Play-the-Winner Rule and Inverse Sampling in Selecting the Better of Two Binomial Populations

In this article two sampling rules are analyzed for the problem of selecting the better of two binomial populations. The first is alternate sampling (vector-at-a-time) and the second is the “play-the-winner” rule introduced by Robbins [3], and discussed by Zelen [8]. The termination rule studied is inverse sampling. One result is that the probabilities of correct selection for these two methods of sampling are exactly equal. It is also found that the play-the-winner sampling is uniformly preferable to the vector-at-a-time sampling rule in the sense that for the same probability requirement the expected number of trials on the poorer population is always smaller.