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To this day, a variety of approaches for providing local interpretability of black-box machine learning models have been introduced. Unfortunately, all of these methods suffer from one or more of the following deficiencies: They are either difficult to understand themselves, they work on a per-feature basis and ignore the dependencies between features and/or they only focus on those features asserting the decision made by the model. To address these points, this work introduces a reinforcement learning-based approach called Monte Carlo tree search for eXplainable Artificial Intelligent (McXai) to explain the decisions of any black-box classification model (classifier). Our method leverages Monte Carlo tree search and models the process of generating explanations as two games. In one game, the reward is maximized by finding feature sets that support the decision of the classifier, while in the second game, finding feature sets leading to alternative decisions maximizes the reward. The result is a human friendly representation as a tree structure, in which each node represents a set of features to be studied with smaller explanations at the top of the tree. Our experiments show, that the features found by our method are more informative with respect to classifications than those found by classical approaches like LIME and SHAP. Furthermore, by also identifying misleading features, our approach is able to guide towards improved robustness of the black-box model in many situations.