Thanks Sylvain.
Sylvain Gelly wrote:
> The results are that in order to keep the same winning rate, you have to
> increase the number of simulations by something a little larger than
linear
> in the board area. From 9x9 to 13x13, you need something like 3 times
more
> simulations for the same winning rate. Same thing from 13x13 to 19x19. As
> the time of one simulation is linear in the board area, to keep the same
> level you have to give a time which increases as power ~2.5 of the board
> area. So between 9x9 and 19x19, you have to give 32x more time per
move for
> the "same play level" (always defined as winning rate against gnugo).
> This is far from being exponential. (maybe if it was exponential, there
> would be little interest to work on 9x9 go).
In terms of board size (i.o. board area) that is: boardsize^5
Remember my post on the 8th Feb 2007:
> What I mean is complexity is not, as one could expect, about
~boardsize^4.
> (The square of legal moves times the square of simulation length.)
But even
> more due to the increase in variance.
As Sylvain verifies it is: bsize^5 > bsize^4 just as I predicted.
Does anyone have an explanation for that other than the increase of
variance in the playouts due to their increased length?
Note that the difference is _exactly the increase in standard deviation_.
(proportional to sqrt(n) where n is proportional to bsize^2.)
BTW. There is another stone in the way of 19x19 computer go. Knowledge.
Humans play much stronger and do much stronger judgment than in 9x9. But
that is is not as easy to predict. A factor of 42 (19/9)^5 in hardware
power won't be enough. I hope. ;-)
Jacques.
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