In another paper, we have argued that the traditional randomized design of clinical trials is ethically infeasible in desperate medical situations and adaptive designs are morally required. We have also argued that in such situations, the appropriate designs must satisfy what we call the “Principle of interchangeability.” In this statistics paper, we show that the statistical model of bandit processes satisfies this principle of interchangeability. Moreover, we demonstrate that when such a model is used as an adaptive design, the total regret of successes lost is smaller when compared with simple randomization. We illustrate the results by the simple deterministic play-the-winner design.