Response-adaptive randomization procedures, such as the Randomized Play-the-Winner (RPW), are treatment allocation rules for clinical trials that use available information on treatment outcomes to skew the allocation probability in favor of the treatment performing better thus far in the trial. Such allocation rules are based on the ethically desirable aim of reducing the share of patients allocated to the inferior treatment. This noble intent is overcome by statistical and logistical issues. One practical implementation obstacle of the RPW method is the estimation of required sample size and expected allocation shares. Unfortunately, this information is not readily available or easy to calculate. We present simulation results to provide a realistic assessment of the power and sample size required for successful implementation of the RPW rule for a study with primary outcome variable that is binary. Additionally, we discuss some practical approaches for sample size determination based on the RPW.