  In a previous paper by the author, it was shown that the One sided Dyck is
uniquely ergodic with respect to the one sided-tail relation, where the tail
invariant probability is also shift invariant and obtains the topological
entropy. In this paper we show that the two sided Dyck has a double-tail
invariant probability, which is also shift invariant, with entropy strictly
less than the topological entropy. We also prove that this probability, along
with the two equilibrium probabilities of the Dyck shift are the only ergodic
double-tail invariant probabilities for the Dyck shift.
