Despite the seedy settings (so evocative that they are almost a character in the story), this is almost a traditional morality play about humility and redemption. In the beginning Eddie is, as Fats notes, as fast as his nickname, slick, cocky, superficial. He wants to win for the kick of it. But inside him, there is someone who wants to win for the beauty of the game, and the honor of doing something surpassingly well. But before he can be a real winner, he must get rid of the part of himself that wants to lose, that is afraid to take a real risk. For that, he has to experience real loss, especially the loss of Sarah.
As Nietzsche said, "That which does not defeat me makes me stronger." Eddie is strengthened so by these experiences and by what he has learned, that he can no longer be contained by what had once been his entire world. Bert's threat that he will no longer be able to play big-time pool is meaningless to him. Even if Bert had offered him a 50-50 deal, he would not have taken it. That world is too small and self- contained for him now.