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Justaminute: It shouldn't be too difficult to construct a game where black gives mate from a distance on move 20.
White moves axb3, bxc3, Na3-c4, Ba3, Qb1. Black moves axb6, Ra6-a5-a4xa3xa1. Then both make random moves on the kingside, and on move 20 Black plays Rxb1 with possible mate.