Bilbo's "offer" here is to go down and have a second look at the dragon, now that he has stolen this golden cup. The dwarves have now been walled into the Lonely Mountain because the dragon has blocked the side door with trees and rocks and things, so Bilbo agrees to go spy on the dragon once more. What do you think the dwarves are hoping Bilbo will achieve here? Isn't there strength in numbers – is this the most sensible plan you can think of for dealing with Smaug? How might the following events of the novel have changed if Bilbo had actually succeeded in catching Smaug asleep a second time? Do you think Bilbo would have it in him to kill Smaug himself, under any circumstances?

From that the talk turned to the great hoard itself and to the things that Thorin and Balin remembered. They wondered if they were still lying there unharmed in the hall below; the spears that were made for the armies of the great King Bladorthin (long since dead), each had a thrice-forged head and their shafts were inlaid with cunning gold, but they were never delivered or paid for; shields made for warriors long dead; the great golden cup of Thror, two-handed, hammered and carven with birds and flowers whose eyes and petals were of jewels. (12.94)

"The Arkenstone! The Arkenstone!" murmured Thorin in the dark, half dreaming with his chin upon his knees. "It was like a globe with a thousand facets; it shone like silver in the firelight, like water in the sun, like snow under the stars, like rain upon the Moon!" (12.95)