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Re: [gnugo-devel] Half and false eye with ko.

From: Daniel Bump
Subject: Re: [gnugo-devel] Half and false eye with ko.
Date: Sun, 25 Nov 2001 14:07:39 -0800

> Yes, this case seems to be fine. What's worse is the difference
> between my case (b) and the modification (b') below
>     .X..
> (b) ..OO
>     OO.O
>     O.OO
>     XOX.
>     .X..
>      .X..
> (b') ..OO
>      OO.O
>      OXOO
>      X.X.
>      .X..
> Notice that while (b') is a 2.5 topological eye, (b) is a real eye
> regardless of ko. I actually had intended to have (b') in my last
> message but mistakenly took the wrong diagram. I'm not sure how much
> this complicates things, but it certainly makes the analysis more
> messy.

This seems to be OK. 

I think there is an arithmetic with 1/4 eyes in Howard Landsman's
paper. The following table converts diagonal sums to
1/4-fractional eyes. The total number of eyes to live would be
2. For example, a group with 8 quarter eyes should be alive, the
example at the end shows. If at any point B takes a ko, W just takes
some other one.

diagonal     number of     meaning
sum          eyes
2.0        1.0           true eye 

2.5         .75          half eye if X wins ko, true eye otherwise

3.0         .5           half eye regardless

3.5         .25          half eye if O wins ko, false eye otherwise

4.0        0.0           false eye



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