Computers can now simulate simple game physics systems hundreds of times faster than real-time, which enables real-time prediction and visualization of the effects of player actions. Predictive simulation is traditionally used as part of planning and game AI algorithms; we argue that it presents untapped potential for game mechanics and interfaces. We explore this notion through 1) deriving a four-quadrant design space model based on game design and human motor control literature, and 2) developing and evaluating six novel prototypes that demonstrate the potential and challenges of each quadrant. Our work highlights opportunities in enabling direct control of complex simulated characters, and in transforming real-time action into turn-based puzzles. Based on our results, adding predictive simulation to existing game mechanics is less promising, as it may feel alienating or make a game too easy. However, the approach may still be useful for game designers, for example, as it allows one to test designs beyond one's playing skill.