Problem diagram.
Black plays.

Source:
Qi Jing Zhong Miao #331 , an ancient collection of mostly kyu level life and death problems.

Analysis:
   Myron Souris

The "official" solutions in books and the Internet disagree on the status of this problem. Some let Black capture White's stones outright. Others only give Black a direct ko.

As seen by the diagrams below, both evaluations seem to be wrong; optimal play seems to give Black an advantageous multi-step ko!

If any reader can show why optimal play by both sides does not give Black an advantageous multi-step ko, then be the 1st person to email the Problem of the Week Editor to win a prize of two back issues of Go World magazine! The Problem Editor's judgement is final.

Solution follows    (or click here to download SGF)

Inferior.
Black 1 is a no-brainer. And White 2 is OK. However, at least 2 Internet problem sites incorrectly give the descent to Black 3 as the solution. White throws in with 4 and Black takes first in this direct ko, which is worth about 23 points.

But see the next diagram for how Black can do even better!

Optimal?
The counter-intuitive Black 3 is the optimal line for Black, but the move doesn't seem to be in any known solution set.

At 1st glance, White 4 seems to greatly increase the size of an apparent direct ko by threatening to spill out down the left side. But through 8, White only has a disadvantageous 2-step ko, i.e., White has to ignore 2 ko threats to win the ko.

See the next diagram for Black's follow up.

Follow up.
Starting from the previous diagram, assume that Black takes the ko, then White re-takes the ko, and then Black makes a ko threat at 9. Then, to have any chance to win the ko, White's approach move on the corner point at 10 has to ignore Black's ko threat at 9. But only after White 10 does the ko become direct!

Black starts this direct ko with 11. White cannot end the ko with the capture of 4 stones at 12, because Black's "under the stones" play at 13 captures the White stones! Note that Black has already made an as yet unanswered move at 9.

So to win this ko, White would have had to have given Black a total of THREE moves elsewhere!

Inferior line.
The book Theory and Practice of Go (and other solution sets) give the inferior White 4. With 5, Black unconditionally captures the 4 White stones.

Note that even in this line, White still had a chance to transpose into the disadvantageous 2-step ko by playing move 4 one space above Black's move 5.

Worst
Some Internet solutions only give the weak defense of White 2, which throws away even the disadvantageous 2-step ko. Through 7, Black wins the semeai.

See the SGF for even more variations.

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