Personalizing treatment according to patient's characteristics is at the core of stratified or precision medicine. There has been a recent surge of statistical methods aiming at identifying so-called optimal treatment strategies, i.e., strategies that assign a given treatment to a patient according to his/her characteristics. However, when data from a randomized controlled trial are used to estimate the optimal treatment strategy, it is not straightforward to estimate and test the benefit of the estimated strategy as compared to not personalizing treatment. In this context, we propose a principled approach for the estimation of the benefit of an estimated treatment strategy, accounting for its uncertainty. This leads to formalizing a strategy that we term the max lower bound strategy. Numerical simulations are used to show it allows proper type I error rate control and coverage probabilities. The approach is extended to multiple covariates using machine learning techniques. It is then applied to the data of a randomized trial in antineutrophil cytoplasmic antibody (ANCA)-associated vasculitis.