James Howells is contemplating the purchase of a municipal landfill in South Wales after his ex-partner unintentionally discarded a hard drive that contained his bitcoin wallet.
Howells has previously lost a high court battle that sought permission to search the landfill for the hard drive, which he is convinced holds bitcoin valued at £600 million.
But is it even feasible to locate it? Let’s crunch some numbers.
Howells, who is an IT engineer from Wales, was an early adopter of bitcoin back in December 2008. By February 2009, he began mining the cryptocurrency on his laptop—this involves using your computer to perform complex mathematical calculations in return for coins.
At that time, there were only five individuals mining the digital currency, and he eventually amassed a fortune of around 8,000 bitcoin.
Initially, these coins had almost no value—the first real transaction with bitcoin occurred in 2010 when a Florida man purchased two pizzas for 10,000 bitcoins.
However, over the past 15 years, the currency’s value has skyrocketed, with a single bitcoin exceeding the US$100,000 threshold in December 2024—meaning that those two pizzas are now worth US$1 billion (£790 million).
Calculating the Odds
No wonder Howells is eager to retrieve his hard drive. But what are the chances of locating a small 10 cm hard drive in an area housing 1.4 billion kg of waste? Is it truly akin to finding a needle in a haystack?
At first glance, this appears to be a straightforward computation. If we randomly select a location within the landfill, the likelihood of the hard drive being there is simply the size of the object compared to the total size of the landfill.
Estimations using Google Maps indicate that the Docksway landfill site covers approximately 500,000 square meters (5 billion square centimeters), a space roughly equivalent to 70 football pitches.
However, we must also consider the landfill’s depth, with years of refuse layered on top of one another. Even a conservative estimate of 20 meters results in a total volume of 10 million cubic meters (or 10 trillion cubic centimeters).
This volume is approximately 3,600 times that of the swimming pool used at last summer’s Paris Olympics.
Howells states the bitcoin is stored on a 2.5-inch hard drive, which has a volume of around 70 cubic centimeters (7 cm x 10 cm x 1 cm). As a result, the probability of finding the hard drive at a randomly selected point is 70/10,000,000,000,000 = 0.000000000007, translating to roughly a one in 143 billion chance.
This probability is over 3,000 times less likely than hitting the jackpot in the UK’s National Lottery. Nonetheless, considering £600 million is at stake, it seems improbable that anyone would approach the search by looking at just one location.
So, the pivotal question here revolves around time and finances. If we know the hard drive is located within the landfill, how long would it take to find it, and what would the financial cost be?
Initially focusing on time, this is essentially an extension of our previous calculation.
If we assume it takes 1 second to search each 1,000 cubic centimeter section of the landfill (a rough estimate as my experience in scouring landfills for hard drives is limited), it would require 10 billion seconds (or 316 years) of constant searching to exhaustively cover the entire site.
However, this duration could be considerably shortened with an entire team searching simultaneously.
Is It Worth the Investment?
Clearly, Howells does not have 316 years to devote to his search, but what if he had the means for one full year of uninterrupted searching?
The odds of locating the hard drive within that year would be 1 in 316, and while the chances remain slim, the potential reward may make this option appealing.
This consideration brings the cost aspect into play. How much would you be willing to invest for a 1 in 316 chance of winning £600 million? The answer relates to the statistical concept of ‘expected value,’ which is the anticipated long-term result of a scenario if repeated endlessly.
For instance, imagine you are rolling a die and will receive £2 if you roll a six, but will incur a £1 cost for any other result.
To evaluate if playing this game is worthwhile, you can compute the expected value. The probability of rolling a six is 1/6, while the probability of rolling any other number is 5/6.
The expected value can thus be calculated as:
E [winnings] = 1/6 * £2 + 5/6 * (-£1) = 2/6 – 5/6 = -3/6 = -£1/2
This means you would expect to lose half a pound (or 50p) on average each time you play this game.
In regard to our bitcoin search, we can view the expected value as the amount one would anticipate making on average after searching the landfill for a full year.
On average, one could expect to find the hard drive (and the £600 million) once out of 316 searches, while failing to locate it 315 times and receiving nothing at all.
This leads us to compute the expected value as follows:
E [£ found] = 1/316 * £600m + 315/316 * 0 = £1,898,734
These calculations can easily be adjusted to account for varying search durations, number of searchers, or different landfill sizes and areas. If Howells ever secures access to the landfill, it may be beneficial to have a statistician available to assist in the search—and of course, I would gladly offer my expertise for a reasonable fee… Craig Anderson, Senior Lecturer in Statistics, University of Glasgow This article is republished from The Conversation under a Creative Commons license. Read the original article.
