Re: computer-go: Ko

["Chris Fant" <Fantius@xxxxxxxxxxx>]

I don't think that is a counterexample.  Let's use some letters:

 Assume that this position has been reached without captures:
 ......
 ..OX..
 .O.OX.
 ..OX..
 ......

 Black takes the ko by playing at 'a'.  Since that was the first stone to
play on 'a', this is a new board.

 ......
 ..OX..
 .Oa.X.
 ..OX..
 ......

White takes the ko back by playing at 'b'.  Since that was not the the first
stone to play on 'a'
, we can't be sure this is a new board.
......
 ..OX..
 .O.bX.
 ..OX..
 ......


----- Original Message -----
From: "Gunnar Farnebäck" <gunnar@xxxxxxxxxxxxxxxxx>
To: <computer-go@xxxxxxxxxxxxxxxxx>
Sent: Wednesday, June 04, 2003 12:33 AM
Subject: Re: computer-go: Ko


> Peter Drake wrote:
> > Is the following statement true?
> >
> > If a stone played at a point is the first stone to ever occupy that
> > point, no subsequent full-board position can be identical to a
> > preceding position.
>
> Definitely not, it doesn't even hold for a basic ko. I.e., assume that
> this position has been reached without captures:
>
> ......
> ..OX..
> .O.OX.
> ..OX..
> ......
>
> Black takes the ko, playing the first stone ever at that vertex
>
> ......
> ..OX..
> .OX.X.
> ..OX..
> ......
>
> If O immediately recaptures we get a counterexample.
>
> /Gunnar Farnebäck
>
>