We explore the potential of stereoscopic 3D (S3D) vision in offering distinct gameplay using an S3D-specific game called Deepress3D. Our game utilizes established S3D design principles for optimizing GUI design, visual comfort and game mechanics which rely on depth perception in time-pressured spatial conflicts. The game collects detailed S3D player metrics and allows players to choose between different, evenly matched strategies. We conducted a between subjects study comparing S3D and monoscopic versions of Deepress3D that examined player behavior and performance and measured user-reported data on presence, simulator sickness, and game experience. Confirming previous results, stereo users reported higher spatial presence. More importantly, for the first time, our game metrics indicate that S3D vision can measurably change player behavior depending on actual game content and level design, without necessarily affecting performance or emotional experience. These findings indicate the potential for optimizing applications for stereo users distinguishing them as a distinct group in HCI research.