The process of randomisation has in recent years come to play such a central part in experimental design that it is of some interest to find that it affords a means of resolving one of the oldest paradoxes which arose in discussions of gaming.Readers of Todhunter’s The Mathematical Theory of Probability will recall his account (sections 187-190, pp. 106-110) of the correspondence between Montmort and Nicolas Bernoulli on the rule by which the players might guide themselves most advantageously in the game called “le Her”.