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Ditgital Currency


Drawing balls from an urn: a problem with blockchain 

Published 23 February 2024 in Technology • 7 min read

A long-term flaw in Bitcoin technology threatens the long-term viability of digital currencies.

Over the past few years, blockchain has been hyped as the holy grail of business, promising to change every aspect of how corporates work as well as disruption in many other areas. As an efficient and, above all, secure way to record information, its promises of transparency and managing smart contracts are undeniably seductive.

At its heart has been its security. A blockchain is what is known as a distributed ledger technology. It is a shared ledger that is maintained by a network of computers instead of a single centralized authority. This makes it very difficult to manipulate in any way, as any change made in the ledger by a computer is visible to the rest of the computers in the network. The best-known example of blockchain in daily use has been the decentralized digital currency Bitcoin.

Bitcoin is created through a process called mining. Miners use powerful computers to solve complex mathematical problems. When a miner solves a problem, they are rewarded with the currency. Via a decentralized consensus mechanism called Proof of Work (PoW), this process validates transactions on the Bitcoin blockchain.

But what if that much-lauded security was not as tight as is claimed? This might sound like the blurb from an airport novel, but flaws in Bitcoin protocol threaten its long-term viability and raise questions about other cryptocurrencies.

CBDC digital currency

How does it work?

A fundamental attribute of blockchain is that it is supposed to be “memoryless”. This is a concept from probability theory that means that previous actions have no dependence on previous events; the past does not affect the future.

The most common example of a memoryless procedure is flipping a coin. The probability of getting heads or tails is always 50/50 regardless of the outcomes of previous flips. In other words, there is no learning in the process. A person flipping a coin in a fair manner cannot learn how to flip that coin in a way that increases the probability of getting the desired outcome.

But if a process is not memoryless, then there is some kind of learning in the process. That is, as if one could learn how to always get a head if flipping a coin often enough. In such a case, bigger players (in other words, those that can toss the coin more often than others) have an advantage over smaller ones. This would suggest that a player who put in twice as much effort as another one would have more than double the probability of winning. This would happen because of the learning effect.

The key part of the sentence here is “more than double”, which implies that there is an “unfair” reward to those putting in extra effort. This unfair advantage that one gains with effort gives smaller players an incentive to merge – because as they do so, their probability of winning increases.

What we found is that the stakes are even more in your favor than that. Blockchain is literally like a lottery. You connect your computer to the system, and your computer has a certain computational capacity, which in the context of blockchain is called the “hash power”.

“Whereas most technologies tend to automate workers on the periphery doing menial task, blockchains automate away the center. ”

For every unit of hash power, the user gets to draw one ball from an urn. There is a predefined number of balls in every urn which may be winning or losing balls.Within a system that is perfectly memoryless, every time that a losing ball is drawn it is then put back in the urn, which is then shuffled, and the participants try again. In that sense, there is no “unfair” learning, and the relationship between effort (hash power) and success, is linear. Hence, other than smoothing the frequency of winning, there are no incentives for miners to pull their resources together and increase their size.

But what happens with blockchain is that once a losing ball has been picked, it is thrown away. This means that in the next round, the probability that a miner picks a winning ball has increased as there is one less losing ball in the urn.

Let’s say that there are 100 balls in an urn, 99 of them are black and one is white. Players are looking for the single white one. A smaller participant can remove one ball at a time while larger players can remove two.That means that the initial probability of a smaller player winning a round is 1 in 100 and for a larger player, it is 2 in 100. The relative advantage of the larger player compared to the smaller player is (2/1).

But if after 10 rounds, the white ball has still not been found, the probability that the smaller player will find the ball has dropped to 1 in 90, while that for the larger one has dropped to 1 in 80. This is the key problem. The relative advantage of the larger player is now (2.25). Hence, the relative advantage of the larger player increases over time without this advantage being accompanied by an additional effort.

