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If I recall correctly:

  1. The agreement was that each dwarf would receive 1/14 of the treasure.
  2. Bilbo takes the Arkenstone, and though unspoken, is willing to give up his share for it.
  3. Bard demanded 1/12 of the treasure.
  4. Bilbo gives the Arkenstone to Bard.
  5. Three of the dwarves die (Fili, Kili, and Thorin).
  6. Dain honors the earlier agreement and gives Bard 1/14.
  7. Bilbo rejects his full share and takes just a couple bags.
  8. The Arkenstone is interred with Thorin.

Interestingly, perhaps, had Dain been given an equal share of the final result, 1/12 would be correct, as the original 14 minus the 3 dead plus the 1 Dale, is 12.

If each living dwarf got 1/14, that would leave 3/14 of the pie (pun intended) unclaimed. Bilbo also left most of his portion, meaning almost 4/14 was not touched.

The Arkenstone, which both Bilbo and Thorin suggested they would be willing to give up their portions for, was buried with Thorin; this may be considered his 1/14, or if not, at least make up for the portion of Bilbo's part left untaken.

So, how was the treasure actually divided? And which agreement with Dain gave him 1/14?

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Bilbo's deal was actually "cash on delivery, up to and not exceeding one fourteenth of total profits (if any)". Bilbo only took a tiny fraction of this in terms of gold and silver although the coat of mithril probably balanced things up. –  TheMathemagician Jul 11 at 14:03
    
Would the coat of mithril, being neither gold, silver, nor gem, nor given as treasure but as thanks, be considered part of the treasure? Though the "up to" is an excellent relevant detail! –  please delete me Jul 11 at 15:06
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While the mithril coat may have been worth ALOT compared to the shire as Gandalf mentions in the fellowship of the ring, In reality to the total horde in the mountain we can easily assume the dwarves had multiple sets of mithril armor. So i wouldn't say that the mithril coat really balances out his total 1/14th share. –  Himarm Jul 11 at 15:40
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Thorin explicitly makes it part of his share: 'Mr. Baggins!' he cried. 'Here is the first payment of your reward! Cast off your old coat and put on this!' –  TheMathemagician Jul 11 at 15:41
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+1 for "3/14 of the pie" :) –  David Conrad Jul 11 at 23:37

2 Answers 2

It looks like your answer contains all the detail that was in the story. All of the dwarves stayed in the lonely mountain so the bulk of the treasure stayed there.

Bard requested a share of the hoard because Smoug sacked Dale, including the emeralds of Girion, which the elven king ended up with because he loved forest green gems so much.

I don't think there was any agreement to give 1/14th away, I imagine Dain handed out gifts and rewards to anyone who helped overthrow the Goblins.

There's no reference in the books, but I always imagined Dain offered Beorn rich rewards too which were turned down.

Also the logistics of counting the value of the entire hoard, balancing the value of gems vs gold and dividing it by 14 would have taken years anyway. Practically I'd say it was more a case of loading some wagons or donkeys with gold and silver cups and plates to redecorate the rebuilt halls of Dale.

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A detail i left out, because i don't remember it, is the gems vs the gold and silver. I know that was a detail somewhere. As for the worth, (found via another question) forbes.com/sites/michaelnoer/2012/04/23/…. A little math could have gotten them a basic number. Or just weight the gold. With 11 dwarves wanting their portions, they would have weighed everything they hadn't stuffed in their pockets in short order. Even if it took a month, each would eagerly await his portion. –  please delete me Jul 11 at 13:11
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I just can't picture the dwarves actually wanting to know exactly what was theirs. They all had more wealth than they could spend and it's not like they could spend it on much anyway. Stage 2 was probably invite as many carpenters, stone masons, musicians, smiths of all types, weavers, bakers, guards, brewers etc to the Mountain to create real wealth. Once they're all established the next priority would be to create small coins so the 11 can buy a pint without paying by "handfull of dragon hoard" –  Mikey Mouse Jul 11 at 13:19
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I understand what you are saying. I happen to think otherwise though. :) I assume a dwarf to be like an accountant when it comes to gold, especially after their rings enflamed their gold lust. –  please delete me Jul 11 at 13:23
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Yeah, no doubt once the brewers are established the fights break out about Bombur having already drank more than his 14th share and they start trying to calculate backwards how much gold he should have been allowed to drag to the pub since they opened shop –  Mikey Mouse Jul 11 at 13:25
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And if they do act like accountants they probably spent the next 10 years arguing over whether that gold coin with the dragon claw has it's value on the balance ledger decreased due to being damaged goods or increased due to rarity. And if that magical harp that Kili played (which stayed in tune throughout the whole dragon occupation) should be valued at more or less than the original gilded cup that bilbo swiped from Smaug... both have sentimental value to consider. Fun to think about... –  Mikey Mouse Jul 11 at 13:45

