# 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.

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 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

### 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)

Bill Spight: See "Eyespace Values in Go" by Howard Landman: 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 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.