Much of Bilbo's good luck in The Hobbit has to do with his possession of the ring of invisibility, which allows him to do things like spy on the spiders in Mirkwood forest and learn Smaug's weakness, which allows the dragon to be killed. Even his initial good luck in finding the Ring happens because the Ring had grown tired of Gollum and was looking for someone new to carry it. In this way, The Hobbit is mainly setting up The Lord of the Rings, and we can see Bilbo's good luck as being the beginning of his relationship with the Ring, which begins well but, by the beginning of The Fellowship of the Ring, is making him feel like "butter spread over too much bread."
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