Smaug the dragon on Forbes billionaires list

[Alzrius]

So I just got the new Kobold Courier, the periodic e-newsletter that goes out from Open Design each time a new issue of Kobold Quarterly is published. It's always an entertaining read, and this time was no different.

One of the articles pointed to a certain piece over on Forbes. I had no idea they did this, but every year alongside their list of billionaires, they also publish the Forbes Fictional 15, an examination of the fifteen richest characters from fiction.

What was really interesting, however, was that the item in the Kobold Courier referenced the Forbes article "How Much is a Dragon Worth?", which examines how they reach these numbers for the Forbes Fictional 15, using Smaug as an example.

And what's more, the author references the d20 Hypertext SRD to do it!

Check out the article. The next time your PCs raid a dragon's hoard, you'll have a much better idea of just how rich they really are!

 

[jonesy]

And they say they were aiming for a conservative minimum. Sheesh, I've never found that much in a dragon hoard. Where'd he even get all that? Stealing all that must have revalued all prices in Middle Earth.

 

[Alzrius]

And they say they were aiming for a conservative minimum. Sheesh, I've never found that much in a dragon hoard. Where'd he even get all that? Stealing all that must have revalued all prices in Middle Earth.

Actually, several posters comment on his article to note that he grossly underestimated Smaug's size. Poster geniesolmyr plugged in the corrected values to get a much more accurate number. Inspired, I did the same. Let's walk through the steps from the original article with the corrected size values and see what we get.

Smaug's hoard is calculated in three parts: the coins he sleeps on, the diamonds embedded in his body, and the Arkenstone of Thrain gemstone.

Smaug is noted as being a "red-golden color" in The Hobbit, and we'll assume that he's of colossal size due to his advanced age. Now the 3.5 Draconomicon notes the body sizes (from the shoulders to the base of the tail) of a colossal gold dragon as being 33 ft. long and 15 ft. wide. By contrast, a colossal red dragon is 35 ft. long and 15 ft. wide. Since we can't say for certain whether Smaug was a red dragon or a gold dragon who went bad (or, like in Eberron, the dragons don't have alignment determined by color), we'll average the measurements. Hence, Smaug's body is 34 ft. long and 15 ft. wide.

Assuming Smaug curls up on his hoard, we'll assume it has a diameter equal to his body length (34 ft.). Since Frodo, who is about 3 ft. tall, had to climb over the hoard, let's assume the hoard is twice his height, or about 6 ft. tall, and then add one extra foot for how Smaug's great weight was compressing it. So the hoard is 7 ft. tall altogether.

To keep it simple, we'll assume Smaug's hoard is a cone. The volume of cone that has a 17 ft. radius and 7 ft. height is (after rounding everything past the second decimal point) 2,118.5 cubic feet.

Now, we'll reduce this by 30% to account for miscellaneous objects in the hoard, such as air pockets, dead bodies from would-be thieves, and various objets d'art. This gives us 1,483 cubic feet of nothing but coins.

Since, as the article notes, Bilbo takes two chests of coins, one of silver and the other gold, we'll assume the hoard is 50% gold coins and 50% silver coins. That's 741.5 cubic feet of each.

The article then gives us the measurements for individual gold and silver coins:

A Kuggerrand, the South African Coin containing 1 troy ounce of pure gold, measures 32.6 mm in diameter and is 2.84 mm thick. Solving for the volume of a cylinder( V= pi r(squared) h), then converting cubic millimeters to cubic inches, then cubic inches to cubic feet gives a volume of 8.371354e-05 (or 0.00008371354) square feet for a single coin, containing one ounce of gold.

Using similar logic, an American Silver Eagle coin (40.6 mm in diameter, 2.98 mm thick), which contains one troy ounce of silver, has a volume of 0.000136 square feet.

This lets us calculate that there are 8.9 million gold coins and 5.5 million silver coins, presuming they were all one (troy) ounce coins.

