Consider designing a clinical trial in stages, with two treatments and N exchangeable patients to be treated. Responses are dichotomous. The problem is to decide how large each stage should be and how many patients should be assigned to each treatment during each stage. Information is updated during and after each stage using Bayes' theorem. In planning stage j, responses from selections in stages 1 to j−1 are available, but interim responses in stage j are not available. Our analytical results consider two stages for two scenarios, when one treatment arm is known and when both treatment arms are unknown. The dominant term for the length of the first stage in an optimal design for general N is found explicitly. In both scenarios the order of magnitude of the length of the first stage is the square root of N. The finite‐N performance of asymptotically optimal allocation is compared with that of the true optimal allocation. Our numerical study also shows that, for a trial of three stages with one known arm, the optimal first‐stage sample size is asymptotically proportional to the cube root of N.