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

[Heikki Levanto <heikki@xxxxxx>]

Roland <goprog@xxxxxxxxxxxxxxxxx> wrote:

> HL> Funny position, I have 181 non-connected stones, and yet I am
> HL> unconditionally alive.

> I think we can lower the limit considerably. All I need is a position
> where I can assure that I control more than half of the board. So
> maybe we can place the limit at around 30-40 stones. This would mean
> we are at most 40 stones from perfect play.

Yes, of course. But if we require strict mathematical proof of it, we can
not accept "a limit around 30-40 stones".

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"