Eventually Theseus would come along and be the undoing of the arrogant king. Despite the fact that Kerkyon was a formidable foe Theseus won because of his superior skill. He promptly killed Kerkyon.
This was one of the rare occasions where Theseus did not have to use trickery to defeat his foe (as he did with Sinis and Periphetes). Or to have outside help (as he did when Ariadne provided magical string to help Theseus find his way out of the Labyrinth. Theseus won purely with his own ability.