The idea of using wind power to charge electric vehicles (EVs) has attracted more and more attention nowadays due to the potential in significantly reducing air pollution. However, this problem is challenging on account of the uncertainty in the wind power generation and the charging demand from the EVs. Simulation-based policy improvement (SBPI) has been an important method for decision-making in stochastic dynamic programming and, in particular, for charging decisions of EVs in microgrids. However, the problem of allocating the limited computing budget for the best decision-making in online applications is less discussed. We consider this important problem in this work and make the following three major contributions. First, we show that the significant uncertainty in wind power generation forecasting could make the policy that is the outcome of an SBPI worse than the base policy. Second, we apply two existing methods to address this issue, namely, the optimal computing budget allocation (OCBA) for maximizing the probability of correct selection (OCBA_PCS) and the OCBA for minimizing the expected opportunity cost (OCBA_EOC). The asymptotic optimality is briefly reviewed. Third, we numerically compare the performance of OCBA_PCS and OCBA_EOC with the equal allocation (EA), a principle-based method, and a stochastic scenario-based method on small-scale and large-scale experiments. This work sheds light on the EV charging decision in general. Note to Practitioners-Together with the growing adoption of EVs in modern societies, there goes the challenge of how to satisfy the charging demand. Given the high uncertainty both in the wind power generation and in the charging demand, it is important to make decisions online using up-to-date estimation on the renewable power generation and the charging demand. Simulation-based policy improvement (SBPI) is shown both theoretically and practically to be useful to improve a given base policy in various applications, including this EV charging problem. However, the high uncertainty in forecasting could sometimes make the output of SBPI worse than that of the base policy. In this work, we first use numerical experiments to demonstrate the risk for such scenarios. Then, we propose to use two computing budget allocation procedures to address this issue. The asymptotic optimality of both algorithms is briefly reviewed. We demonstrate their performance on numerical experiments when there are only several EVs and when there are 100 EVs.