I don't want to delete my old answer, but after reading all the comments and thinking about it while cycling to work. I think this is a more accurate answer.

As the Mathemagician pointed out, no agreement to give each dwarf an equal share was ever mentioned in the books. It does seem very unlikely that Thorin was going to divide up the hoard that was his fathers and his father's fathers into 14 equal parts. No doubt he intended to claim the hoard as his and reward his followers and friends as he felt they deserved.

The special agreement with Bilbo was drawn up to convince him to leave his comfortable home behind and come with them to the mountain. His share was to be "one fourteenth share of total profits, if any".

By this, no doubt they were thinking of any profits they made on the journey to the mountain (such as the pot of gold coins they took from the trolls, Bert, William and Tom) or anything that he might be able to steal from the dragon. Even Gandalf didn't think they would end up killing the dragon and claiming the entire hoard.

"that is why I settled on Burglary."

As Gandalf put it, it was a chance for Bilbo to make his fortune.

"Very amusing for me, very good for you - and profitable too"

When they drew up his contract, they were probably thinking: at the least they'll have to offer him a fair share of anything he burgles from under the nose of a dragon.

So 13/14 of the treasure was officially Dain's (as Thorins cousin and heir to the treasure) and it stayed in the mountain. From this, Dain no doubt paid every one of the surviving companions with wealth and titles.

Bilbo took the Arkenstone as his 1/14, gave it to Bard. Bard agreed to trade it to Thorin for the 14th share in gold (wrought and un-wrought) and Dain honored the agreement of the dead.

So, that's how the treasure got divided.

(Also is anyone else really excited to see how Billy Connelly portrays Dain in the upcoming movie?)

Ok, I'll replying to Brians comment in here, because there's so much more space:

I do agree Thorin considered the Arken Stone at much higher than 1/14, and was happy to write off 1/14th of his hoard to buy back the stone. He probably would have given over half of it, if it was the only way he could get the stone back.

Here's the quote about him choosing his reward:

“Now I am a burglar indeed!” thought he. “But I suppose I must tell the dwarves about it—some time. They did say I could pick and choose my own share; and I think I would choose this, if they took all the rest!”

Here are his last words at the Gate, which he took back later.

"I am betrayed!" It was rightly guessed that I could not forbear to redeem the Arkenstone, the treasure of my house. For it I will give one fourteenth share of the hoard in silver and gold, setting aside the gems; but that shall be accounted the promised share of this traitor, and with that reward he shall depart, and you can divide it as you will. He will get little enough, I doubt not. Take him, if you wish him to live; and no friendship of mine goes with him."

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"Bilbo took the Arkenstone as his 1/14" Was that ever agreed to? Agreement's usually require both sides to be happy with it. –  please delete me Jul 16 at 12:57
    
I got the impression Thorin did agree. He was about to throw Bilbo to the rocks, but then softened. "I will, and I will you go at that. Get down now to your friends" "And that shall be accounted the share of this traitor". Oh I forgot the quote about Bilbo being allowed to pick and choose his share of the treasure. So Thorin agreed that the Stone was at least valued at 1/14 and that Bilbo could pick and choose his 1/14 –  Mikey Mouse Jul 16 at 13:00
    
I thought Thorin was agreeing to let him keep the mithril armor (which was given, iiuc, as a reward for saving their lives). Thorin would never have agreed to give the Arkenstone. He was also willing to give his entire share for it. According to this answer, you suggest that Thorin was to keep 13/14s of the pile, meaning the Arkenstone was worth--to Thorin--13/14, not a measly 1/14. :) –  please delete me Jul 16 at 13:09

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