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[This question refers to the major revisions made to the Gollum chapter, Riddles in the Dark, not to the multitude of minor changes made elsewhere.] In the original 1937 edition of The Hobbit Gollum was genuinely willing to bet his ring on the riddle game, the deal being that Bilbo would receive a present if he won. Gollum in fact was dismayed when he couldn't keep his promise because the ring was missing.
In The Hobbit, set 60 years before the events in The Lord of the Rings, Tolkien relates the story of the seemingly accidental finding of the Ring by another hobbit, Bilbo Baggins, who takes it to his home, Bag End.