Hello,

some piece of information for those who are interested
in a strange branch in the history of Monte Carlo game tree search.

I found some very nice work by people in "theoretical" combinatorics.
It seems that the starting point was a paper by Chvatal and Erdoes
in 1978: Biased positional games, Annals of Discrete Math. 2 (1978), 221–228. 
Jozsef Beck went forward in their direction, and coined the
term "probabilistic intuition" in a paper from 1993. What he meant
by "Probabilistic intuition" is well described in another paper by him 
from 1998: J. Beck, Foundations of Positional Games, Random Structures 
and Algorithms, 9 (1996), 15–47.
On bottom of p.15 Beck writes:
"... in many complicated games, the outcome between two perfect palyers
is the same as the 'majority outcome' between two 'random players' (random
game)."
Built on his work is for instance a paper from 2009 by Gebauer and Szabo
http://www.inf.ethz.ch/personal/gebauerh/Connectivity.pdf
where also the new name "random graph intuition" instead of "probabilistic
intuition" is introduced.

To state it clearly: Very likely these results will not help in search
for a perfect Monte-Carlo go player. Nevertheless, I find it interesting
that "pure theory in combinatorics" found such a way to classify
some deep games by means of Monte-Carlo.

Ingo.
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