Here’s another fun 9x9 position I found with some interestingly deep tactics. Black to move and achieve a draw, Chinese rules, 7 komi.
Despite looking fairly simple, I feel like this is one of those positions that anyone below pro level would be unlikely to play correctly without AI assistance, especially in a real game. Although of course knowing that this might be a pro-level problem to begin with is very helpful.
Actually I’m not 100% sure of the AI analysis either, because when I dig into some deep lines there are still a few blind spots in the net I’m using. I didn’t find any that would refute the critical lines, but take this as also not 100% confirmed, there’s a some chance of mistakes.
Details hidden here in case you want to think about it yourself a bit first
So, the first major thing about this position is that if black connects, white will clamp and black can’t cut it off because white would live in the upper left (exercise left for the reader). That’s no good for black.
So what should black do instead?
Black could consider simply protecting here, but it’s too slow, barely.
White can just take.
Next white exchanges A for B in sente to create a ko, and then leaves it hanging to take the gote endgame at C. White has more ko threats than black, so despite leaving it hanging, white can still win it, and white barely wins the game, by 2 points.
This also still the case even if black attempts to reduce white’s ko threats by making fewer hanging connection shapes, such as by playing C7 at B7, or by playing G6 at H6.
So black needs to find a way to do one point better. (one point more for black will also be one point less for white by area scoring, and give a draw).
So in the variation where white won by 2 points, white got into A6. What if black occupies it, playing here or at A, gaining that point back? Now if white captures at B and the same thing happens as before with white winning the ko, black is happy and gets a draw or even a win by 2 points.
But white has this move instead:
And white can live in the corner!
In this variation, white now has miai of A or B to live.
Obviously the variations are very complicated. But it seems like this is a failure for black as well. What should black do instead?
As best I can tell with AI assistance, this appears to be the unique move for black to obtain a draw. Of course, there might be a mistake in the analysis or even something obvious missed in the analysis. But if true, it’s very cool.
So firstly, this move also prevents white from getting into the A6 point. That’s barely enough for a draw, if white simply captures the one black stone in the lower right.
So now we investigate the variation where white tries to live.
With this variation:
It turns out that because the black stone is at A instead of B, this is barely enough to break white’s miai to live that we had before, so black plays 8 here instead of defending the upper left.
With the stone at B instead, white would live like this:
Anyways, white continues like this. Actually white is not dead here…
Because white still gets a ko! Black’s clever move at A7 has only managed to turn white’s unconditional life into a ko for life.
Fortunately, black has a ko threat factory starting at A. However, it is not as big as the ko at the top side, for the life and death of white’s whole group. So, apparently, in the main line
from here it appears white will ignore the threat to win the ko and live, while black eats some white stones in the lower right. In the end, black wins by 2 points.