It seems that there are at least three cases:
1: Choosing a random move from a uniform distribution
2: Choosing a random move from a nonuniform distribution (patterns etc.)
3: Choosing a move taking into account what has been chosen before
The concensus seems to be that numbers 1 and 2 are MC and 3 is QMC.
I don't think 3 is an accurate description of MC. Generally, MC is a
process where a number of "paths" (aka sequences of random numbers) are used
to sample some function. In go, a path would be a single playout, and the
function is the score. QMC is when the paths are constructed using variance
reduction techniques, meaning that they are more representative of the
sample space. AFAIK no one has used any QMC techniques in go; I really
doubt they would be much help because the function (the score) is not smooth
in the inputs (that is, small changes in the path are not small changes in
the score).
I think what is confusing the matter is the sample space--i.e. what games we
are evaluating. The standard MC engine's sample space is all games that
don't fill an eye. Better might be all games that don't fill an eye and
don't play self-atari. Mogo has an even more restrictive sample space,
designed to be a much better evaluation function.
Finally, UCT is not MC. MC is an evaluation function, UCT is a tree search
technique. You could just as easily use UCT with any other (stochastic)
evaluation fuction, or MC with any other tree search. It turns out that UCT
has proven to be very effective using MC evaluation.
So, one could say Mogo is UCT, with a MC evaluation function, with
heuristics to improve the MC games.
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