 Reichenbach’s discussion of the relations of probability and causality was begun in his doctoral thesis, and continued in his 1925 paper (Reichenbach 1925d) which, until The Direction of Time, he often cited himself with approval. In The Direction of Time Reichenbach acknowledges that the 1925 claims were incorrect and formulates a new “Principle of the Common Cause” this way: “If an improbable coincidence has occurred, there must exist a common cause” (p. 157). In any instance, he says, the conclusion of the principle is not certain but only probable, the more probable the more frequent the coincidences. He formulates four conditions he says are satisfied when an association of simultaneous occurrences of A and B is due to a common cause, C, simultaneous with neither A nor B: C is not independent of A or of B, but A and B are independent conditional on C and also independent conditional on ~C. He says the principle is sometimes used in a weaker sense, requiring only that the probability of A and of B be raised by the occurrence of C, but he says, that the independence can usually be established “by the use of a more detailed description [of] the cause C” (p. 161, n.2). Reichenbach does not say that his conditions are sufficient for C to be a common cause of A and B, and as Artzenius has noted, they are not (Artzenius 1993 and the entry  Reichenbach’s common cause principle).  