The longer that the game progresses, the more it becomes tilted in the favor of the larger players. In other words, there is learning in the mining process within each of the blocks.

Why should you care?

Currently, the impact of probability is negligible because the number of balls or units of hash power is enormous. But this is very much like the Y2K problem. If you are an executive considering using a blockchain product for any kind of business purpose, then you need to be aware of one risk that you have been building within your company which may become very relevant.

The Y2K problem was a widely anticipated computer problem that was expected to occur at midnight on 31 December 1999 as the world’s computers rolled over to the year 2000. The problem arose from the fact that to save memory space, many early computer programs were designed to store dates using only two digits for the year, rather than four. This meant that many computers were unable to distinguish between the years 1900 and 2000, which could have led to a wide range of problems.

The problem could only be addressed by first making everybody aware that we had a problem, and second by taking a step-by-step approach and rewriting the technical aspects of the software used.

For blockchain-based products, there are two Achilles heels that could lead to a Y2K effect. One is a significant increase in the hashing capacity of miners (which could be given by more miners joining the system, or by graphic cards becoming more efficient, which, given the speed at which companies like Nvidia are growing – partly because of the spike in the demand of graphic cards needed for the development of AI – should not be a surprise.

Figure 1 from shows the remarkable growth of the hash power of the Bitcoin network since its start. Every time that the hash power increases, we reach the area in which the “learning” will start to lead to more proportional rewards.

The other is quantum computing – a much-heralded field that uses quantum mechanics to perform computations in parallel that are too complex for classical computers. Although the technology has taken much longer to emerge than expected – many believe that it will be another 10 to 15 years until it does – it could still cause problems for digital currencies because the number of balls that can be drawn from an urn speeds up.

Any data ecosystems that rely on blockchain to govern the relationship between the data owners and data buyers could be vulnerable in this new world. Take digital currencies, for example, a topic that central banks are seriously discussing at the moment. In mid-November 2023, both the European Central Bank and the Monetary Authority of Singapore (MAS) announced that they were pushing forward with their own plans.

Given the inherent flaw of any currency backed by a Bitcoin-style protocol, what central banks are doing is opening the door for a massive attack on the financial system. There are ways to avoid the problem. First and foremost, it is to change the technology used. Our observations are based on the commonly used PoW blockchain technology rather than the Proof of State (PoS) blockchain technology.

Although both are consensus mechanisms used to validate transactions and secure blockchain networks, they work in different ways. Aside from the fact that its lower energy consumption means that it is more environmentally friendly, PoS blockchain avoids the technological issues that we have highlighted in proof-of-work systems.

The actual danger of the PoW blockchain technology remains unknown, but business leaders need to understand that there is one and that the threat remains unknown.

“This article is adapted from a paper originally published in Computational Economics, 31 October 2023. Interestingly, the original Bitcoin paper was published on 31 October 2008. ”


José Parra-Moyano

José Parra-Moyano

Professor of Digital Strategy

José Parra-Moyano is Professor of Digital Strategy. He focuses on the management and economics of data and privacy and how firms can create sustainable value in the digital economy. An award-winning teacher, he also founded his own successful startup, was appointed to the World Economic Forum’s Global Shapers Community of young people driving change, and was named on the Forbes ‘30 under 30’ list of outstanding young entrepreneurs in Switzerland. At IMD, he teaches in a variety of programs, such as the MBA and Strategic Finance programs, on the topic of AI, strategy, and Innovation.

Karl Schmedders - IMD Professor of Finance

Karl Schmedders

Professor of Finance at IMD

Karl Schmedders is Professor of Finance at IMD. In his research, he applies numerical solution techniques to complex economic and financial models, shedding light on relevant market issues and industry problems. He is also Director of IMD’s new online certification course for structured investment products in partnership with Swiss company Leonteq, teaches in the Advanced Management Concepts (AMC) and Executive MBA programs, and is an advisor on International Consulting Projects in the MBA program.


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