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General Eye Definition
   

Here is an attempt to give a general (not specific) definition of what is an eye (or sometimes called real eye). It is slightly modified from the 2/4 - 1/2 - 1/1 rule.

If a group has two or more real eyes, then it is a living group.

Note that the concept of miai is deliberately left out in this definition.

Also see the two-headed dragon where a living group is formed using two false eyes.


General definition of an eye

To qualify as an eye, the group must satisfy the following two conditions. If only the first condition is satisfied but not the second, then it is deemed as a false eye.

  • The group must surround at least one empty point.
  • The group must posess the following properties described below.

(The properties described below will use black eyes, please switch the colours around if we are discussing white eyes.)

[Diagram]
Diag.: An eye in the centre.

For an eye in the center, white stones must not be able to occupy at least three out of the four marked points.


[Diagram]
Diag.: An eye at the side.

For an eye at the side, white stones must not be able to occupy any of the marked points.


[Diagram]
Diag.: An eye at the corner.

For an eye at the corner, white stones must not be able to occupy the marked point.



Examples

[Diagram]
Diag.: Real eye.

This is a real eye. There is no need for black to play at a to secure this eye.


[Diagram]
Diag.: False eye.

This is a false eye because white occupied the two marked points.


[Diagram]
Diag.: Unsettled half eye.

This is an unsettled half eye. If black plays at a, it is an eye. If white plays at a, it becomes a false eye.


[Diagram]
Diag.: Two real eyes.

This group has two real eyes. Note that white can never get to occupy the point a to make b a false eye, as this move is suicide. Similarly, playing at b is prohibited, so a is a real eye.


[Diagram]
Diag.: Two real eyes.

Two real eyes at a and b.



Proof that a false eye is not an eye

Here is a proof that a false eye is not an eye.

[Diagram]
Diag.: False eye.

We consider this false eye.


[Diagram]
Diag.: External liberties filled up.

Say white fills up external liberties by playing at the marked points. Now the three marked black stones are under atari.


[Diagram]
Diag.: Black connects.

If black connects at 1, the first condition is failed and so there is no eye here.


[Diagram]
Diag.: White captures.

If black allows white 1 to capture the three marked stones, there is obviously no eye here.

Therefore, we proved that a false eye is not an eye.



Proof that a "false" eye might be an eye after all:

[Diagram]
Diag.: Two False Eyes?

MattNoonan: Constructive proofs are nice. :) Also, see InstantEyeTester for a position in which black has two living eyes, but all the diagonal points of those eyes are occupied by white.


See also:


Contributors:

  • unkx80
  • (Add your name here.)


This is a copy of the living page "General Eye Definition" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.