Sunday Problem #59

Published 18 Jul 2021 by antti (last edited 25 Jul 2021)

This is a classic life-and-death problem which most readers are probably familiar with. From an endgame point of view, however, the status of the resulting corner shape is quite interesting and worth thinking about.

Black to play.

Black’s failure
Most people know the attachment of black 1, here, but the follow-up with 3 and 5 is wrong: White lives with 4 and 6.
White’s failure
The combination of black 1 and 3 here is correct. Here, White’s straightforward sequence with 4 and 6 fails because black 7 links up underneath thanks to White’s shortage of liberties.
Approach kō
White can actually play elsewhere after black 3; and if Black then for example plays 5, 6–7 still starts a kō for White’s life in the corner. Now we are getting closer to what this corner is really about.
Correct for White
It is locally slightly better still for White to exchange 4–5 here before playing elsewhere. After black 5, even if Black gets to play
a and b, White is still not unconditionally captured, so after 5 Black needs three more moves. In the previous diagram, after black 3, only an additional net two moves would capture White.
Best for Black?
Four gote moves to capture the white corner sounds like a lot of work, so most likely Black should instead play 5–7 here. If White next plays
a, the corner lives in a seki, but a sente seki is actually pretty good for Black compared to a possible four-move kill.
More likely, however, White will ignore black 7 and play elsewhere. In the endgame, then, we either have white
a and a net score of 0, or black a and the average of white 7, black 19 points, i.e., black 6 points.
Paperthin difference
Surprisingly, then, in games where Black can get the
b descent in sente, there is still a very small difference between white c and d. Of these, c is still strictly better, securing five points of White corner territory; but d is not a ‘big mistake’ that lets Black create a severe kō, but instead an endgame mistake that makes White’s corner territory worth roughly 1.5 points.

Comments (1)

antti wrote 1 year ago:

‘Solution’ added.