In an intragalactic empire organized as an aristocracy (from Execs to lowly Sevens) the empire's ships are being attacked in hyperspace by the ships of the Misfits. To shoot a Misfit ship in hyperspace requires a Guesser to predict where the ship will have maneuvered to by the time the weapon beam reaches them. A Guesser is the main character of the story, and while his intuition and precognition are useful, he gets stranded on a planet with no way out.