Significant attention has been given to developing data-driven methods for tailoring patient care based on individual patient characteristics. Dynamic treatment regimes formalize this approach through a sequence of decision rules that map patient information to a suggested treatment. The data for estimating and evaluating treatment regimes are ideally gathered through the use of Sequential Multiple Assignment Randomized Trials (SMARTs), though longitudinal observational studies are commonly used due to the potentially prohibitive costs of conducting a SMART. Observational studies are typically powered for simple comparisons of fixed treatment sequences; a priori power or sample size calculations for tailored strategies are rarely if ever undertaken. This has lead to many studies that fail to find a statistically significant benefit to tailoring treatment. We develop power analyses for the estimation of dynamic treatment regimes from observational studies. Our approach uses pilot data to estimate the power for comparing the value of the optimal regime, i.e., the expected outcome if all patients in the population were treated by following the optimal regime, with a known comparison mean. This allows for calculations that ensure a study has sufficient power to detect the need for tailoring, should it be present. Our approach also ensures the value of the estimated optimal treatment regime has a high probability of being within a range of the value of the true optimal regime, set a priori. We examine the performance of the proposed procedure with a simulation study and use it to size a study for reducing depressive symptoms using data from electronic health records.