While reinforcement learning (RL) has been applied to turn-based board games for many years, more complex games involving decision-making in real-time are beginning to receive more attention. A challenge in such environments is that the time that elapses between deciding to take an action and receiving a reward based on its outcome can be longer than the interval between successive decisions. We explore this in the context of a non-player character (NPC) in a modern first-person shooter game. Such games take place in 3D environments where players, both human and computer-controlled, compete by engaging in combat and completing task objectives. We investigate the use of RL to enable NPCs to gather experience from game-play and improve their shooting skill over time from a reward signal based on the damage caused to opponents. We propose a new method for RL updates and reward calculations, in which the updates are carried out periodically, after each shooting encounter has ended, and a new weighted-reward mechanism is used which increases the reward applied to actions that lead to damaging the opponent in successive hits in what we term "hit clusters".