Taming Randomness: How Modern Finance Evolved From Gambling — History of Finance III

John Maynard Keynes, one of the grandfathers of modern economics, once said that the business of investing is intolerably boring and over-exacting to anyone who is entirely exempt from the gambling instinct. Little has changed since, and the same is true on the blockchain — at first glance, there are the ‘degens’, who YOLO their life savings away at the faintest rumor, and there are the serious investors who only invest on sound principles.

Yet, the reality is not as clear-cut. If you look deep into the wallet of a serious investor, it’s not uncommon to see some HOSKY tokens looking back at you. In this article, we will be exploring how modern financial principles evolved from understanding games of chance, and what effects this has on current investors.

This article is the third in a series on the history of money and trade, but they’re written in such a way that they can be read in any order as they’re self-contained. We welcome you to read them chronologically, as they build on each other, but it’s not a requirement.

Today, we will be discussing how it is that we have managed to tame randomness enough to begin to make financial decisions, models, and systems that account for reality in all its complexity.

Divine will

The ancient world did not have a good conception of probability. Not because they were incapable of seeing randomness expressed in the universe, but because rather than seeing probability as a web of interconnected and chaotic variables, they saw it as the will of the gods.

If someone gambled and won, then that meant that some powerful entity allowed it to be so. If, on the other hand, the gods were displeased with the person for their lack of humility, or their unwillingness to share these new gifts with the gods, then they would be punished.

Even so, ancient peoples understood randomness and harnessed it. For example, there is the “Game of Kings” — a sort of Backgammon predecessor where you used dice to get game pieces from one side to the other — invented by the Sumerians 4500 years ago [1].

The Royal Game of Ur

It’s worth noting that dice themselves have their origin from astragalomancy, or tossing bones in order to interpret the will of the gods [2]. There were also the substance-taking oracles who would mumble nonsense, but their utterances got reinterpreted as sage wisdom [3]. These mechanisms are a means of taking random processes and assigning order and agency to them.

In not so many words, this is what tradition is — a means of engaging with reality, which was successful enough throughout the ages, so as to get passed on to the next generation.

The problem with this approach is that without a coherent framework to interpret randomness, mistakes can be made. Just ask Croesus, the king of Lydia (now a part of Turkey), who asked the Oracle of Delphi whether he ought to go to Persia, the response was “If Croesus goes to war he will destroy a great empire.” Pleased with himself, he went to war — along with Thales of Miletus of Tradfi Tales fame — and lost it all by taking his victory for granted [4].

It turned out that the great empire that would be destroyed was his own.

He was sentenced to be burned alive by his enemies, along with fourteen Lydian nobles. The legend goes, that as the flames rose he uttered a prayer to Apollo and a sudden rain put out the flames. Clearly, there was something hiding in the randomness, an almost divine will, with its own rules and logic. But it wasn’t a prophet who finally began to discover and tame this force of nature, but a man who’s been characterized as close to insane, a card cheat, a possible murderer, and a mathematical genius — Gerolamo Cardano [5].

Gambler’s fallacy

It’s perhaps not a coincidence that the first person to systematically lay out how probability works was someone who was at the crossroads of mathematics, games of chance, and divination. The polymath, gambler, and astrologer Gerolamo Cardano first laid out the theory of probabilities in the Liber de ludo aleae ~ “Book on Games of Chance” in the mid-XVI century, by explaining how to calculate the chances of any dice combination. Worth mentioning as well, that once he laid out how to understand probabilities, he also explained how to cheat in gambling games [6]. It remains unclear whether Cardano fully understood the consequences of the intellectual seeds that he had planted.

Girolamo Cardano

At that same time, in the Dutch Republic, farmers and merchants began to experiment with deferring payments into the future or bringing future benefits into the present. These were the first widescale derivative tools, which are financial instruments that derive their value from some underlying asset and attach conditions on the payment terms. Through this abstraction of finance, farmers were able to normalize their earnings by having a guaranteed buyer in the future and merchants could also use these same tools as a form of proto-insurance.

The true complexity of the market was not realized until the creation of the Dutch East India Company (VOC) — the first multinational corporation in the world and also the first to have publicly traded stocks. The VOC brought retail interest into the market, whereas before future contracts had mainly been for parties interested in the delivery of commodities, now people in the market could speculate with non-physical goods.

