Sequential, multiple assignment, randomized trial (SMART) designs have become increasingly popular in the field of precision medicine by providing a means for comparing more than two sequences of treatments tailored to the individual patient, i.e., dynamic treatment regime (DTR). The construction of evidence-based DTRs promises a replacement to ad hoc one-size-fits-all decisions pervasive in patient care. However, there are substantial statistical challenges in sizing SMART designs due to the correlation structure between the DTRs embedded in the design (EDTR). Since a primary goal of SMARTs is the construction of an optimal EDTR, investigators are interested in sizing SMARTs based on the ability to screen out EDTRs inferior to the optimal EDTR by a given amount which cannot be done using existing methods. In this article, we fill this gap by developing a rigorous power analysis framework that leverages the multiple comparisons with the best methodology. Our method employs Monte Carlo simulation to compute the number of individuals to enroll in an arbitrary SMART. We evaluate our method through extensive simulation studies. We illustrate our method by retrospectively computing the power in the Extending Treatment Effectiveness of Naltrexone (EXTEND) trial. An R package implementing our methodology is available to download from the Comprehensive R Archive Network.