In this paper, a new allocation rule for treatment assignments in sequential clinical trials is proposed. The stratified and randomized play-the-winner rule (SRPWR) is an extension of the randomized play-the-winner rule to more than two treatments. It is applicable to cases where the probabilities of success of a treatment depend on both treatments and known confounders (e.g., patient's age, gender and disease status). On average, demonstrate that the SRPWR assigns more patients to the better treatment, while eliminating the selection bias and allowing delayed responses to treatments.