Asymptotic approximations to the expected sample size are given for a class of tests of power one introduced in . Comparisons are made with the method of mixtures of likelihood ratios, and an application is given to Breiman's gambling theory for favorable games.
"The Expected Sample Size of Some Tests of Power One." Ann. Statist. 2 (3) 415 - 436, May, 1974. https://doi.org/10.1214/aos/1176342704