Forum for Two-eye-formation
Turning a two-eye formation into a non-two-eye formation [#1611]
Let me check my understanding:
![[Diagram]](diagrams/40/a707fbb7ac4318570c511420af3dadd6.png)
, Black has a two-eye formation. After I think you are correct. Let's have a look at the position after capturing:
![[Diagram]](diagrams/20/b7b49b172bcce94aa3dcdf879f9591e1.png)
The marked stone plus the string of five black stones plus the empty intersections a and b do not form a two-eye-formation, because the marked stone is also adjacent to another empty intersection (namely c).
I think black can force a two-eye-formation from this position, but it's rather complicated. Black must fill at c. Then if white plays d some time, it's a two-eye-formation. If not, then black can play d, then either wait for white to fill the empty intersections next to d, or else black can play on those intersections, and so on...
The fact that a two-eye-formation can be forced makes it seem slightly less counterintuitive, but I agree that it is surprising.
Note: I'm far from being an expert on this topic. I'm just reading the definition carefully and hoping that my reasoning is correct!
Correct.
If you want a stronger concept than two-eye-formation, then you might define "partition of the board into two-eye-formations". This would contain less surprises but it would be useful for different applications only.
For further surprises, study a double ko seki and understand why it does not contain any two-eye-formation.
BTW, the simplest method for destroying a two-eye-formation is to fill one of its eyes...
I added this position as an example. Hope it's okay with you.
With respect to double-ko seki, it violates "each of the strings is adjacent to each of the two intersections". No?
(Here, I take adjacency between a string and a point to mean that there exists at least one stone in the string that is adjacent to the point. This may partially satisfy Dieter's comment in the other thread.)
What is violated depends on which set of intersections you test for possibly forming a two-eye-formation. E.g., if you do not include the ko stone, you create a different violation.
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