Half Eye

  Difficulty: Beginner   Keywords: Life & Death

A half eye is an unfinished eye. It is a potential eye that can be completed or destroyed depending on who plays first. Typically, the moves at a half-eye are locally small for both players, and are only played in order to make a group live or die, or to force it to run further.

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]
One eye, two half eyes  

One eye and two half eyes make a living group.


[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 complete a second eye.

[Diagram]
Four half-eyes  

Half-eyes can be used to count up to two 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  
[Diagram]
Edge capture 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.


See also:


Half Eye last edited by 218.212.219.136 on April 19, 2015 - 15:57
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