On game space size

["Imrich Kovac" <imrich_kovac@xxxxxxxxxxx>]

I was following this list for a while and
this is my first contribution.
So I would like say hello to all participants.

I would try answer some questions and put some additional notes
on this topic.


> I don't quite know what you do with the map. But this is what I 
think:
 ...
> So if you could abtain a 3-D table (size_of_board, 
stones_on_the_board,
> %_of_illegal_positions), then you would make a significant 
contribution to
> the computational go theory. :)

I thing Pieter is trying to do not use map and calculate only 2-D 
table
(size_of_board, %_of_illegal_positions). No matter how many stones for
each side and how many stones on the board at all.
But I think it is not a big problem to create your 3-D table or 4-D 
table
(size_of_board, stones_of_one_color, stones_of_second_color,
%_of_illegal_positions) using Pieter's method.


> How are you generating your configurations?? ie how do you know
> how many pieces to put on of each color? Is it all random from 
scratch
> i.e. pick X random blacks Y random white's put generate X random
> coordinates for black Y random coordinates for white, place on 
board,
> evaluate for legality, repeat?
>
> Or do 'grow' your board? w/ resets? i.e randomly place a black piece
> (evaluate) randomly place white piece (evaluate), repeat, all the 
while
> counting and dropping all configurations which are illegal, until 
the
> board gets filled up, and then repeat.
>
> Also are you using an acceptance/rejection criterea at all for
> test configurations? i.e. how would the numbers be different if you
> biassed your sampling w/ a move evaluation function from a
> generic go playing program?  (Using scheme 2)

Generating of configurations:
For each place on  board pick randomly from (-1,0,1) 
(black,empty,white).
May be that is the same as yours scheme 1?

Evaluation of configuration:
Generate random configuration 'C'
In 'C' flood empty positions into white positions
If any white stays
  'C' is illegal   (1)
else
  In (initial !)'C' flood empty positions into black positions
  If any black stays
    'C' is illegal   (2)
  else
    'C' is considered as legal (3) // I will have note for this
end if;

My notes are:
I'm not sure about that all (3) must be legal positions.
I already sent example of configuration of only one stone
which is white. This is legeal for method above but not legal
in Go.

Some configurations can be legal for black on move but
illegal for wihe on move.

Also there could be configurations diferent numbers of stones
for each color but with no mark of capturing (enclosed path...).

... so not all configurations (3) are achievable from empty board.

I think we can use results of Pietar's method as upper bound
and try to found some additional validations fo reduce (3).

Regards
Imrich Kovac

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