| Abstract: | The efficiency of a sequential test is related to the “importance” of the trials within the test. This relationship is used to find the optimal test for selecting the greater of two binomial probabilities, pα and pb, namely, the stopping rule is “gambler's ruin” and the optimal discipline when pα+pb≤ 1 (≥ 1) is play-the-winner (loser), i.e. an α-trial which results in a success is followed by an α-trial (b-trial) whereas an α-trial which results in a failure is followed by α b-trid (α-trial) and correspondingly for b-trials. |
