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Two Eyes Can Die
    Keywords: Problem

Yes I bet every rook has this blinding flash of 'novel insight' but just in case (probability too low to specify !) I truly am posessed of a miraculous insight I'm gonna post it.

If U have an eye big enough to contain an opponents group with an eye shape then he can kill your 2 eyed group.

[Diagram]
Diag.: corner

A play at a kills white , no ?

Sc4rM4n



BillSpight: B a captures White. White is already dead. :-)


Yes, but White would have to be a very sloppy player to allow this to happen :-) Take for instance this situation:

[Diagram]
Diag.: corner

Black, having memorised the GoProverbs, plays at the point of symmetry. White must now pass 8 times in a row to get captured.

White can either take immediate counter-action and make a second real (ie only 1 space) eye of his own or let Black squander a few moves, only returning when Black is coming close to capture, or, more likely, building a living group. When building a living group inside White's territory is Black's objective, 1 is not such a good move; in fact Black'd better try elsewhere.

So: yes, groups with two open spaces can die, but groups with two open spaces of one intersection each cannot.

Invasions like above used to throw me off (see BeginnersQuestionAboutInvasion) but now I keep cool and deny the invader connections to the edges and most importantly EyeSpace.

JanDeWit

HolIgor: This is a question of definition. I would never call an eye an enclosed space containing a group of the opposite colour with an eye (or ability to form an eye). If your opponent has an eye then you group has to have two independent eyes to be certain of life, otherwise it is a semeai and nothing else. The result of it can be a death of one of the groups or a seki. Everything can happen. And remember that a seki is life.



Dieter:

In spite of having as much as four eyes, the White group in the next diagram is killed by Black 1.

[Diagram]
Diag.: Four eyes can die


(still Dieter)

Obviously, one can't call all surrounded spaces "eyes". There is, however, a problem with HolIgor's statement: "A surrounded space in which the opponent can make an eye, can't be called an eye". This statement is self-recurrent. Therefor we must clearly distinguish between an eye and EyePotential when making defintions. In every day speech, however, it is custom to call clear cut eye-potential "an eye".


BillSpight: A typical but unstated assumption when talking about the status of groups (alive or dead, connected or not, etc.) is that of local alternating play. It may be possible to construct contexts in which this assumption is invalid. However, given how humans used language, I think that this assumption is appropriate. In CGT terms, it amounts to the assumption of independence.

Kos have a way of destroying independence. For instance,

[Diagram]
Diag.: White can die

Black can capture this White group while White takes and wins a three step ko.

But I think that it is fine to say that the White group is alive. It's just not unconditionally alive. ;-)



[Diagram]
Diag.: How many eyes?

One a similar note, I don't think anyone would say that the white group here has two eyes, would they? Of course it has two Eyepotentials :-)



JanDeWit: I've read somewhere (not on this site) that you need about twenty points of open space for an invasion to succeed. Is that true?


--Stefan: It's among the proverbs on Jan van der Steen's site, as follows: "To invade, need 20 points in open area; otherwise, keshi is best. -- Yang Yilun, 7 dan pro."


mat: normally everybody does distinguish between eye and eye potential. Or would anybody say white has two eyes here ;-) ?

[Diagram]
Diag.: How many eyes?




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