In the Multi-Robot Patrolling Problem, agents have to continuously decide which place to move next, after clearing their current location. This article proposes a distributed solution to the problem based on Bayesian decision. The system is modeled according to its current state, thus automating the local decisionmaking process in order to effectively patrol an area.Two strategies are presented and compared. In the first one, robots are self-interested and aim to maximize their local gain. The second strategy is more complex, taking into account gains as well as the distribution of agents in the space to reduce interference and foster scalability. In order to validate the proposed solution, realistic simulations, comparing with five state-of-the-art approaches, as well as experiments with physical multi-robot systems were conducted.