Play-the-Winner sampling for a fixed sample size with curtailment

In this paper exact expressions are derived for the probabilities of various events connected with the selection of the better of two binomial populations using a fixed sample size and the Play-the-Winner sampling rule. Sampling can be curtailed in some cases without altering the decision that would have been reached had the sampling been continued. This will result in a saving in the number of observations and also in a smaller number of observations on the poorer treatment.