By being able to speculate on stocks instead of physical goods, if you made a mistake in a futures contract, you just accrued debt, and you didn’t have to deal with half a ton of wheat delivered to your front door by tomorrow.

People are willing to shoulder the debt burden for their gambling addiction, but never a public embarrassment. The derivatives trade became streamlined over a surprisingly short time. When it first started, you needed to file contracts with notaries and undergo considerable expenses. A short while later though, private trades were normalized and traders mainly just had to sign duplicate contracts to be able to prove a derivative contract’s existence. If there was any disagreement, the matter would go to the courts [7].

New forms of derivatives, like options, where the instrument owner has the right to buy or sell an asset at a given price at a given date, soon started to come into vogue. Then came short selling, where traders would borrow a number of stocks, and sell them at current prices with the intention of repurchasing them later when they had fallen.

The sheer volume of derivatives proved to be a concern for the government, and while the Dutch authorities threatened severe regulation, they proved to be quite hands-off, at least compared to their contemporary ruling bodies, as the entry barriers were sufficiently high that only people who could afford to lose money and meet their obligations were able to enter into such agreements… at least initially.

From the mid-seventeenth century onwards, trading clubs entered the scene and through this even participants of lower standing were able to participate. As the Dutch economic historian Dr Petram put it “Amongst the participants of these clubs, peer pressure took over the role of a reputation based on wealth or built up over a large number of transactions.” [8]

Peer pressure, FOMO and YOLOing your funds away, has a long history in financial markets.

It’s worth noting that all these complex financial transactions developed prior to the possibility of being able to properly price them. However that didn’t stop speculators from trading derivatives in the Dutch Republic, perhaps accidentally revealing people’s willingness to gamble, rather than invest on sound economic and mathematical principles.

After all, Cardano had merely hinted at how probability might be calculated. Then came the French Mathematicians Blaise Pascal and Pierre de Fermat, who further expanded on Cardano’s understanding of probability by trying to solve a gambling puzzle by fellow gambling friend and writer Antoine Gombaud [9].

But proper financial understanding was still several centuries away!

From sinners to saints

The development of the science and mathematics that would underpin the financial markets cannot be extricated from the gambling dens of ill repute. Of course, over time, the field became more formalized.

Half a century later, after the Dutch commonfolk began gambling their life savings away on instruments they barely understood and Blaise Pascal and Pierre de Fermat worked on the mathematical underpinnings of gambling, came the first formalization of the ideas of probability and its connection to real-life events.

In 1713, Jacob Bernoulli came up with the idea of the Law of large numbers, which posited that the more observations one has of a phenomenon, the more statistically significant the average of those observations is [10].

This might seem obvious to a modern audience who grew up with calculus classes and statistics talk in the background. Of course, seeing more versions of an event gives you a more accurate representation of what is how it could behave. Yet, this is said with the benefit of hindsight, first understanding that the messy and changeable real world was computable and predictable is a civilizational game-changer.

Suddenly, the inferences and rules developed for card games could be used to build models with predictive power, and thereby price financial instruments in a way that was no longer guesswork. Between the sixteenth and the eighteenth century, randomness began to be tamed.

No longer was it the will of Apollo smiting Croesus of Lydia for his hubris, but events happening (or not) became a computable phenomenon. Entire lives could be predicted through the Law of Large Numbers — if you take a thousand people at random, you might not know who will die of a heart attack, but you will roughly know how many will with a scary level of accuracy.

Mid-eighteenth century, this is an inference that two Scottish clergymen, Alexander Webster and Robert Wallace, came to when trying to solve the issue of how much money to give widows of parish ministers, but without bankrupting the Church of Scotland’s treasury. As such, they used existing actuarial tables, showing the life choices of Scots, and along with their business acumen and probability mathematics, they valued a clergyman’s life in monetary terms, thus creating one of the first accurate estimates for pricing life insurance [11].

Scottish Widows' Fund poster (1888)

A game of dice has the exact same mathematical underpinnings as an insurance payout, a loan, or any financial derivative — it’s merely a matter of taking the buy-in price, the probability of a successful outcome, and the potential payoff, in order to see whether an investment opportunity is fairly priced.

