Airports are attractive targets for terrorism, as they are designed to accommodate and process large amounts of people, resulting in high concentration of potential victims. A popular method to mitigate the risk of these attacks is through security patrols, but resources are often limited. Game-theory is often used as a methodology to find optimal patrol routes for security agents, such that security risks are minimized. However, game-theoretic models suffer from payoff uncertainty and often rely solely on expert assessment to estimate game payoffs. Expert knowledge should not be the only source of information since key domain features, such as attacker behaviour, which contribute to the game payoffs are hard to estimate precisely. To address this shortcoming, we propose a novel approach to estimate payoff uncertainty through agent-based modelling. We simulate different attacker and defender strategies in an agent-based model to estimate game-theoretic payoffs, while the framework of game-theory is used to find optimal defender policies. The results of the experiments show that the optimal security patrol gives special emphasis to high-impact areas, such as the security checkpoint, to reduce the total security risk. Our results further show that by strategically randomizing patrol routes, higher expected rewards for the security officer are achieved.