How do Odysseus and his companions expect to be treated by the Cyclops? 

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When Odysseus and his crew find the cave of the Cyclops, along with all his animals and cheese, the crew begs him to take some food and return immediately to the ship.  The men seem to sense, intuitively, that they should not be found in the cave.  Even Odysseus had had a bit of a premonition, before he left the ship, that he would "meet a man arrayed in mighty power, a savage, ignorant of rights and laws."  He was right, because Polyphemus -- although he isn't ignorant of rights and laws -- chooses not to adhere to the codes that most ancient Greeks found acceptable.  

Odysseus, hoping that the Cyclops would feel bound by the religious imperative to provide hospitality to travelers, since they were believed to be protected by Zeus himself, refuses his men, and he stays to meet the owner of the cave in the hope that "he might offer gifts."  Odysseus believes he might get a gift because, often, a host would offer such a guest-gift to a traveler as a kindness.  Despite his premonition, he still seems to expect the Cyclops to behave hospitably, and this was a big mistake!

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