This paper explores teachers' beliefs about the ways in which the use of digital games in schooling contexts impacted upon students who they believed to be in some way at risk of educational or social alienation or failure. Drawing upon the theoretical resources provided by Gilles Deleuze and Felix Guattari, the paper explores opportunities games-based learning created for students who had previously been positioned in narrow, limiting, or marginalized relationships to academic achievement or social acceptance. In describing teachers' beliefs about the various lines of flight that games-based learning was able to spark, the paper argues the importance of continuing to explore how at-risk learners might benefit from particular uses of games in schools.