Half Eye

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  Difficulty: Beginner   Keywords: Life & Death

A half eye is either an eye or not an eye, depending on who plays first. It is so called because two half eyes are effectively a whole eye, as they are miai.

[Diagram]

A half eye for Black

The marked point is a half eye for Black...

[Diagram]

A half eye for Black

because by playing first, it becomes an eye; and...

[Diagram]

A half eye for Black

White can remove the eye by playing first (it becomes a false eye).


[Diagram]

Black group with a half eye

This black group has a half eye at a.

The key point is of course b, because if Black can play there, Black will make two real eyes and will live; but if White plays there, White will kill Black by making a a false eye.

Half-eyes can be used to count up to two eyes; the rule is that a player lives if he either has two eyes, or 1 1/2 eyes and sente (provided the sente is used correctly).

[Diagram]

Four half-eyes

In this example, White has four half-eyes at a, b, c and d, which is equivalent to 1/2 + 1/2 + 1/2 + 1/2 = 2 eyes, so White lives.


Some common half eyes on the edge of the board

Assume in these examples that Black connects through black+square to the rest of the group. All White's stones are assumed alive.

[Diagram]

Half eye

[Diagram]

Half eye

[Diagram]

Half eye

[Diagram]

Corner half eye



(Add similar).


Appendix on CGT

So the result of this game is

  • 2 eyes for Black, if Black goes first.
  • 1 eye for Black, if White goes first.

(This is denoted { 2 | 1 } in Combinatorial Game Theory, I believe)

-- Jan de Wit

Bill Spight: See "Eyespace Values in Go" by Howard Landman: [ext] http://www.msri.org/publications/books/Book29/files/landman.pdf

Jan de Wit: Another nice reference is Martin Mueller's Ph.D. thesis "Computer Go as a Sum of Local Games: An Application of Combinatorial Game Theory" which can be found at [ext] ftp://ftp.inf.ethz.ch/pub/publications/dissertations/th11006.ps.gz. This also has the most accessible introduction to Combinatorial Game Theory which I've found so far. Further discussion moved to Combinatorial Game Theory.


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This is a copy of the living page "Half Eye" at Sensei's Library.
(OC) 2009 the Authors, published under the OpenContent License V1.0.
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