: How would the discovery of El Dorado impact the price of gold? I have gold in my long-term investment portfolio and I am worried about sudden over-supplies of gold. If a City of Gold (e.g. El Dorado) or the Nazi gold train

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I have gold in my long-term investment portfolio

This is unwise. An investment is something producing return:

Forest grows
Bonds pay interest
Stocks pay dividend
Real estate pays rent

With an investment, today will be more than tomorrow.
However, gold has no inherent return mechanism. It just is, not becoming anything more. Gold is digged from underground in gold mines, and then stored underground in vaults. The only true value gold has is that it it used in minuscule amounts in some manufacturing processes such as integrated circuit / electronics manufacturing. Even then, you would be much better off investing into a gold mine rather than "investing" (or more accurately, speculating) with physical gold. For a short-term speculative portfolio, physical gold could be a speculation instrument but then you're 50% guaranteed to lose some money.
Part of the appeal of gold is that it is inflation protected. In the current environment of low interest rates (below inflation), having something inflation protected could be beneficial. However, forest, stocks and real estate are inflation protected too, and have much less risk (price volatility) while at the same time having true yield.

I am worried about sudden over-supplies of gold

An over-supply of gold would destroy the value of your investment.

how can I reliably estimate the effect on gold prices?

The problem is, you can't. Gold prices are based on psychology, not on any true value.

How can I protect my portfolio against a free-fall in gold prices caused by the sudden realization that worldwide gold reserves are much larger than previously thought?

If you have 100 pounds of gold, and if you protect your portfolio for the value changes in 100 pounds of gold, you essentially have a risk-free instrument. Well, except: holding on to the 100 pounds of gold does not pay interest unlike a true risk-free bond would do.
Why would you invest into 100 pounds of gold and protect your portfolio against value changes in 100 pounds of gold? You're much better off investing to risk-free bonds.

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To make a reasonable answer to your specific questions,
A) The ElDorado idea is silly
B) There's about 30,000 tonnes of gold bullion. (FYI see the discussion on this specific figure, it may be bigger.) From time to time, a few 100 or even 1000 tonnes is discovered; as you would expect there is no effect. The urban-legend "Nazi gold" is a couple of hundred tonnes. So even if it was real and not a story, it's nothing. Miners dig up that much gold all the time, it's a non-issue.
C) Note that demand for gold swings wildly all the time. If you are worried about a (tiny) increase in supply, that is not rational, since demand swings tremendously.
D) You don't really "invest" in gold. You take a position if, on the time scale of let's say, 5 to 10 years, you believe the price of gold is about to shoot up.
Essentially it's a "political-economic" trade or position.
If you think the world's going to enter a period of perhaps unrest, hyperinflation, war, or other trouble with government currencies, you take a big position in gold and hope that, indeed, it is one of the many times when gold skyrockets in price.
So it's not really an investment, it's a "hedge", a "swing trade" or a "long-term position".
(It's rather like trying to guess about real estate. You may think something like "over the next ten years, this city will boom" or "because of the aging population, this state will boom" or "Eastern Europe is surely the next Riviera .." It's very much a "5 to 10 year" type of thing.)
{Some people say you should keep a small amount of your folio in gold - let's say a few percent, maybe 5% - as a kind of hedge against economic unrest, hyperinflation, or the like. I think this is completely stupid. Say your overall wealth is m, and you set aside ,000 against the zombie apocalypse. So, there's a war or the like. Your million completely disappears. Your ,000 shoots up ...... to a whole ,000. Yay. It's kind of a pointless strategy.}
Just one general point if you're thinking of buying some gold. As of writing (2020) I'd just completely forget it, for the very simple reason that the price just shot up for the last couple years.

It would be completely pointless buying after such a runup, unless, you are a totally dedicated full-time trader with specific ideas and vast intimate day to day knowledge of the market.
I'd just completely forget about it for 5 or 10 years, and then look in again. Fooling with gold is rather like having a wine cellar, from time to time you just have to forget about stuff in there for the odd 10 years.