Three-Face suffers from multiple personality disorder. Its physical manifestation is his face split in two radically different halves. A third face has grown at the top of his head.He bases his decisions on the flip of a coin. He has two villainous personalities and one benevolent one. The latter is typically outvoted and told to shut up.
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With most Dorkham Asylum patients being parodies of Batman villains, Three-Face is rather obviously based on Two-Face. His flipping a coin however is also reminiscent of the “Flip Decision” (February, 1953), a classic Donald Duck story by Carl Barks.