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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.
The Hobbit (book, movies, and creative franchise) Let's start with the obvious, the ring. The one ring is the object that Tolkien uses to tie his initial stories about Middle Earth together; Bilbo finds it, leaves it for Frodo and then Frodo meanders off on a quest to destroy it. Although it started of as simply a ring (and not the ring), it nevertheless plays an important role in both stories.