Re: Re[2]: computer-go: perfect play

[Matthew John Saffell <saffell@xxxxxxxxxxx>]

The analysis of the proposed problem below is a bit trickier, I think. 
You have to also prove that GoDevil can't surround the black stones from
the outside and create a semeai (capturing race) that he can win.  I'm
sure GoDevil would kill me, or at the very least take my corner areas away
by creating seki.  :-) 

Matt


On Thu, 28 Sep 2000, Heikki Levanto wrote:

> One way to approach a proven limit would be to figure the minimal number of
> stones that will not let white get anything alive. Then fill half board with
> this pattern (make necessary adjustments for the edge), and we ought to get
> to a number that is easy to prove.
> 
> 
> There has been some discussion if white can invade a corner surrounded by
> black stones on the tenth line. I would expect it to be possible to prove
> (exhaustively, if need be) that a 6x6 corner, all empty, surrounded by black
> stones, should be black territory.
> 
>    - - - - - - - -
>   |+ + + + + + X +  (diag. 1. White (O) to invide and live)
>   |+ + + + + + X +  (top left corner of the board)
>   |+ + + + + + X +
>   |+ + + + + + X +
>   |+ + + + + + X +
>   |+ + + + + + X +
>   |X X X X X X X +
>   |+ + + + + + + + 
> 
> The corners give black 4x36 = 144 points of territory. If black passes to
> all white moves outside the corners, white can surround a large cross-shaped
> area of (19x19) - 4x(8x8) = 361-256 = 105 points, a clear victory for black
> with 44 stones.
> 
> Reducing the square to 5x5 empty points gives black 100 points, and white
> gets (19x19)-4x(7x7)= 361-196= 165 points. A loss of 65 points, with 36
> stones handicap, and assuming a pass on every outside move. It ought to be
> possible to resist the buildup of white territory on the "outside", but if
> that can be proven to be effective enough, I can not say tonight.
> 
> So, Roland, your estimate of 30-40 stones was not badly off. Anyone with a
> lower (provable) limit? 
> 
> - Heikki
> 
> P.S. I am not certain what this says of the strength of GoGod. I would be
> surprised if the number of hadicap stones would be linearily additive to so
> high numbers. 
> 
> 
> -- 
> Heikki Levanto     LSD Levanto Software Development   heikki@xxxxxxxxxxxxxxxxx
>                "In Murphy we Turst"
>