Largest capture that still can't live
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It is well-known that a group with a large eye space has a better chance of living. In particular, any group with a non-defective eye space of more than seven spaces is known to live independently or in seki; an example is butterfly seven which is guaranteed to live at least with a seki. However, a group with a larger eye space may be killed if its eye space contains defects.
On this page, we study eye spaces created by the capturing a single chain of stones. In particular, we ask: What is the largest capture that still can't live? Igo Hatsuyoron contained a famous life-and-death problem where a 16-stone chain is captured but still can't live, and for about 300 years 16 has been taken as the maximum number. On 2004 May 1, Robert Pauli constructed a problem involving a 17-stone capture. This new record stood until 2009 September 9, when a 18-stone capture is constructed. As of 2009 September 11, the current known record is 18 stones.
asmobia?: I simplified the first case of 18 stones.
Herman: Yes, but isn't it "White to play and fail to live" now? It seems slightly more interesting to me to have "Black to play and kill" :-)
Here as applet.
From Hirose Heijiro's Book of definitions...
There has been disagreements whether a move inside such a large eye space with defects is considered a nakade. It appears that Japanese professionals such as Hirose Heijiro and Hayashi and historians such as John Fairbairn consider it nakade. For example, John Fairbairn describes Hayashi's definition as follows: The base meaning is a "move inside". Hayashi does not restrict this to any particular shape except to say that the surrounding group is "continuous". From the examples I have seen, it is safe to say that the shape into which the "inside move" is played is always fully enclosed. It may, however, have defects.