Because during the unexpected party, Thorin promised Bilbo 1/14th payment of the treasure in return for Bilbo's services as a 'thief'. Though Bilbo did not do much in the way of being a thief, he did save the dwarves from Thranduil, as well as help them gain entrance into the mountain. They also wanted him on the journey because it would have been unlucky to take on their journey with 13 members. At the end of their adventures, Bilbo had obviously earned his 1/14th share, so Thorin fulfilled his promise and sent Bilbo home with a chest of treasure (though it is hinted later on in LotR that Bilbo ended up receiving more).
He had borrowed several handkerchiefs from Elrond. He had complained of having left home without any of them. Bilbo left him 'such small gifts as he would accept' when they stopped on the return trip.
At the unexpected party, Gandalf gives Thorin a map of the Lonely Mountain, which has information about a secret door and the key to the secret door.
Well, as he justifies it to himself, he was entitled to a one fourteenth share of the treasure and which fourteenth was not specified. Though he was pretty sure that the Arkenstone would not be a part that he would get.
Bilbo never intended to keep the Arkenstone. He only took it because he saw the feverish greed that overtook the Dwarves when the saw their long lost treasure. Knowing how badly Thorin coveted the Arkenstone, Bilbo kept it and later used it to bargain for his share of the treasure (which he intended to share with Bard and Thranduil). What it revealed was that deep at heart, Bilbo was a good person and only wanted to do what was right. It was why Gandalf was drawn to him in the first place.
He is hoping that the desire for the Arkenstone would force Thorin to negotiate with the Men and Elves instead of fighting with them.Bilbo believes that if the men and elves have the Arkenstone, which Thorin values even more than gold, they may be able to convince the dwarves to bargain with them. If an agreement can be reached, it will spare a good deal of bloodshed.Also, Bilbo is getting quite tired of being trapped in the mountain, and wants to be somewhere with green grass underfoot and better meals.
He had borrowed several handkerchiefs from Elrond. He had complained of having left home without any of them. Bilbo left him 'such small gifts as he would accept' when they stopped on the return trip.
At the unexpected party, Gandalf gives Thorin a map of the Lonely Mountain, which has information about a secret door and the key to the secret door.
Bilbo snuck out of the Dwarves camp and delivered the Arkenstone to Bard.
Well, as he justifies it to himself, he was entitled to a one fourteenth share of the treasure and which fourteenth was not specified. Though he was pretty sure that the Arkenstone would not be a part that he would get.
It clearly shows that they are serious about the adventure and that it would be dangerous. They agreed to give Bilbo one 14th of the haul and to cover any funeral expenses if needed.
Bilbo never intended to keep the Arkenstone. He only took it because he saw the feverish greed that overtook the Dwarves when the saw their long lost treasure. Knowing how badly Thorin coveted the Arkenstone, Bilbo kept it and later used it to bargain for his share of the treasure (which he intended to share with Bard and Thranduil). What it revealed was that deep at heart, Bilbo was a good person and only wanted to do what was right. It was why Gandalf was drawn to him in the first place.
He is hoping that the desire for the Arkenstone would force Thorin to negotiate with the Men and Elves instead of fighting with them.Bilbo believes that if the men and elves have the Arkenstone, which Thorin values even more than gold, they may be able to convince the dwarves to bargain with them. If an agreement can be reached, it will spare a good deal of bloodshed.Also, Bilbo is getting quite tired of being trapped in the mountain, and wants to be somewhere with green grass underfoot and better meals.
That was the agreement when they hired Bilbo to go with them as a burglar. Bilbo carried the letter with him throughout the journey: Terms: cash on delivery, up to and not exceeding one fourteenth of total profits (if any); all traveling expenses guaranteed in any event; funeral expenses to be defrayed by us or our representatives, if occasion arises and the matter is not otherwise arranged for.
{| |- | Gandalf did not give Thorin a gold chain. Gandalf gave Thorin the key that he had gotten from Thorin's father. Thorin then took the key and placed it on a gold chain that he was wearing around his neck. |}
Gandalf only gives Thorin the key and the map (they go together) because they are rightfully his( being given to Gandalf by Thorin's relatives).
Bard keeps the arkenstone and will give it back to Thorin later if he can receive part of the share
Bard told Thorin that Thorin must give Bard a portion of the treasure to rebuild Esgaroth, or he would be considered the foe of the lake-town.