Matchmaking connects multiple players to participate in online player-versus-player games. Current matchmaking systems depend on a single core strategy: create fair games at all times. These systems pair similarly skilled players on the assumption that a fair game is best player experience. We will demonstrate, however, that this intuitive assumption sometimes fails and that matchmaking based on fairness is not optimal for engagement. In this paper, we propose an Engagement Optimized Matchmaking (EOMM) framework that maximizes overall player engagement. We prove that equal-skill based matchmaking is a special case of EOMM on a highly simplified assumption that rarely holds in reality. Our simulation on real data from a popular game made by Electronic Arts, Inc. (EA) supports our theoretical results, showing significant improvement in enhancing player engagement compared to existing matchmaking methods.