When Odysseus finally reveals his identity to King Alcinous of Phaeacia, he says, "I am Odysseus, son of Laertes, who for all craft am noted among men, and my renown reaches to heaven." In other words, then, Odysseus knows that his craftiness and cunning are a big part of his identity, so much so that he references them in his own introduction.
After the crew's tragic encounter with the Ciconians at Ismarus, Odysseus does not send all his men ashore the next time they land somewhere. He lost six men from each ship at Ismarus and is intelligent enough to know that another such loss would be devastating to his fleet. Therefore, he "select[s] two" sailors and "a herald as a third" to go ashore in the Land of the Lotus-Eaters. This way, he cannot lose more than three men.
Later, when he and a handful of his men are trapped in Polyphemus's cave, Odysseus cleverly tells the Cyclops that his name is "No man" or "Nobody" (depending on your translation). Then, when the monster cries for help...
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