["Journal of Applied Econometrics, EarlyView. ", "\nABSTRACT\nThis paper introduces a novel method to adaptively design randomized experiments. For randomized experiments with a pilot stage, or multistage experiments, Hahn et al. (2011) propose an adaptive experimental design that adjusts the next stage's propensity score based on data from the previous stages. This paper discusses how the discretization of covariates affects the precision of the estimation of the average treatment effect (ATE) through the estimated propensity score for the next stage. Also, this paper proposes an algorithm using the bootstrap technique to find the optimal level of discretization of covariates. Monte Carlo simulations and an application with actual data show that the suggested method performs well.\n"]