James Howells is considering the acquisition of a municipal landfill in South Wales after his ex-partner unintentionally discarded a tough drive that contained his bitcoin pockets.
Howells has beforehand misplaced a excessive courtroom battle that sought permission to go looking the landfill for the onerous drive, which he’s satisfied holds bitcoin valued at £600 million.
However is it even possible to find it? Let’s crunch some numbers.
Howells, who’s an IT engineer from Wales, was an early adopter of bitcoin again in December 2008. By February 2009, he started mining the cryptocurrency on his laptop computer—this includes utilizing your pc to carry out advanced mathematical calculations in return for cash.
At the moment, there have been solely 5 people mining the digital foreign money, and he finally amassed a fortune of round 8,000 bitcoin.
Initially, these cash had virtually no worth—the primary actual transaction with bitcoin occurred in 2010 when a Florida man bought two pizzas for 10,000 bitcoins.
Nonetheless, over the previous 15 years, the foreign money’s worth has skyrocketed, with a single bitcoin exceeding the US$100,000 threshold in December 2024—which means that these two pizzas at the moment are price US$1 billion (£790 million).
Calculating the Odds
No surprise Howells is keen to retrieve his onerous drive. However what are the probabilities of finding a small 10 cm onerous drive in an space housing 1.4 billion kg of waste? Is it actually akin to discovering a needle in a haystack?
At first look, this seems to be an easy computation. If we randomly choose a location throughout the landfill, the chance of the onerous drive being there may be merely the scale of the item in comparison with the entire dimension of the landfill.
Estimations utilizing Google Maps point out that the Docksway landfill web site covers roughly 500,000 sq. meters (5 billion sq. centimeters), an area roughly equal to 70 soccer pitches.
Nonetheless, we should additionally think about the landfill’s depth, with years of refuse layered on high of each other. Even a conservative estimate of 20 meters leads to a complete quantity of 10 million cubic meters (or 10 trillion cubic centimeters).
This quantity is roughly 3,600 occasions that of the swimming pool used finally summer time’s Paris Olympics.
Howells states the bitcoin is saved on a 2.5-inch onerous drive, which has a quantity of round 70 cubic centimeters (7 cm x 10 cm x 1 cm). Consequently, the likelihood of discovering the onerous drive at a randomly chosen level is 70/10,000,000,000,000 = 0.000000000007, translating to roughly a one in 143 billion likelihood.
This likelihood is over 3,000 occasions much less possible than hitting the jackpot within the UK’s Nationwide Lottery. Nonetheless, contemplating £600 million is at stake, it appears unbelievable that anybody would strategy the search by taking a look at only one location.
So, the pivotal query right here revolves round time and funds. If we all know the onerous drive is situated throughout the landfill, how lengthy wouldn’t it take to seek out it, and what would the monetary value be?
Initially specializing in time, that is primarily an extension of our earlier calculation.
If we assume it takes 1 second to go looking every 1,000 cubic centimeter part of the landfill (a tough estimate as my expertise in scouring landfills for onerous drives is restricted), it might require 10 billion seconds (or 316 years) of fixed looking out to exhaustively cowl your entire web site.
Nonetheless, this length might be significantly shortened with a complete group looking out concurrently.
Is It Definitely worth the Funding?
Clearly, Howells doesn’t have 316 years to commit to his search, however what if he had the means for one full 12 months of uninterrupted looking out?
The percentages of finding the onerous drive inside that 12 months can be 1 in 316, and whereas the probabilities stay slim, the potential reward might make this feature interesting.
This consideration brings the price side into play. How a lot would you be keen to speculate for a 1 in 316 likelihood of profitable £600 million? The reply pertains to the statistical idea of ‘anticipated worth,’ which is the anticipated long-term results of a state of affairs if repeated endlessly.
For example, think about you might be rolling a die and can obtain £2 in case you roll a six, however will incur a £1 value for some other consequence.
To guage if enjoying this sport is worth it, you’ll be able to compute the anticipated worth. The likelihood of rolling a six is 1/6, whereas the likelihood of rolling some other quantity is 5/6.
The anticipated worth can thus be calculated as:
E [winnings] = 1/6 * £2 + 5/6 * (-£1) = 2/6 – 5/6 = -3/6 = -£1/2
This implies you’ll anticipate to lose half a pound (or 50p) on common every time you play this sport.
In regard to our bitcoin search, we will view the anticipated worth as the quantity one would anticipate making on common after looking out the landfill for a full 12 months.
On common, one may look forward to finding the onerous drive (and the £600 million) as soon as out of 316 searches, whereas failing to find it 315 occasions and receiving nothing in any respect.
This leads us to compute the anticipated worth as follows:
E [£ found] = 1/316 * £600m + 315/316 * 0 = £1,898,734
These calculations can simply be adjusted to account for various search durations, variety of searchers, or totally different landfill sizes and areas.
If Howells ever secures entry to the landfill, it could be useful to have a statistician out there to help within the search—and naturally, I might gladly provide my experience for an inexpensive charge…
Craig Anderson, Senior Lecturer in Statistics, College of Glasgow
This text is republished from The Dialog below a Inventive Commons license. Learn the unique article.
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