 '20 at 21:58
  • For clarity, the board image should be extended to the right and downward, including the implication that the black stones cannot be killed. A question to Zags: will black defend the space?
    – fred_dot_u
    Dec 20 '20 at 1:51
  • @PJTrail. Yes, exactly. I'll add that clarification
    – Zags
    Dec 20 '20 at 15:41
  • 1
    @fred_dot_u Assume black will defend the space move-for-move.
    – Zags
    Dec 20 '20 at 15:41
1

I've seen and played a version of this were you put the black stones along the center lines of a regular 19x19 board so you carve out a 9x9 space. White is then supposed to create a living group inside. For players of equal strength this is approximately a fair game. I'm not sure what the result of perfect play for either side would be but I'm pretty sure this is the edge case. So 8x8 should be killable if both sides know what they are doing and 10x10 should live. The interesting lines of play for a 9x9 space usually start with white playing the 3-3 point and black answering on the 2-2 point.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.