monte-carlo a go-go

I came across this article on a Go-playing program and thought it was interesting. Particularly this aspect of it (from wikipedia):
One major alternative to using hand-coded knowledge and searches is the use of Monte-Carlo methods. This is done by generating a list of potential moves, and for each move playing out thousands of games at random on the resulting board. The move which leads to the best set of random games for the current player is chosen as the best move. The advantage of this technique is that it requires very little domain knowledge or expert input, the tradeoff being increased memory and processor requirements.
Categories: dereferenced, monte-carlo methods, technology
I wonder if there’s a structured random sample that would converge more surely…
Yes, quasi monte carlo methods use a variety of suitably abstruse techniques to just this end