This article focuses on personalised games, which we define as games that utilise player models for the purpose of tailoring the game experience to the individual player. The main contribution of the article is a motivation for personalised gaming, supported by an extensive overview of scientific literature. The motivatin concerns (a) the psychological foundation, (b) the effect on player satisfaction, (c) the contribution to game development, and (d) the requirement for achieving ambitions. The provided overview of scientific literature goes into the subject of player modelling, as well as eight adaptive components: (1) space adaptation, (2) mission/task adaptation, (3) character adaptation, (4) game mechanics adaptation, (5) narrative adaptation, (6) music/sound adaptation, (7) player matching (multiplayer), and (8) difficulty scaling. In the concluding sections, the relationship to procedural content generation is discussed, as well as the generalisation to other domains.