Again, the article then gives us the value of an ounce of gold and silver:

At the moment gold is trading at $1423.8/ounce and silver at $37.5/ounce

From this, we calculate a grand total of $12,671,820,000 USD in gold coins, $206,250,000 USD in silver coins. Hence, the total coin value of Smaug's hoard is $12,878,070,000 USD. We'll round that down to $12,878,000,000 USD.

Now, on to the diamonds.

Presuming the body proportions above, and that a single scale covers a 6 inch square area, Smaug would have 2,040 scales on his body. We'll subtract 5% to account for the unprotected area that eventually led to his death, for a total of 1,938 scales that are covered with diamonds.

The article again lays out some basic figures and assumptions:

According to Diamond Helpers, diamonds above 5.99 carats are priced individually, so let's simplify and assume that all of Smaug's diamonds are 5.99 carats, priced at approximately $16,700 per carat or just over $100,000 each. Fifty diamonds per six-inch square dragon scale seems adequate to ward off most arrows

So in other words, each of Smaug's scales is worth $5,000,000 USD. With 1,938 of them like that, he has a total of $9,690,000,000 USD worth of diamonds.

Now, that just leaves the Arkenstone. The Hobbit tells us that it's worth 1/14 of the hoard's total value. So, let's run the numbers. The diamonds and coins together have a total value of $22,568,000,000 USD. To get the total value of the Arkenstone, we'll need to get the total value of the hoard and subtract the value of the coins and diamonds from that.

Since we don't want to skip to the magic number too early, we'll multiply 22,568,000,000 times 1.076923 (the percentage value of 14/13) and then subtract 22,568,000,000. This leaves us with $1,735,998,264 USD. We'll round that up to give the Arkenstone of Thrain a final value of $1,736,000,000 USD.

Add them all together and you get a total hoard value of $24,304,000,000 USD, in 2011's money.

So yeah, that hoard entering the market probably did throw off Middle Earth's economy pretty good.

 

[jonesy]

Add them all together and you get a total hoard value of $24,304,000,000 USD, in 2011's money.

Hmm. A thought occurs. Why was Sauron hanging aroung Mirkwood? I mean, Mirkwood specifically? Might he have been planning a little heist before Bilbo's gang showed up? Gandalf did say something about Sauron wanting to control Smaug.

 

[Theo R Cwithin]

Looks like Smaug's hoard, Tolkien-style, is way more fabulous than the same by D&D reckoning, though.

Using 3.5e assumptions, 50 coins per pound, and assuming troy weights, and a gold price of $1500/ounce:

One gp = 1/50th lb = 1/3rd ounce, or roughly $500 per gp.

Assuming Smaug is a great wyrm, CR26, with triple standard treasure, his hoard is valued at 80k gp (for being 20th level); plus 12 major magics at 40k gp each for being 6 levels over 20th; all that tripled.

That comes to 3x(80k + (12x40k) ) x $500 per gp = $840million.

D&D 3.5e dragons are veritable paupers!

 

[Alzrius]

Using 3.5e assumptions, 50 coins per pound, and assuming troy weights, and a gold price of $1500/ounce:

One gp = 1/50th lb = 1/3rd ounce, or roughly $500 per gp.

I think your math is slightly off.

I'm pretty sure you're assuming that 50 gold coins equals one troy pound. Currently, a troy ounce of gold is worth $1,475 USD; one troy pound is twelve ounces, so a troy pound of gold is worth $17,700 - divide that by fifty (since D&D 3.5 presumes fifty coins to a pound), and each coin is worth $354 USD. Now, multiply that by a great red wyrm's treasure hoard, valued as you noted at 1,680,000 gp, and that's only worth $594,720,000 USD.

I'm not sure that D&D assumes the troy weights at the pound level, though. I can't prove this, but I think that D&D 3.5 expects us to assume that the 1 pound generated by 50 gold coins is equal to 1 pound of food, despite the fact that the two have different weight (the former is troy, the latter is avoirdupois).

