Half Eye

  Difficulty: Beginner   Keywords: Life & Death

Chinese: -
Japanese: 半眼 (hangan)
Korean: -

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.

A three-quarter-eye (where forming one eye threatens to form a second) is sometimes also be referred to as a half eye.

A half eye for Black  

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

A half eye for Black  

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

A half eye for Black  

White can remove the eye by playing first.

One eye, two half eyes  

One eye and two half eyes make a living group.

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.

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.

Half eye  
Half eye  
Half eye  
Corner half eye  
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

  • Fractional eye — Eyespace regions that can be considered to be ⅓ eye, ⅔ eye, ¾ eye, 1¼ eye and 1½ eye. Also refers to Landman’s paper cited above by Bill Spight.

Half Eye last edited by PJTraill on June 27, 2019 - 00:44
RecentChanges · StartingPoints · About
Edit page ·Search · Related · Page info · Latest diff
[Welcome to Sensei's Library!]
Search position
Page history
Latest page diff
Partner sites:
Go Teaching Ladder
Login / Prefs
Sensei's Library