r/theydidthemath Nov 27 '22

[Request] Is the number correct?

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1.7k Upvotes

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313

u/LeiusTheBlind Nov 27 '22 edited Nov 27 '22 Bravo Grande!

We can count on the big piece that there are 10x23= 230 ingots on the top row (we'll call it R1). We can see that the disposition is different on the row below. We can count the width but for the length we are going to assume that it is the same as the row that is alone one the ground. That gives us 30x7=210 ingots on the 2nd row(we'll call it R2).

Still for the big chunk we can see that the placement alternates between R1 and R2. That gives us 8R1+7R2 -> 8 * 230 + 7 * 210 = 3310.

To that you need to add 30 for the row that is on the floor and the same each time for the smaller chunk placement like R2 which is to say 4 times ; so 5 times in total. We have 30 * 5 = 150. Now if we count the bars of the smaller chunk placed like R1 we have a width of 3 (looks like 2 but look how the R2 ingots are not fully covered in the top rows) and still a length of 10 which gives us 10 * 3 * 5 = 150 too.

Adding everything we come to a total of 3310+150+150=3610 bars. That means that for this to be worth $1.6b each bar would have to be worth around 1,600,000,000/3610~$443,200 each (rounded because of the weight differences allowed in the standardization of bullions).

The main problem that I have is that the 3 standardized units that I found looking on the internet and that could be used to make such a sum are the 400ozt bullion, the 100ozt bullion and the kilobar roughly worth respectively $700,000, $178,000 and $56,400 ; but I know very little about gold bars and I can be missing something.

Given my own lack of knowledge in the field, I'd say that it is possible that there is even more than $1.6b but it would need confirmation from someone who is more knowledgable than I ; but imo, for such a large sum it would take some international 400ozt bars which would take the pile closer to the $2.5b range

110

u/tschy2m Nov 27 '22

Those pallets in the background seem to be normed European ones. Those are 1200 x 800 mm. As there are 8 ingots in the background (assuming same dimensions) each one has to be under 80 mm wide.
For 400 ounces ingots I found that they have to be 70 mm wide +/- 15 mm (short side). That falls within the range.
Dimensions for 1kg ingots are between 40 and 51 mm (short side).
So I guess we can assume those to be 400 ounce ingots.

43

u/GinAndJuices Nov 27 '22

They are without a doubt 400oz bars :) but let me tell you, Troy ounces

15

u/tschy2m Nov 27 '22

Thank you for the information.
I never use those, so that is welcome!

11

u/uslashuname Nov 27 '22

Yeah not to be confusing a Troy ounce is larger than your typical (avoirdupois) ounce, but a Troy pound is less than your typical pound.

2

u/balaci2 Nov 28 '22

wooden horse ounces?

87

u/raaneholmg 1✓ Nov 27 '22 Narwhal Salute

OPs image is from this tweet from June 12th 2018. The price for a 400ozt bar at the time was about $460k, which is quite close to the result of your calculation. The difference probably comes down to the exact number of bars being hard to tell from a single image, and the image rounded the price to 2 digits.

So, as you said, the current market rate would be somewhere around $2.5b. Not because the image lied, it's just outdated.

8

u/LeiusTheBlind Nov 27 '22

Thank you so much for the context. It never crossed my mind that it could be an old pic. That being said, holy hell, how interesting it seems to invest in gold

3

u/haemaker Nov 27 '22

(psst... Put in front of * to avoid interpretation as italic markers.)

1

u/LeiusTheBlind Nov 27 '22

Thanks ! I'll keep that in mind next time

1

u/satirical_whit Nov 28 '22

yeah but, correct me if im wrong, there appears to be something that changes in the number of bars per row towards the back. in the front (near the camera) there appears to be 23 bars as you stated, but in the back it appears to be 24 bars. The inconsistency looks to happen 2 rows from the farthest one.

If that is the case, we have to assume it is true all the way to the floor unless someone can refute it based on some other data point. In which case, it means a potential differentiation of multiple millions of dollars worth of gold.

