Jacques Basaldúa wrote:
Very good analysis and I would like to contribute a 4th reason:
As Luke Gustafson pointed out, we have to contemplate the simulation
as a _stochastic process_. We want to determine the conditional
probability of a win given a particular move is made. And that depends
on the _length of the simulation_. Dramatically! This is a reason
against scalability of global search MC/UCT. If the simulation is
500 moves long (Chinese rules with recaptures, etc.) the observed
variance at an early move blurs out everything.
Just a simple stochastic process: Count a dollar each time you
correctly predict a p=1/2 coin thrown n=500 times. The expected
average is (obviously) 250, but the expected variance of that measure is
n·p·(1-p) = 125 proportional to n.
Good point. This leads to another thought that I have been wondering
about. That is I question whether using more time to search more
simulations in the opening is the best approach. For the opening,
selecting reasonable robust moves that tend to lead to more favorable
options is probably a good objective. The lengths of the simulation are
perhaps too long to expect anything better. Later towards the
pre-middle to middle game it is very critical to play such that the
positions tactical potential is exploited such to secure connections and
eye space, etc. It would seem to me that focusing the highest
concentration of time and number of simulations during this part of the
game might be most advantageous.
It would be interesting for someone with a decent MC player to do an
experiment like this with one version concentrating highest number of
simulations in the opening and one concentrating in the middle game, but
otherwise equal and see which version wins more often.
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