Bilbo and Smaug riddle their way into a discussion. What is the purpose of this conversation?

The purpose of the riddles in the interaction between Samug and Bilbo is Smaug's desire to know the hobbit. Unlike the play between Bilbo and Gollum, there are no rules, and Bilbo's words are spontaneous and unplanned. Bilbo's interaction with Smaug, however, is an attempt to hide who is is without angering Smaug by leaving his questions unanswered.