Chess

Chess, Go, and gomoku are proven to have unbeatable strategies (Zermelo's theorem). The theorem proves they exist—not what they are. In gomoku, the winning strategy is known, so tournaments use modified rules.

Napoleon once lost a chess match to the 'Mechanical Turk,' a machine that seemed to play on its own. It wasn't artificial intelligence — a person was hidden inside making the moves. People were fooled because lifelike automata were fashionable at the time.