Coincidences are a source of amusement and occasional unease in our lives. They often appear to defy the laws of probability – even to demand a supernatural “explanation”. Probability theory reveals the root cause of this disparity between expectation and reality. As I shall show, it stems from the fact that our intuitive estimate of the probability of a coincidence occuring becomes increasingly inaccurate the more “outlandish” the coincidence seems to be.