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How is Bilbo's share of treasure determined according to Thorin in The Hobbit?
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Bilbo's share of the treasure in The Hobbit is determined by a contract signed by Thorin, which promises him "cash on delivery, up to and not exceeding one fourteenth of total profits (if any);" along with covered travel and funeral expenses. Although initially promised this share, conflicts arise over the Arkenstone, leading to tensions with Thorin. Ultimately, after Thorin's death, Bilbo is given an equal share of the treasure.
In the classic fantasy The Hobbit, or There and Back Again by J.R.R. Tolkien, Bilbo joins a quest to regain the treasure of the dwarves from Smaug the Dragon in the Lonely Mountain. He is recruited by Gandalf the wizard to join 13 dwarves as the expedition's burglar. At first, Bilbo is skeptical and frightened, but then his hidden adventurous nature takes over and he decides to go along with them. After a party at his hobbit-hole the night before, Bilbo wakes up late and the dwarves have already left. However, Gandalf tells him of a message on his mantle that directs Bilbo to meet them at the Green Dragon Inn in Bywater. The note, which is signed by Thorin, gives precise details of Bilbo's share of the treasure:
Terms: cash on delivery, up to and not exceeding one fourteenth of total profits (if any); all traveling expenses guaranteed...
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in any event; funeral expenses to be defrayed by us or our representatives, if occasion arises and the matter is not otherwise arranged for.
Bilbo has to run out his door and hurry as fast as he can to Bywater, where he finds the dwarves mounted on ponies packed with supplies and ready to set off. That's how Bilbo's amazing journey begins, and those are the terms of the deal that Thorin and his company make with him.
Thorin says that Biblo will get an equal share if Bilbo the burglar helps Gandalf and the band of thirteen dwarves steal the treasure from the dragon Smaug. The dwarf Thorin wants the treasure because it belonged to his father, and he promises Biblo a share of the treasure if they find it. When they do, Bilbo can sneak off because he has the ring. Bilbo rescues the Arkenstone of Thrain, which he thinks will make him a hero because this is a very important Dwarf jewel. Thorin gets angry when he finds out that Bilbo has it, because he thinks Bilbo is keeping it from him. Thorin refuses to share the treasure, but when he dies Biblo is given an equal share.
How does Thorin determine Bilbo's share of the treasure in The Hobbit?
It is at the beginning of Chapter 2 when we are presented with the terms of the contract for hiring Bilbo Baggins' services as a thief. When Bilbo wakes up after the party the night before, he sees a note that the dwarves have left him, detailing the arrangements:
Terms: cash on delivery, up to and not exceeding one fourteenth of total profits (if any); all travelling expenses guaranteed in any event; funeral expense to be defrayed by us or our representatives, if occasion arises and the matter is not otherwise arranged for.
Bilbo is thus promised a fourteenth of the share of the treasure, which of course he uses by taking the Arkenstone to Bard to prevent an outbreak of violence between the dwarves and the elves and men.