[computer-go] .. if Monte-Carlo programs would play infinite strong

[Jacques Basaldúa]

Maybe I did no explain my point well enough.

The problem with infinite is that we get a better approximation to a 
wrong value.

With few simulations we get that value with, say 1/10 error. With an 
astronomical amount
of simulations we get the same value with an error of 1e-200, but it's 
still wrong!. It is
proved that simulating a go position converges, but it does not converge 
to the same
value as if the position was played by perfect players, it only 
converges to the asymptotic
limit of random play.

I am not an MC developer, but as far as I know, UCT keeps a limited 
(i.e. n-ply) tree
in memory and intentionally unbiasses the nodes to make the convergence 
faster, that
does not change anything, assuming constant tree size.

A simple test :
1: after 100 simulations, choose the highest number in (0.96, 2.1, 3.18)
2: after 1e9 simulations, choose it in (0.9999999, 2.0000001, 3.000001)
You chose the same value (= same move).

That's why, I insist, if you don't increase the size of the tree and 
only get a better
approximation to a wishful but frequently misconceived value (the limit 
of random
play) witch is *not* a good evaluation of the game, you don't 
significantly improve
your play. Of course, if you increase the tree, you reach perfect play, 
that's not
the point.

Jacques.