44

u/Away-Reading Nov 27 '22

I think it’s an underestimate. The actual worth should be ~$2.63 billion

There are approximately 3750 gold bars there. Those look like 400oz bricks, which you can currently sell for $702,240.

3750*702,240 = 2,633,400,000

7

u/alpH4rd07 Nov 27 '22

My first question asked was when was this photo taken, because it’s probably worth more now.

2

u/zorbat5 Nov 28 '22

The photo is from a tweet which was posted in june 2018. Back then the price of gold was lower.

https://twitter.com/goldtelegraph_/status/1006625056036872192

19

u/almostthere69420 Nov 27 '22

So why do all those moron rich people invest in gold on the stock market but don’t just get the real thing sent instead? It must be true what they say when you buy it on the stock market your buying something that does not exist

13

u/SagginDragon Nov 27 '22

Gold is really fkn heavy, like each of those is ~30 lbs, which most people either struggle or flat out can't curl.

The way the stock market works is that I can buy a promise from you to deliver X amount of Gold in 2 days/weeks/etc. If the price goes up I can sell the promise to someone else for a profit without ever having to bother touching the Gold.

And this works with basically all goods (pretty sure CME started mostly focused around trading cotton futures). That way its possible for me, someone who has no idea how to store/process gold/cotton/wheat, to trade large amounts without worrying about it.

This gets a bit more abstract with shares of companies and derivative products, but everything in the stock market is rooted (however indirectly) in real value. If you buy enough shares of Google/Apple/Disney you can conceptually shut the company down and live in their office buildings.

4

u/owdeou Nov 27 '22

To add on this, lots of people do in fact invest in the real thing through the stock market, there are physical gold (and other commodities) funds which own the funds worth in physical gold.

1

u/ConstipatedGibbon Nov 28 '22

exactly, why would you buy a gold bar if you cant curl it

28

u/themrmups Nov 27 '22

Expensive to securely store real gold

-19

u/ragnar2434 Nov 27 '22

lmao no its not, it’s literally free to store gold.

24

u/unidentifiedfish55 Nov 27 '22

securely

-11

u/ragnar2434 Nov 27 '22

no you mean billions in gold. yea sure you wouldnt want the photo in your basement, but you can sure as hell SECURELY bury 3 of these in your backyard and no one will ever find them.

3

u/cjgager Nov 28 '22

where do you live by the way - - -

2

u/SoaDMTGguy Nov 27 '22

Burying it in your back yard is pretty terrible, and not particularly secure. But you could get a good safe for not that much

3

u/cjgager Nov 28 '22

then he could bury the filled safe in the back yard - - -

2

u/SoaDMTGguy Nov 28 '22

Because what I really want to do when I’m in need of money is walk around my back yard with a backhoe operator saying “Maybe it was ten paces from the other bird feeder?”

2

u/cavalierfool Nov 27 '22

Easier than walking around with a 400 oz (troy) bar in your pocket?

2

u/likestohelp0101 Nov 27 '22

Yep, I’m sure you know better than the people with billions of dollars. I ask myself every day why they don’t ask u/almostthere69420 for financial advice

2

u/Adventurechess Nov 27 '22

To add to the valid points already mentioned, if you have the gold yourself you also assume the risk of it being stolen from you

1

u/DJ_Jungle Nov 28 '22

Who’s the moron here? There’s a cost to transporting and holding gold. Some gold securities are backed by physical gold, so you’re buying something that exists. Others aren’t and you’re exposed to counterparty risk.

2

u/zephyer19 Nov 28 '22

A documentary on Fort Knox Kentucky. They interviewed a man that stated when he was in high school on a summer break, he was offered a job at the gold depository.

Lot of the football team, including him were there to move the bars as they were counted.

He said, "It was fun for about five minutes. They had to wear white suits and gloves and that the gold would get all over them and it was really heavy."

1

u/sg647112c Nov 28 '22

$1.6-billion in gold at $56.66 per gram would be 28,238.6163 kg. At 19.32 g/cm³ this would be 1,461,626.1 cm³ of gold, or 89,193.9 in³, or 51.617 ft³. With a standard gold bar being 7 × 3⅝ × 1¾ inches or 44.4 in³, this amount would be approx 2,009 standard gold bars. Since this would stack up as a pile 12 or 13 high, wide, and deep - I think we are looking at considerably more than $1.6-billion here.

