Research examining teachers' decision making is abundant for pedagogical activities, yet a neglected area is the study of factors influencing teachers when selecting mathematical games. This article sheds light on the factors considered when teachers' select a specific game to use in their primary mathematics classroom. Data from 248 Australian primary teachers was gathered via a questionnaire and thematically analysed. Results indicated four strongly endorsed factors: Mathematics is central; Accessibility and differentiation; Classroom management; and Engagement and enjoyment. Implications are discussed of how this study can inform the decision making of educational leaders, policy makers, and game designers.