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Half Eye
Path: EyesCollection   · Prev: EyePoint   · Next: EyeSpace
  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.



[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.



Some common half eyes on the edge of the board

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

[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.


Andre Engels: 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).


This page is part of the Eyes Collection.



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This is a copy of the living page "Half Eye" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.