Here is the initial position again, but with some markup for discussion:
General Discussion
Perhaps the most striking feature of this position is that black has a 12-stone chain, marked with A, in atari. This would make it seem that playing at X would be a high priority for either player, in order to capture or save those stones. The chains marked with B and C are also in atari, with B also depending on a potential play at X, and C is capturable by White with a play at Y. The life and death status of the chains D and E, as well as much of the rest of board, also depends on the status of these stones.
Another interesting feature is the position of the chains F and G, neither of which has two eyes, but G seems to have an advantage from having one eye, while F does not have an eye. However, clearly the status of chain A affects the balance between F and G. They share five liberties around Z, and this specific number will matter, as we will see in the analysis.
Overall, the position seems to appear unstable, with strings in atari and possible temporary sekis, but they seem to depend upon each other in a circular fashion. In fact, this position was called a “circular hanezeki”.
Hanezeki is a surprising type where stones can be atari, yet actually capturing initiates a sequence that puts the first to play at a disadvantage. This particular position adds further complications to this concept by arranging multiple chains in a circular dependency. The example hanezeki on the Sensei’s Library page is much simpler and helps clarify that core concept.
Black plays first at X
If Black plays first at X, then White must answer at G3. From there, black could try two tactics. if Black attacks White’s D chain, then Black will actually lose a capturing race:
Alternatively, if Black tries to attack White’s F chain, then black will again lose the capturing race:
However, note that Black came just one liberty short from killing White’s F chain.
Hence, Black playing at X causes all Black stones to die
White plays first at X
White could play at X to capture the 12-stone Black chain A:
Black is compelled to play the snapback at E3 and white must play G3:
However, from that position, White is doomed to lose the capturing race:
Hence, White playing at X also does not work
A potential mistake by Black in response to White first at X
The next three figures shows how a mistake by Black (playing 4 at F3 instead of J2) would play out:
A local (but temporary) seki is established in the bottom right, however, this it will eventually collapse and all of Black’s stones will ultimately be captured by White, since Black’s G chain and then stones at J6 are capturable.
White plays first at Y
White could play first at Y to capture Black’s C chain;
However, this also leads to a capturing race that White will lose:
Hence, White playing at Y also does not work
Black fills a shared liberty around Z
Earlier we saw the five liberties around Z prevented Black from saving chain E by first capturing White’s chain F. However, if Black attempts to first reduce liberties around Z, White can then play at X and capitalize on the reduced liberty count:
The net result is that White has gained far more points than Black in the exchange.
Hence, Black filling around Z leads to a worse outcome
White fills a shared liberty at Z
For completeness, we can also consider what might happen if White initiates play by filling a liberty around Z. However, that will allow Black to play next at X:
This now works since Black can win the capturing race by attacking White’s F chain to save the Black’s A and E chains:
Hence, White filling a liberty at Z does not work
Conclusion
All of the potential plays analyzed above lead to a much worse outcome for the player initiating the play. Hence, all of the stones are alive, with all (besides White’s top-right and bottom-left corners) being alive in a bizarre type of seki, known as hanezeki.