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We consider the problem of inferring an ancestral state from observations atthe leaves of a tree, assuming the state evolves along the tree according to atwo-state symmetric Markov process. We establish a general branching ratecondition under which maximum parsimony, a common reconstruction methodrequiring only the knowledge of the tree, succeeds better than random guessinguniformly in the depth of the tree. We thereby generalize previous results of(Zhang et al., 2010) and (Gascuel and Steel, 2010). Our results apply to bothdeterministic and i.i.d. edge weights.

Sufficient condition for root reconstruction by parsimony on binary trees with general weights