Many classical sequential procedures model the partial sum difference process between two competing alternatives as a Brownian motion process. In this paper, the marginal probability of eliminating the best alternative is considered while modeling the partial sum difference process. We adaptively allocate the total amount of the probability of incorrect selection to every time point where the comparisons between alternatives are conducted and set the continuation regions to ensure the marginal probability of eliminating the best alternative does not exceed the probability assigned to each time point . We show by examples that under our framework, the procedure can be easily developed for both indifference-zone (IZ) and IZ free formulations.