Hmm... Gollum wasn't being fair either. You can't really reason with him. So Bilbo used that as an advantage. If Bilbo was eaten, a whole chain of events would have destroyed Middle-Earth.
|Me freaking out because Middle Earth could be destroyed|
Gollum could have found it again and taken it to Sauron. Or the Arkenstone was found and given to Thorin. Then the Battle of the Five Armies could have been won by the evil and everything would be so horrible! There are so many possibilities.
So no, it wasn't fair. But sometimes bad things have to happen in order for good to triumph in the end. It wasn't fair that all the people who fought in any war were killed. But good won in the end.
What do you think of Bilbo's last riddle?