Two Eyes Can Die

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  Difficulty: Intermediate   Keywords: Problem

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Dieter: During the 17/10/2006 WME, I didn't quite know how to preserve this discussion of a common misunderstanding.

tapir: I would only keep Bills comment. And links to some related tsumego.


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

If you have an eye big enough to contain an opponent's group with an eye shape then he can kill your two-eyed group.

[Diagram]

corner

A play at a kills White, no?

Sc4rM4n


Bill Spight: Black a captures White. White is already dead. :-)

DrStraw: Does this mean that we need the concept of "seeing eyes" -- those that are useful and cannot be killed?


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

[Diagram]

corner

Black, having memorised the Go proverbs, invokes "play on the point of symmetry". White must now pass (or tenuki) 8 times in a row to get captured.

White can either take immediate counter-action and make a second real eye (i.e. only 1 space), 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 had better try elsewhere.

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

  • It's better than that - two open spaces where every intersection of the space is a liberty of the surrounding group cannot be captured -- Eratos

Invasions like the above used to throw me off (see Beginners Question about Invasion) but now I keep cool and deny the invader connections to the edges and most importantly eye space.

Jan de Wit


Jasonred Either I suck more than I thought possible at life and death, or it's silly to answer invasions like the above... You could probably tenuki at least 3 times and still kill the group.

HEY, how about a ConstructionProblem6? Let's see how many times you can tenuki before you have to answer. For black, how many moves do you have to waste in order to gain a (couple of?) ko threats?


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 seki. Anything can happen. And remember that seki is life.


Ofcourse HolIgor is right. In fact the definition given at the top is false. Some territory is not per se an eye. It is only an eye if it can not contain a living group of the opposing colour and none of the stones surrounding the eye can be captured.

[Diagram]

corner

I would even say that this group does not have two eyes because:

[Diagram]

corner

The larger 'eye' can contain a living group of the opposing colour.

A group with two eyes is unconditionally alive. Ergo if it can theoretically be killed, it does not have two eyes.

A group with two eyes is alive, but 'alive' is not necessarily a group with two eyes.

--Skelley


Dieter:

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

[Diagram]

Four eyes can die


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. Therefore we must clearly distinguish between an eye and eye potential when making definitions. In everyday speech, however, it is custom to call clear cut eye-potential "an eye".


Bill Spight: 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 Combinatorial Game Theory terms, it amounts to the assumption of independence.

Kos have a way of destroying independence. For instance,

[Diagram]

White can die

Black can capture this White group while White takes and wins a two move approach ko.

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


[Diagram]

How many eyes?

On 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 eye potentials. :-)


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

[Diagram]

How many eyes?

0, both false eyes. :)


Eratos 26k - As I commented above, if every point in a surrounded area is a liberty of the surrounding group, that must make a true eye.

[Diagram]

Surrounded space is all liberties

[Diagram]

Surrounded space still all liberties

Play at all of the liberties is simply not possible, and invading group must share liberties with the surrounding group

[Diagram]

Not all liberties

Capture is possible, but would require incredibly dumb play by black. This is because the Squared points would be liberties for an invading white group, but not for the surrounding black group.


Mef: As an aside to the discussion above, there are some situations involving superko where two-eyed groups may be sacrificed.

[Diagram]

W to play. Chinese rules, 0 komi

In this position white can use the sending 2 returning one to create a superko problem for black. Should black be naive:

[Diagram]

W5 circled, B6 = Pass, W7= W1

After playing through the cycle once black cannot capture again after W7. After black passes again, white will capture the upper left group, winning the game. In order to win, black must give up a different two-eyed group.

[Diagram]

W5 circled

After playing B6 the lower right group is dead, but black will have no more restrictions from superko and will win the game 41 to 40.


RobertJasiek: Presumably Francois Lorraine discovered the eye filling tesuji first for a position with a 1-eye-flaw. In general such positions are extremely rare on the 19x19 (fewer than 1 in 10 million games?) because they require non-existence of ordinary tenukis in territory. For small boards, the probability is a bit higher.


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