By learning a range of possible times over which the effect of an action can take place, a robot can reason more effectively about causal and contingent relationships in the world. An algorithm is presented for learning the interval [t1min , t1max ] of possible times during which a response to an action can take place. The algorithm was implemented on a physical robot for the domains of visual self-recognition and auditory social-partner recognition. The environment model assumes that natural environments generate Poisson distributions of random events at all scales. A linear-time algorithm called Poisson threshold learning can generate a threshold T that provides an arbitrarily small rate of background events (T) if such a threshold exists for the specified error rate. Keywords Contingency, poisson threshold learning, developmental robotics, causality, self-recognition, social partner recognition