Smallest Group with Two Eyes

Path: LifeAndDeath   · Prev: KillingShapes   · Next: BasicLivingEyeShapes
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This is a list of the smallest groups with two eyes. They do not need a single further stone to defend them, no matter how many stones may be played to attack them.[1][2]

For others see Basic Living Eye Shapes.

See also Unconditional Life.


In the corner

In the corner, six stones are the minimum needed to complete a group with two eyes.

[Diagram]

First corner group



[Diagram]

Second corner group



[Diagram]

Third corner group



[Diagram]

Fourth corner group




On the side

On the side, the smallest groups with two eyes have eight stones.

[Diagram]

First side group



[Diagram]

Second side group



[Diagram]

Third side group



[Diagram]

Fourth side group




In the center

In the center, 10 stones are required to make a group with two eyes.

[Diagram]

First center group



[Diagram]

Second center group



[Diagram]

Third center group



[Diagram]

Fourth center group




All 16

Here's a board containing all of the above groups:

[Diagram]

Smallest groups with two eyes


Off Topic

Below are some small live groups that must be defended against attack to stay alive.

Robert Pauli: Parked'em here. To be deleted in, say, 2005.

[Diagram]

Fifth corner group

[Diagram]

Sixth corner group

[Diagram]

Seventh corner group

6 stones, 6 different eye shapes, 7 different stone shapes
--Xingta: Shouldn't the last three examples really be 7 stone shapes even if they are alive with 6. The last example has a false eye too - how does that work?

[Diagram]

Fifth side group

8 Stones but 4 different eye spaces.
Anonymous: Does this really count as an 8 stone group? White has a ko threat at "a" inside the group that he will play eventually, making this a 9 stone group for black. Ian: My guess is that there is no point in playing a stone inside this group. Black will respond by connecting and have 2 eyes.

Ellbur: I don't think that groups which can be threatened to add a stone or stones should be included in Smallest Group With Two Eyes, as this could be extended to include a one stone living group: one lone stone on the 3-3 point.


Authors


[1] Currently all entries are for a "big" rectangular board. Taking a smaller one cuts the number of stones needed. The minimum is one stone in the center of a 3x1.

[2] Robert Pauli: Hmm, thought I made it clear (BTW, thanks for watching me, Bill ;--), but what about

[Diagram]

rest white too

Does the black group have "two eyes" ? :--))

Dieter: One thing is sure: White is in atari.

RP: Right :-)

Should we restrict eyes to be minimal at the top ?

Bill: That's an interesting rules question, Robert. ;-) By J89 and my rules, no. How about by yours?

Robert Pauli: No "control" for Black if White can make seki or two eyes after Black's capture: Black should capture before end!

But the question remains, "minimal eyes" ?

RobAnybody: 4 stones with two eyes, a and b :)

[Diagram]

rest white too



Robert Pauli: That's three eyes, Rob - one almost filled. :--)

Under (unofficial) "can't escape = dead" rules the white stones in the almost filled eye are dead, that's the problem. On the other hand, Black neither can convert his group to two minimal eyes (including the big eye!). So, it seems more appropriate to regard the whole thing as seki. This suggest to define "having two eyes" as being able to form two minimal eyes . . .


Another living group in the corner... made with 5 stones... - but can be forced to add another one if B plays at a . . .

[Diagram]

W Black seems alive here with a threat

Robert Pauli: Minimal eyes would rule out this case too.


Path: LifeAndDeath   · Prev: KillingShapes   · Next: BasicLivingEyeShapes
This is a copy of the living page "Smallest Group with Two Eyes" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.
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