Consider a clinical trial to compare two treatments where response is dichotomous and patients enter the trial sequentially. This paper investigates the conduct of such a trial where the “Play the Winner Rule” (PWR) is used to assign patients to the different therapies. The implementation of the PWR in a clinical trial tends to place more patients on the better treatment. Both theoretical and numerical investigations show that over a wide range of situations this rule leads to near optimum results when used in a two-stage manner. Furthermore, these results are insensitive to optimum sample size requirements.