  We consider the problem of computing the probability of regular languages of
infinite trees with respect to the natural coin-flipping measure. We propose an
algorithm which computes the probability of languages recognizable by
\emph{game automata}. In particular this algorithm is applicable to all
deterministic automata. We then use the algorithm to prove through examples
three properties of measure: (1) there exist regular sets having irrational
probability, (2) there exist comeager regular sets having probability $0$ and
(3) the probability of \emph{game languages} $W_{i,k}$, from automata theory,
is $0$ if $k$ is odd and is $1$ otherwise.
