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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 eyeTo 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 properties described below will use black eyes, please switch the colours around if we are discussing white eyes.)
For an eye in the center, white stones must not be able to occupy at least three out of the four marked points.
For an eye at the side, white stones must not be able to occupy any of the marked points.
For an eye at the corner, white stones must not be able to occupy the marked point. Examples
This is a real eye. There is no need for black to play at a to secure this eye.
This is a false eye because white occupied the two marked points.
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.
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.
Two real eyes at a and b. Proof that a false eye is not an eyeHere is a proof that a false eye is not an eye.
We consider this false eye.
Say white fills up external liberties by playing at the marked points. Now the three marked black stones are under atari.
If black connects at 1, the first condition is failed and so there is no eye here.
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:
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:
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. |