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Reinforcement learning has shown much success in games such as chess, backgammon and Go. However, in most of these games, agents have full knowledge of the environment at all times. In this paper, we describe a deep learning model in which agents successfully adapt to different classes of opponents and learn the optimal counter-strategy using reinforcement learning in a game under partial observability. We apply our model to FlipIt, a two-player security game in which both players, the attacker and the defender, compete for ownership of a shared resource and only receive information on the current state of the game upon making a move. Our model is a deep neural network combined with Q-learning and is trained to maximize the defender's time of ownership of the resource. Despite the noisy information, our model successfully learns a cost-effective counter-strategy outperforming its opponent's strategies and shows the advantages of the use of deep reinforcement learning in game theoretic scenarios. We also extend FlipIt to a larger action-spaced game with the introduction of a new lower-cost move and generalize the model to $n$-player FlipIt.