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You haven’t accounted for the increased price of gold since publication.
The date of publication of Smaug's net worth is not the date of publication of the book, but the recent date on which Forbes estimated it as being behind 14 US private citizens. $51bn in 1937 is more than half the entire GDP of the USA ($93bn). It's likely that the US citizen with the highest net worth in 1937 was John D Rockefeller at around $1.4bn, with Andrew Mellon and Henry Ford being the other contenders.
gbj_tester
You haven’t accounted for the increased price of gold since publication.
The Hobbit came out in 1937. The US Gold Reserve Act of 1934 raised and fixed the price of gold at $35/oz. Today, the same ounce ≈ $1286, a 36x increase. Perhaps not a literal mountain, at least not by our (Hu)Man standards, but significantly more than your initial estimation.