Re: On game space size

["Imrich Kovac" <imrich_kovac@xxxxxxxxxxx>]

Pieter Cuijpers wrote:
> > 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;
>
> The initial is not nescessary because if initial 'C' <> 'C' the position
> is regarded illegal by (1)
By 'initial' I mean before first flooding.
If you remove some white stones in first flooding you can make new libreties
for black and make position legal from illegal.
May be I misunderstood your way of flooding ?


Pieter Cuijpers wrote:
> Imrich: I have a contra-example - the position with only one white stone. 
> This
> is legal according to logic above, but it is not possible to get it because
> black starts move.
>
> Answer: In theory it is possible to get it since black is allowed to pass 
> on the
> first move and since all black stones just may have been captured... 
> (Indeed
> those positions will never occur but they belong to the Game Space.)
OK, I forgot that player can pass move :).
Now I see that it is possible to make any positinon from (3) using pass 
rule.
(as Robert Jasiek proved)


Avijit Ghosh wrote
> > 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?
>
>
>    If you do it this way aren't you are sampling a
> gaussian distribution around w,b,e around 33% w 33% b 33% e?
> However I would guess that there should be a bias towards
> empty boards.. i.e. there are many more legal board positions
> when there are more empty settings than when there are less.
> So if you sample using a uniform distribution on w,b,e I would guess
> it will be harder to hit the board space w/ empty boards thus making
> the % legal boards / total boards lower than it should be??
Probability of empty positions is higher than black or white ofcourse
but only in real games. But we was talking about total game space
without consideration of probability of particular configurations
in real games. Thus an uniform distribution is correct.

Pieter Cuijpers wrote:
> I define the number of black and white stones and the boardsize.
> After that I make an empty board of boardsize x boardsize.
> Then I randomly pick a specified number of vertices to put the black stones 
> on.
> Then I randomly pick a specified number of vertices to put the white stones 
> on.
Only small question to which I'm not sure about answer:
If I put all black first and all black afterwards will it make black
configuration depend on white one ??
Can it change something on uniformity of samples final result ??


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