I'm bored at work, so I did some bad math with totally arbitrary assumptions.
Since we're talking about Vicky it's safe to assume we want ducats from the time period! Let's go with the 1836 ducat minted for the coronation of Ferdinand I of Austria, I guess that's a good place to start:
View attachment 266332
According to
CoinArchives.com last year a coin like this one was auctioned off for EUR 850, significantly more than the melt value of approximately
USD 140 (the coin weighs 3.5 grams and is 0.9860 pure).
Now, please somebody correct me if I get this part wrong, but I couldn't fine this coins dimensions, but think the Austrian ducat was
19.5 mm in diameter. Gold's density at room temperature is about
19.3 g/cm3 , the surface area is (d/2)^2*pi = 2.9865 cm2 so the thickness would be mass/(density*area) = 3.5/(19.3*2.9865) = 0.0607 cm. Pretty thin (half that of a US nickel) but not that uncommon for Austrian pure gold coins
apparently.
Let's go to the bucket part. Now I might go the easy route and just assume a common modern bucket, but I'm still bored, so let's find a 19th century, Victorian bucket!
After some googling I've found an
antique store which carries this:
View attachment 266333
Technically it's a coal bin, but it's copper-bound oak and looks fantastic! The store lists a height of 342.9 mm and width od 304.8 mm as well as a price of GBP 160 (in case we include the bucket with the ducats as part of payment).
How many ducats fit in a bucket? Glad you asked!
I'm going to do a few simplifications here, but feel free to model a more perfect bucket yourself and see how
your calculations differ from mine First of all: I'll assume a perfect cylindrical shape of the bucket, with the width being the external diameter of our awesome-looking vessel. We do not know what the internal diameter is, but that's fine - I'll leave it for now, we'll get back to this later.
The most ducats we can get in a line flat on the bottom of our bucket is 15 - they would form a 292.5mm line so a 16th one would be outside the bucket. That leaves us 12.3mm for the total width of both walls so a 6.15mm thick wall... yeah, let's say that's reasonable, our bucket has precisely 6.15mm walls!
I'm going to use
a cool tool that tells me that with those parametres I can fit 172 ducats at the bottom of my bucket, like this:
View attachment 266342
Well, the
optimal way to place as many ducats in a bucket as possible is to melt them down - we'll tackle that problem in the end. Let's just handle unmelted ducats here and see what we can do with my limited knowledge of geometry and tools at my disposal.
The first layer of ducats is only 0.607mm thick as we established earlier. If the bottom of our bucket is as thick as the walls then we have 336.75 mm of bucket to fill, which gives us about 555 layers (rounded slightly up, so watch out not to spill ducats!) or 95,460 ducats! Wow!
Our ducats weigh 334.11 kg now,
which is about as much as a large calf hitting puberty, so assuming the bucket somehow doesn't fall apart let's take it to auction and we get EUR 81,141,000 or about USD 90,126,960 (plus USD 208 for the bucket).
That's a hefty sum for a bucket of ducats, but the economist in me says that we're flooding a rare-commodity market with more product than feasible to keep prices high (and quite probably with more Ferdinand I coronation ducats than there were minted). Besides there's all that empty space in the bucket. Let's just get all the ducats we can find lying around, and melt them, fill our bucket and sell as gold! Will we get more than selling vintage coins?
With an internal diameter of 292.5 mm and a height of 336.75 mm (no spilling this time!) of our perfectly cylindrical, heat and pressure resistant Victorian bucket we'll get a volume of 22,628,159.25 mm3 or 22628.15925 cm3 (22.63 litres, about six gallons). Using the gold density listed above and price of $40 per gram we get 436,723.5 grams (436.7 kilograms so
about as much as a grand piano) which we could sell for
only USD 17,468,938.94.
Fun fact - Paradox Interactive is a
listed company on NASDAQ. At 105,600,000 shares which are traded for SEK 71.25 as of today, to purchase the company you'd need SEK
7,524,000,000 or USD 856,839,891.60 but to buy 50% of shares +1 only USD 428,361,642.88.
So to buy a controlling share in PDX you'd need about 42 buckets of ducats unmelted or 216 of melted ducats (and I included the price of buckets for you). Which by the way means that PDX is worth 94,048.89 kg of gold.
Then OP you'd be able to literally buy Vicky3 with buckets of ducats!
EDIT: I forgot about the fact that metals expand when heated. So the density of liquid ducats will be lowered and the number of buckets needed to buy Vicky increased. Will amend post in spare time.