Mathematical games can be used to engage learners, promote fluency and deepen conceptual understanding. When considering the level of engagement of students, sometimes a small change can have a large impact. Something as simple as switching dice for cards in a game and, importantly, introducing a 'non-replacement' mechanism to the gameplay, can help promote a higher level of strategic thinking. This article presents four mathematical games and how they can be modified using non-replacement, adding a level of complexity to classroom gameplay for both whole-class and small group games and helping to make these experiences more cognitively and emotionally engaging.