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Half Eye
   

A half eye is either an eye or not an eye (false eye), depending on who plays first.

[Diagram]
Diag.: A half eye for black

The marked point is a half eye for black, because if he plays first, it becomes an eye.


[Diagram]
Diag.: A half eye for black

White can remove the eye if she plays first.



[Diagram]
Diag.: 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, he will make two real eyes and will live; but if white plays there, she will kill black by making a a false eye.



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)

-- JanDeWit

BillSpight: See "Eyespace values in go" by Howard Landman: [ext] http://www.msri.org/publications/books/Book29/files/landman.pdf

JanDeWit: 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:



This is a copy of the living page "Half Eye" at Sensei's Library.
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