In this article there has been considered a modern method of machine learning, which is called reinforcement learning. In tasks, that are solved based on interaction, is often impractical to try to get the desired behavior examples of an intellectual software agent, that would be both correct and appropriate for all situations, since the uncertainty conditions exist, arising from incomplete information about an environment and possible actions of other bots or humans. Therefore, the software agent should be trained on the basis of its own experience. An important advantage of the reinforcement learning is the possibility of learning a bot Ā«from scratchĀ» by the balanced combination (search of the compromise) of the Ā«explorationĀ» ā Ā«exploitationĀ» modes and learning of the strategies, which allow to sacrifice some scores at this stage for the sake of greater benefit in the future. Researches in the field of the reinforcement learning can be considered as a part of the overall process, that developed over a last few years. It consists of an interaction of an artificial intelligence and other engineering disciplines that is why reinforcement learning develops ideas drawn from the optimal control theory, stochastic optimization and approximation, following common and ambitious goals of the artificial intelligence. In this work there has been presented the mathematical apparatus of reinforcement learning with the usage of the model-free Q-learning method, practical aspects of its application have been shown, also an effective strategy for the bot learning in an artificial environment (computer video game) has been developed. The role of the observed object variables is accepted by the information used by the agent, and the hidden variables are long-term estimates of the benefit it gains. Depending on the current status of the environment and bot activities is calculated the benefit function, which is received by the agent at the next time moment. With the usage of the developed software, experimental researches of the considered method have been performed. The optimal setting parameters, curves and time learning of the bot have been obtained. The research results may be useful for computer systems of various functional purposes; they can be used in modeling and design, in automatic control and decision making systems, in robotics, in stock markets, etc.