This set the basis for a financial revolution, as once you had the mathematical underpinnings of being able to model and calculate financial instruments, you can suddenly be less risk averse, lower the barriers to entry and provide your services en masse.

The availability of capital, and the growing ability to design machinery that bends nature to one’s will, allowed for the most extraordinary developments in human history. From being able to sustain a population of millions, we went to billions and gave many of them lives comparable to the kings of old.


From divination to games of chance, to mathematical modeling and pricing financial products, every culture has had to find a means of processing and dealing with randomness.

Each step on this journey has helped us understand the different facets of our world. Divination first gave us the opportunity to think that we may have a chance to interpret the chaotic will of the heavens. Then, gambling took all that complexity and simplified it so much as to make it farcical; while perhaps we had not tamed it at that point, we managed to take infinite randomness and constrain it to an understandable extent, which helped us process and develop frameworks for it. After this, came the mathematicians who began to extrapolate our constrained games and expand it to the size of reality itself.

This particular story is far from over though. While initially, we had great success harnessing probability for pricing financial products, and designing scientific models, this had its limitations.

Now we don’t talk about deal execution times of days or weeks, as in the times of the Dutch Republic. Instead, we talk about the microseconds and decades ahead. For us to develop as a society, it is essential that our understanding of probability and modeling matches our ambitions.

In the twentieth and twenty-first centuries, we have once more had to contend with the fact that we are not all-knowing. Chaos theory, the science of explaining how infinitely small variables can have ripple effects that change the whole system, has begun to overturn our whole understanding once more.

How we engage with trade says a lot about who we are as a society — what is permissible, what is not, and what we do with greater knowledge is one of the great markers of our civilization. If there is one lesson that we can take from this overview of gambling and statistics it is to not be too disdainful of what seems to be less intellectual pursuits.

Yes, the crypto space is primarily a vehicle for speculators and ‘degens’ to gamble their life savings away. But that does not mean that it is without merit. On the contrary, by harnessing base desires, we can often reach much higher heights than if we had aimed for them in the first place.

One day we will look back and say “It was obvious that early crypto speculators were on to something deeper, something so groundbreaking and new that they could scarcely begin to imagine it.”

Let’s begin to imagine the unimaginable, together!


1 Finkel, Irving (2007), “On the Royal Game of Ur,” in Ancient Board Games in Perspective, ed. Irving Finkel. London: British Museum Press, pp. 16–32.

2 Reece, David S. (2000). “Worked Astragali” Kommos: an excavation on the south coast of Crete volume IV: the Greek sanctuary. Princeton: Princeton University Press. pp. 398–401.

3 De Boer, Jelle Z., John R. Hale, and Jeffrey Chanton. “New evidence for the geological origins of the ancient Delphic oracle (Greece).” Geology 29.8 (2001): 707–710.

4 Herodotus The histories. (1996). United Kingdom: Penguin Publishing Group. Book I: chapters 45‑140

5 Bidwell, James K., and Bernard K. Lange. “Girolamo Cardano: A Defense of His Character.” The Mathematics Teacher 64.1 (1971): 25–31.

6 V.J. Katz, A History of Mathematics: An Introduction, 3rd edn. (Boston: Pearson Education, 2009). p.48

7 Petram, Lodewijk Otto. The world’s first stock exchange: How the Amsterdam market for Dutch East India Company shares became a modern securities market, 1602–1700. Diss. Universiteit van Amsterdam [Host], 2011.

8 ibid

9 Pascal, Blaise, Pierre de Fermat, and Michel Boy. La Correspondance de Blaise Pascal et de Pierre de Fermat. ENS Editions, 1983.

10 Bernoulli, Jakob (1713). “4”. Ars Conjectandi: Usum & Applicationem Praecedentis Doctrinae in Civilibus, Moralibus & Oeconomicis (in Latin). Translated by Sheynin, Oscar.

11 Sibbett, Trevor. “The Scottish Ministers’ Widows’ Fund, 1743–1993. Edited by A. Ian Dunlop (Saint Andrew Press, Edinburgh, 1992).£ 20.00.” Journal of the Institute of Actuaries 120.2 (1993): 387–388.