No matter the opinion of Peter Jackson's The Hobbit trilogy, most will agree that Bilbo and Smaug's conversation is a great adaptation of the novel. Bilbo knew he could be eaten at any second, yet he managed to keep a conversation going with the dragon for a good amount of time. However, up until this point, Bilbo had spoken normally to everyone he met. So why did he speak in riddles when talking to Smaug?
It had already been established that Bilbo was good at riddles, as he spoke told to Gollum during their conversation under the Misty Mountains. But this wasn't by choice, as Bilbo was simply entertaining Gollum's wishes as he tried to find a way out. It was much later on, when Bilbo snuck into Erebor's treasure room, that Smaug the dragon awoke to confront the tiny burglar and decided to introduce himself through riddles and cryptic names.
Towering over the tiny Hobbit, Smaug asks, "Who are you and where do you come from, may I ask?" After some stuttering, Bilbo replies, "I come from under the hill... And under hills and over hills my paths lead. And through air, I am he who walks unseen." While this line may seem a bit random, it actually works in Bilbo's favor, as Smaug is far more intrigued by these titles and asks for more.
While it could be down to simple nerves, Bilbo was hesitant to give the dragon his full name. He was well aware of the destruction Smaug could cause and didn't want to give him any hints as to where he may live. And so, Bilbo chose to speak in riddles, of which The Hobbit author J.R.R. Tolkien writes, "This of course is the way to talk to dragons, if you don't want to reveal your proper name (which is wise), and don't want to infuriate them by a flat refusal (which is also very wise). No dragon can resist the fascination of riddling talk and of wasting time trying to understand it."
This not only reveals that Bilbo was avoiding his real name, but it also shows that Smaug enjoyed the riddles. Dragons are incredibly intelligent beings in Middle-earth, so something that required a little extra thought was appealing, especially for a dragon who had laid dormant for many years. The Hobbit novel also reads, "There was a lot here which Smaug did not understand at all... but he thought he understood enough, and he chuckled in his wicked side." This showed that Bilbo's plan worked, as he managed to keep Smaug somewhat entertained.
While it's unclear if Bilbo knew the riddles would help him, they quite possibly saved his life. Smaug viewed most people as simple insects, but Bilbo was, at the very least, able to stimulate his brain and likely gave the dragon a far calmer reaction than most. It also sums up Bilbo perfectly, as he was able to find a way to stall without fighting and once again was underestimated for his size.