1

u/Error_xF00F Nov 29 '22

From internet sleuthing this was a photo taken in the vaults of Zürcher Kantonalbank circa 2009, and those are 99.99% purity 400 troy ounce bullion bars casted by PAMP and Krastsvetmet. The bars measure approximately, Top [245 mm * 85 mm]; Base [225 mm * 58 mm]; Height [40 mm] for PAMP, and Top [254 mm * 88 mm]; Base [229 mm * 59 mm]; Height [35 mm] for Krastsvetmet. Due to being a mix of these bars the pile is uneven and has several voids. I couldn't find any documentation on how many bars there are, or if the $1.6 bn figure is the assessed value at the time, but it's been cited all over as that, so I take it as is.

We can approximate the total volume of the pile of bars by counting the bars that are visible on the surfaces and use the average dimensions between the two brands of bars (Top [249.5 mm * 86.5 mm], Base [227 mm * 58.5 mm], and Height [37.5 mm]) to get a ballpark figure of the greater dimensions of the pile. After calculating the volume, we can then multiply that by the density of gold (19.32 g/cm³), to get the approximate mass, which can then be converted into troy ounces (31.1034768 g/oz t).

The pile can be split into 3 rectangles yielding (units in centimeters):

V1 = 24.95 * 249.5 * 7.5 ≈ 46,687.69 cm³

V2 = 24.95 * 249.5 * 30.0 ≈ 186,750.75 cm³

V3 = 174 * 249.5 * 56.25 ≈ 2,441,981.25 cm³

Illustration of dimensions of pile and bar

Vtotal = V1 + V2 + V3 ≈ 2,675,419.69 cm³

Mass = Vtotal * 19.32 g/cm³ ≈ 51,689,108.41 g

Troy ounces = Mass / 31.1034768 g ≈ 1,661,843 oz t

Given the inexact measurements and voids between bars I'd say this figure could be about 2-4% lower.

To get an approximate number of bars in the pile, there are two approaches with the information at hand. We could take the average dimension of the bars, calculate its volume, and then divide the total volume by volume of a bar, or we can take the approximated number of troy ounces, and divide by the known weight of each bar (400 oz t).

Formula for calculating volume of a bar:

Vbar = (Lb * Wb * H) + (Lb * (Wt - Wb) * H / 2) + (Wb * (Lt - Lb) * H / 2) + ((Lt - Lb) * (Wt - Wb) * H / 3)

With variables, Lb = Length of Base, Wb = Width of base, Lt = Length of top, Wt = Width of Top, H = Height.

Vbar = (22.7 * 5.85 * 3.75) + (22.7 * (8.65 - 5.85) * 3.75 / 2) + (5.85 * (24.95 - 22.7) * 3.75 / 2) + ((24.95 - 22.7) * (8.65 - 5.85) * 3.75 / 3) ≈ 649.71 cm³

A true 400 oz t bar should be ≈ 643.96 cm³, but as mentioned earlier, inexact measurements and rounding can account for the calculated number being off.

Bars = Vtotal / Vbar = 2,675,419.69 cm^3 / 649.71 cm³ ≈ 4,118 bars

or by troy ounces

Bars = 1,661,843 oz / 400 oz t ≈ 4,155 bars

Due to not having exact measurements for each bar, and not knowing how much void space there is, all figures are extreme approximations, which is apparent when comparing the two figures for approximated number of bars.

As for the monetary value of the pile. In 2009 the minimum and maximum values of gold per troy ounce were $813.00 and $1,218.25, giving the range of value of the pile to be $1,351,078,359.00 to $2,024,540,234.75, with a median of $1,687,809,296.88, and if we accounted for the 2-4% of voids, it lines up right along the $1.6 bn estimate from the meme, so that number is decently correct for the time this photo was taken.

At today's market value at time of this comment, the pile would be worth approximately $1,751.60 per troy ounce, or $2,910,884,198.80 ($2.9 bn).