Re: computer-go: perfect play : a new fractal algorithm

[Serge Boisse <boisse@xxxxxxxxxxxx>]

"Johan Roos (QCS)" wrote:
> 
> My thought was,
> 
> As the center cross maps to the center cross of the board level above, and the center point is best on a 5x5
> board it should 
> 
> /Johan

You have a point, but not for the good reason ;-).
The idea of the center cross shared by all board is just one way, among others,
to reduce boards. But any reduction sheme wil manage to keep roughly the same
proportion of white, black and empties in the center area.
So you're right, since center (3-3) is the best opening on a 5x5 board it should
translate all the way up...

But wait. 

Suppose a 19x19 -> 13x13 -> 9x9 -> 7x7 -> 5x5 distribution of "fractal" boards.
When uploding the 3-3 point from 5x5 to 7x7 board, it expands to an area of 3x3
intersections, located in the center of the 7x7 board, with best probablity of
the center 4-4 point. 

   1     2    (3)    4     5     5x5 board, () best point
   1   2  (3   4   5)  6   7     7x7 board , () area uploaded

but the local recursive search in the 7x7 board comes into play, 
looking further to decide which of these 9 points is the best.
Then it may select 3-3 point instead of the 4-4, because 3-3 is a better opening
than 4-4 on a 7x7 board. 

then you expand from 7x7 to 9x9 as follows, ginving a 2x2 area (3-3 to 4-4)
point :

   1   2  (3)  4   5   6   7    5x5 board, () best point
   1  2 (3  4) 5  6  7  8  9    9x9 board , () area uploaded
   1  2 (3) 4  5  6  7  8  9    9x9 board,  () point selected by search

the local search on the 9x9 board will gibe 3-3 point as the best opening.

Then you upload that (9x9)3-3 point to the 13x13 board, giving an area of size
3x3 located in the southwest : points 3-3 to 5-5

   1  2 (3) 4  5  6  7  8  9  9x9 board
   1 2(3 4 5)6 7 8 9 A B C D  13x13 board, () area aploaded
   1 2(3)4 5 6 7 8 9 A B C D  13x13 board  () 5-5 point selected.

again the local search runs, and my come with the 3-3 point as a result on the
13x13 board (and we know that 3-3 or 3-4 are the best opening on 13x13).

Then you upload that (13x13)3-3 point to the 19x19 board, giving an area of size
3x3 located in the southwest : points 3-3 to 5-5

   1  2 (3) 4  5  6  7  8  9  A  B  C  D  13x13 board
   1 2(3 4 5)6 7 8 9 A B C D E F G H I J  19x19 board

And so we come with the result that we expected : 3-3, 3-4, 4-4 and 4-5 (and
perhaps 5-5 and 3-5) are the best first move on a 19X19 board.

So you see that the center opening on the 5x5 board does not "translate all the
way up to 19x19.". Insted, because of local searches, it expands in the very
familiar openings in the corner that we are used to.


> -----Original Message-----
> From: Serge Boisse [mailto:boisse@xxxxxxxxxxxxxxxxx]
> Sent: den 2 oktober 2000 09:31
> To: computer-go@xxxxxxxxxxxxxxxxx
> Subject: Re: computer-go: perfect play : a new fractal algorithm
> 
> "Johan Roos (QCS)" wrote:
> >
> > Interesting.
> >
> > I suppose this algo would suggest a move in the center as a first move?
> >
> > /Johan
> >
> NO !
> suppose you play on a (level zero) 19x19 board, and the level 1 board is 13x13 :
> then the best openings on a 13x13 are 2-3, 3-3 and 3-4 points, wich translates
> into 3-3, 3-4, 4-4 and 5-4 points when "uploaded" onto the larger board (simple
> linear coordinate transfo).
> Then the fractal algo will open the game with one of these points, which are the
> bests ones one a 19x19 booard (at least, these are the most common)