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(Odysseus, in his tale:) ‘Cyclops, in the end it was no weak man’s companions you were to eat by violence and force in your hollow cave, and your evil deeds were to catch up with you, and be too strong for you, hard one, who dared to eat your own guests in your own house, so Zeus and the rest of the gods have punished you.’ (9.475-479)
Translation: "How do you like me now?"
(Odysseus:) 'So they spoke, but could not persuade the great heart in me, but once again in the anger of my heart I cried to him: "Cyclops, if any mortal man ever asks you who it was that inflicted upon your eye this shameful blinding, tell him that you were blinded by Odysseus, sacker of cities. Laertes is his father, and he makes his home on Ithaka." (9.500-505)
Odysseus managed to get (most) of his men off of the Cyclopes' island, but he just can't let a good thing be. He had to go and open his big mouth, practically giving Polyphemos his address and Facebook password. Smooth move, big guy.
(Polyphemos, in Odysseus's tale:) '"But tell me, so I may know: where did you put your well-made ship when you came? Nearby or far off?" 'So he spoke, trying me out, but I knew too much and was not deceived, but answered him in turn, and my words were crafty: "Poseidon, Shaker of the Earth, has shattered my vessel. He drove it against the rocks on the outer coast of your country, cracked on a cliff, it is gone, the wind on the sea took it […]." (9.279-285)
Polyphemos is trying to trick Odysseus, but the man of lies is one (or two, or three) steps ahead of him. You can't play a player, especially when that player is world-renowned for his game.