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1. Literally, a variation on traditional chess that involves multiple boards positioned at different heights. Also known as "3D chess." No, I'm not playing three-dimensional chess with you—I can barely play regular chess!
2. By extension, a very complicated or complex game, system, or strategy involving a deep understanding of the situation that one's opponents or adversaries lack. Everyone thinks he messed up by leaking that information, but he's just playing three-dimensional chess. He's eight moves ahead of all of us. Coaching against him is like trying to play three-dimensional chess.
See also: chess