Can James Howells Find His Bitcoin Hard Drive in a Welsh Landfill?

James Howells is exploring the possibility of purchasing a council landfill site in south Wales after his former partner inadvertently disposed of a hard drive holding his bitcoin wallet.

Howells has already failed in a high court attempt to gain permission to search the tip for the drive, which he says holds bitcoin valued at £600 million.

Yet could it actually be recovered? Let’s work through the numbers.

Howells, a Welsh IT engineer, was among the earliest users of the cryptocurrency bitcoin in December 2008. By February 2009, he was mining coins on his laptop – a process in which a computer performs complex mathematical calculations in return for coins.

At that point, only five people were mining the currency, and he ultimately built up a holding of around 8,000 bitcoin.

Bitcoin’s early days and soaring value

At first, the coins were effectively worth nothing. The first real-world purchase involving the currency took place in 2010, when a Florida man paid 10,000 bitcoins for two pizzas.

Over the 15 years that followed, though, bitcoin’s value rose sharply. One bitcoin exceeded US$100,000 in December 2024 – putting the current value of those two pizzas at US$1 billion (£790 million).

Calculating the search odds

It is easy to see why Howells wants the hard drive back. But what is the likelihood of locating a small 10 cm drive in a site containing 1.4 billion kg of rubbish? Is this genuinely comparable to finding a needle in a haystack?

At first glance, the maths appears straightforward. If we choose one location at random within the landfill, the chance that it contains the hard drive is simply the object’s size divided by the landfill’s total size.

A Google Maps estimate puts the Docksway landfill site at about 500,000 square metres (or 5 billion square centimetres), approximately equivalent to 70 football pitches.

We must also allow for the landfill’s depth, however, as waste has accumulated in layers over many years. Even a cautious depth estimate of 20 metres produces a total volume of 10 million cubic metres (or 10 trillion cubic centimetres).

That is about 3,600 times the volume of the swimming pool used during last summer’s Paris Olympic Games.

Howells says the bitcoin are stored on a 2.5-inch hard drive with a volume of roughly 70 cubic centimetres (7cm x 10cm x 1cm). The probability of finding the bitcoin at one randomly selected point is therefore 70/10,000,000,000,000 = 0.000000000007 – or around a one in 143 billion chance.

This is more than 3,000 times less likely than hitting the jackpot in the UK’s National Lottery. Still, with £600 million at stake, it is improbable that anyone would simply arrive and inspect a single spot.

The more relevant issue is therefore one of time and cost. Assuming the hard drive is somewhere in the landfill, how long would a search take and what would it cost?

Starting with the time involved, this is essentially an expanded version of the initial calculation.

Imagine that searching every 1,000 cubic centimetre portion of the landfill takes 1 second (an imperfect assumption, as my experience of looking through landfill for hard drives is limited). Covering the entire site would then require 10 billion seconds, or 316 years, of uninterrupted searching.

Naturally, a team carrying out searches simultaneously could reduce that timescale considerably.

Is searching the landfill financially worthwhile?

Howells plainly does not have 316 years for the search. But suppose he had the resources to conduct continuous searches for one full year.

The likelihood of recovering the hard drive over that year would be 1 in 316. The odds are still low, but the possible payoff may make them appear appealing.

This brings us to cost. How much would you pay for a 1 in 316 opportunity to win £600m? The answer involves the statistical idea of ‘expected value’: the average long-term outcome of a situation if it could be repeated endlessly.

For instance, imagine rolling a die where rolling a six earns you £2, while any other result costs you £1.

Calculating the game’s expected value tells us whether it is worth playing. The chance of getting a 6 is 1/6, while the chance of any other number is 5/6.

The expected value can consequently be calculated as:

E [winnings] = 1/6 * £2 + 5/6 * (-£1) = 2/6 - 5/6 = -3/6 = -£1/2

Put another way, you would lose half of £1 (or 50p) on average each time you played.

For the bitcoin, expected value is the average amount you could anticipate making by searching the landfill for a full year.

On average, we would recover the hard drive – and the £600 million – 1 time out of 316. In 315 out of 316 cases, we would not find it and would receive nothing at all.

We can therefore calculate the expected value as:

E [£ found] = 1/316 * £600m + 315/316 * 0 = £1,898,734

In practical terms, searching the site for a year would be expected to yield £1.9 million on average. If the search cost less than that, it would be expected to turn a profit on average and could be viewed as a worthwhile investment.

If the search cost exceeded £1.9 million, however, you would expect to lose money on average, meaning it would not be worthwhile.

The figures can readily be altered to reflect varying search durations, numbers of searchers, or different landfill and search-area sizes.

Should Howells ever obtain access to the dump, having a statistician available to direct the search could be worthwhile (and naturally, I would be pleased to offer my services for a modest fee…).

Craig Anderson, Senior Lecturer in Statistics, University of Glasgow

This article is republished from The Conversation under a Creative Commons licence. Read the original article.