This article proposes a mathematical model that helps to track a player’s game actions and present them in a structured form. The gaming process is presented as a set of states that are connected by a player’s actions. Each state is a set of predicates that characterize the player’s knowledge about the game. This mathematical model was developed as a step in achieving the general goal of the research branch, which is to increase the safety of an information system from social engineering attacks by developing a serious game. This serious game is aimed at improving players’ skills in recognition and counteraction to social engineering attacks as well as at raising awareness among employees.