As a key component of collaborative robots (cobots) working with humans, existing decision-making approaches try to model the uncertainty in human behaviors as latent variables. However, as more possible contingencies are covered by such intention-aware models, they face slow convergence times and less accurate responses. For this purpose, we present a novel anticipatory policy selection mechanism built on existing intention-aware models, where a robot is required to choose from an existing set of policies based on an estimate of the human. Each of these intention-aware robot models anticipates and adapts to a different human’s short-term changing behaviors. Our contribution is the Anticipatory Bayesian Policy Selection (ABPS) mechanism which selects from a library of different response policies that are generated from such models, and converges to a reliable policy after as few interactions as possible when faced with unknown humans. The selection is based on the estimation of the human in terms of long-term workplace characteristics that we call types, such as level of expertise, stamina, attention and collaborativeness. Our results show that incorporating this policy selection mechanism contributes positively to the efficiency and naturalness of the collaboration, when compared to the best intention-aware model in hindsight running alone.