Hi, why in diagram 46 the upper space ‘a’ is categorized as a false eye? I have in mind that if I surround all the stones of the opponent group, I can put my stone in this space and capture everything. This definition satisfies all diagrams except 46. The only thing I could think of is a domino effect (since the lower ‘a’ is a false eye, immediately the upper one becomes one too, as soon as the 3 lower stones are captured). But if this is the reasoning, in all diagrams the second space should also be categorized as a false eye.
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Does it help if you imagine a black stone at the lower a?
Rather than thinking about a false eye being where white can capture, as that definition fails on a single true eye, think instead about it being where black can save some stones in (future) atari by connecting, but then there is no empty eye point.
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The second space, as you put it, is not a false eye but just a single eye. Therefore it is not marked with an “a”.
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True, my definition sucks. But I didn’t understand yours, could you clarify it? For example in diagram 43, why would the left space be a real eye? I imagine a black stone in “a” and then … the remaining stones in atari cannot be saved, right?
Right, they cannot be saved by connecting, so it’s not a false eye. They cannot be saved by not connecting either, so they are not alive. They have one real eye.
One could try
Can one capture at least one of the 1-or-more
adjacent / surrounding (this would be more
complicated if the maybe-eye has more than 1 space)
1-or-more stone chains without capturing all of those chains?
.
Black has a false eye
and Black has a real eye
The main difference is that in the first picture, Black’s is not connected but consists of two strings of stones.
In the following picture, Black’s surrounded group is dead
and in the following picture, Black’s surrounded group is alive in seki.
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I think sometimes that’s enough for seki?
Filling the “false” eye would result in death. So apparently even a false eye does sometimes have some enduring value.
Interestingly in the above example the answer seems to be NO. So maybe the false eye has become real? But actually in NZ rules White can play S2 T1 suicide and then eventually get to YES in a silly way. Not sure how to interpret this question.
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For people who are looking for a definition, I usually say that an eye is real when the adjacent stones are all linked through paths along controlled intersections that don’t include the surrounded empty intersection under evaluation. This definition also captures eyes of two-headed dragons.
And by “controlled” I mean a friendly stone or empty but self-atari or suicide for the opponent.
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@Feijoa :
It’s an attempt at how AllanFelipe could think of eyeness.
(“But I didn’t understand yours, … in atari cannot be saved, right?”
A decent definition, though I think mine of essentially “it’s a false eye if they can play atari to make me fill it in” is more functionally what Alan needs to grok.
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Your definition says they are real eyes, but many consider them false, indeed the Japanese term is “false eye life”. They are locally false, but globally real. Which camp they land in is really just a matter of definition and endless forum arguing.
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No there is a difference. You can capture some stones delimiting the fake eye without the need to capture all the stones, while to capture the real eye you will need to surround everything.
The two bottom dias are about fake eyes.black will have to fill the hole or it will be captured. The hole is therefore just a dream.
At the top it’s still only an eye and you know you need 2 to live. Here it’s more resilient as a fake one because white has to surround the whole to be able to play in the hole.
So to help to distinguish fake and real, you need to control (with the edge, a stone or another eye) 3 of the 4 circled point. 2 is not enough.
@gennan mentioned the 2 headed dragon which is very rare and uncommon life with 2 “fake” eyes that you can ignore yet but here’s a link for your interest
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@jlt @Groin Yes, that’s what I always had in mind with the idea of false eyes, but it fails with the upper “a” in Diagram 46, doesn’t it? If I surround everything I can immediately capture just the lower group and not the middle stone on the edge.
Doesn’t the same thing happen in 46? If I imagine a black stone in the lower “a” nothing else can be saved neither connecting nor not connecting and the whole group is not alive.
In diagram 46, Black is decomposed into three strings of stones:
- cross
- square
- triangle.
Once all external liberties R1 and T6 are filled, there remain only liberties A, B and C.
A is common to strings 1 and 2.
B is common to strings 2 and 3.
C only belongs to strings 3.
Only C is a real eye, A and B are false eyes.
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I see the situation you described, and even knowing the fate of black group, I feel like calling “b” a real eye because of what I had in mind about surrounding everything and being able to capture a string (apparently I need to forget that). Is the idea of liberties being shared by more than one string what led you to you categorize “b” as a false eye?
In order to survive indefinitely, every chain needs at least two liberties that can never be taken away.
In the example above, all liberties A, B and C can eventually be removed, so the black stones are dead.
Even so, there is a difference between these inside liberties, which is the distinction between (false) eyes. Essentially an eye is an inside liberty that can only be removed as the last liberty. (Hence two eyes yield life, since not both can be removed at once)
So in the example above, black can remove the liberty A by capturing the X stones, hence A is a false eye. Afterwards black can remove liberty B by capturing the square stone, so B is also a false eye. Liberty C can only be removed as the very last capture. So C is an eye.
The idea of eyes is to ensure life when paired together. Fake eyes never ensure life even if you put them together (besides the very rare and special case of double headed dragon).
An eye is this hole in the middle of stones. Is it fake or not? It’s real only if the only way to kill the whole group of stones is to occupy this hole after being fully surrounded. If you can destroy this hole by capturing a piece of the stones forming the hole before that it’s no more an eye.
Validating eyes as fake or not is crucial so to be sure to be alive (or not).
Maybe these next diagrams will help.
The situation on the left side is usually much more understandable for humans. Some stones are in a threat to be captured,. The situation on the right side is the same but less obvious to see.
Here is a small beginner problem to illustrate
White to play
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Yes.
Do you think that’s a problem?
It’s not, it means my definition is working well.
Actually I think I see your confusion. You are applying “save” to the group as a whole, not the chain in atari.
An eye being false is a simple local property about opponent being able to play atari and you answer by connecting the stones in atari, thus filling in the eye and saving those stones from immediate capture from that atari*. The “save” is short term and refers to the chain in atari. It doesn’t refer to the group as a whole which might have 0 or 1 or 2 or more real eyes further away and might be eventually capturable so not long term “savable”.
/ * the connect and die lower false eye in dia 46 complicates this as after connecting you are still in atari, arguably not that atari but a different atari.