If we assume that one pound of gold coins in D&D weighs the same as one pound of everything else, however, then D&D gold coins actually weigh more, and thus are worth more, than we got from our previous calculation. Since the smallest unit of measurement in troy and avoirdupois, a grain, is equal weight in both systems, we can figure out the difference.

As noted, a troy ounce of gold is worth $1,475 USD. Since a troy ounce has 480 grains, that's a worth of $3.07 USD per grain.

Now, an avoirdupois pound has seven thousand grains in it (incidentally, an avoirdupois pound is made up of sixteen avoirdupois ounces at 437.5 grains each). Divide that seven thousand grains by fifty, and each coin has 140 grains, making it worth $429.80 USD (thus fifty gold coins in D&D 3.5 is worth $21,490 USD).

So, given that a great red wyrm's treasure hoard has a gp value of 1,680,000 gp, that's worth a total worth of $722,064,000 USD, which is closer, albeit still smaller, than the value you got.

 

[Theo R Cwithin]

D'oh! Good catch. Looks like my big error was forgetting that troy pounds are only 12 troy ounces. As for the rest, yeah, I was just assuming D&D uses troy weights and taking gold at $1500/ounce, for simplicity.

Either way, D&D dragons just don't seem to have the nearly swag that Tolkien dragons do. I feel a little swindled, now.

 

[Fifth Element]

Smaug's fortune is actually worth precisely zero, since he's dead and some sneaky dwarves took all his stuff. I believe he's the only one on the list who's deceased in his own continuity, though chances are I'm wrong.

 

[Alzrius]

Either way, D&D dragons just don't seem to have the nearly swag that Tolkien dragons do. I feel a little swindled, now.

It's worth noting that part of Smaug's incredible wealth is that his gold and silver coins are measured differently than the gold coins (and, by extension, the silver coins) in D&D...which also affects the overall value of the Arkenstone, to boot.

Smaug's gold coins are each one troy ounce of gold, and his silver coins are each one troy ounce of silver; 480 grains per coin.

A D&D 3.5 gold coin is - if we assume that they're weighed in troy - 115.2 grains; a bit less than one-fourth of a troy ounce of gold. If we assume they're weighed in avoirdupois then that ratio rises to 140 grains; slightly less than one-third of an avoirdupois ounce of gold.

Even wackier is the D&D 3.5 silver coin. This coin is both one-fiftieth of a pound (again, either troy of avoirdupois, depending on how you read the rulebooks) and one-tenth the value of a gold piece of the same mass. Using the current USD value of silver, this is impossible - we'd have to assume that the economic value of silver in D&D 3.5 is exactly one-tenth that of gold, making it have a value of $147.5 USD per troy ounce, or just slightly under $0.31 USD per grain.

Even taking that into account, however, I can't recalculate the value of Smaug's hoard based on D&D coinage since, in order to calculate the total volume of coins in the hoard, I'd have to know the dimensions of a gold and silver coin.

I suppose I could try to calculate the dimensions of the coins based on their weight, since mass is conserved (presumably meaning the results would be the same either way since the radius and thickness would always remain proportional), but that's beyond me, presuming that it's even right. Likewise, I don't know if it's possibly to simply adjust the dimensions of Smaug's coins proportionally to the differences in the weight of his coins versus D&D 3.5's coins, but even presuming that would provide accurate values, that's also beyond me.

Hence, without knowing the radius and thickness of D&D gold and silver coins, there's no way to adjust for the fact that Smaug's coins are worth more than a great red wyrm's.

 

[MatthewJHanson]

Anybody want to take a crack at what the Shire might be worth?

I thought it was interesting that the Frobes article discounted, "other valuable items in Smaug’s hoard – rare suits of armor and so on," when Gandulf claimed that Bilbo's mithril shirt was "greater than the value of the whole Shire and everything in it."