Re: On Game Space Size

[Avijit Ghosh <aghosh@xxxxxxxxxxxxxxxxx>]

On Thu, 29 Apr 1999, Pieter Cuijpers wrote:

> I will try to answer the questions I got in the last few mails now...
> 
> ----------------------------------------------------------------------------------
> Avijit: How are you generating your configurations ?
> 
> Answer: 
> 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.
> 
> Futhermore there are no 'moves' involved when trying to estimate the
> game space.
> In my definition the game space is the number of states a go-board can be in. Every legal configuration of stones on the board that 
> theoretically can be created using the rules of go is a board state.


	I see so its uniform from scratch (no acceptance, rejection
criterea and no moving along a path given a legal board)  and you are
defining (and gridding) all possible configurations of black,white.  There
are a ton of possible b,w,e configurations to test tho no?  I think the
number is something like  given N board positions M types of pieces, what
are the number of ways we can distribute N into M boxes (w/out
regard to distinguishability)? which i believe the formula is
something like 

	 (N + M -1)!                 (363!)          363*362*361
         -----------       or        ---------   =   ----------
         (N-M)!(M!)                  (360!)(3!)          6

or something like 8 million MC runs you have to do?? It would be
nice to sample over that rather than just running all those
configurations.. 


	-avi