What is a probability of winning?
Or probability that the game tree node is a game-theoretic win? What
does this mean? One game node is either win or not, so there is no
stochastic experiment. You need to have a repeated experiment or a
population larger than one object to be able to speak of probabilities.
You have this larger population because your evaluation function has
to generalize to a huge number of positions. With 'real world' limited
computing power you will not be able to store all possible positions
independently or describe them perfectly by some limited number of
parameters. Consequently there will be multiple positions that
(implicitly) map to the same (or highly similar) internal state, thus
providing a basis for statistics.