If you are similar to myself, it is likely that you like to play the game of entrepreneurship. The act of creation truly captivates me, although I must confess that I am less inclined towards the managerial aspects. The process of bringing a concept to life, including the challenging task of identifying and exploiting the perfect market-product fit, provides an exhilarating experience. It is comparable to standing triumphantly atop the Eiger after an arduous ascent. However, when it comes to implementing the necessary business processes to scale the venture, I would willingly pass the torch to more experienced managers. It becomes boring. And I don’t do boring. Beyond the act of creation, I find no intellectual gratification in the endeavour. Thus, I seamlessly transition to my next entrepreneurial venture, quietly working behind the scenes towards another profitable (partial) exit over a span of preferably three to five years.

The monkey on a cliff

Most entrepreneurs are considered “one-off,” which means that they have had a successful idea at some point and have then grown it into a mature company over several decades before eventually exiting it. On the other hand, serial entrepreneurs have a seemingly insatiable intellectual appetite and continuously engage in repeated risk-taking. When discussing the repeated exposure to risk, it is intuitive to state that the probability of ruin over time increases.

Serial entrepreneurship is not simply a matter of intuition. From a philosophical standpoint, it can be perceived as a stochastic process. This process entails a sequence of random steps within a mathematical space. Despite these attempts to explain it, many still consider it to be too vague. To provide a concrete illustration, consider the analogy of a discrete monkey standing precariously on a cliff.

The monkey is poised to take random steps in a sequential manner. These steps are characterized by their lack of correlation, meaning that each new step is entirely independent of the preceding one. Furthermore, the monkey’s steps are unbiased, indicating that there is no inherent inclination in any particular direction. It is important to note that a single step to the right will result in an unfortunate outcome for the monkey. However, let us contemplate a scenario in which the monkey first takes a step to the left, followed by a succession of additional random steps. In light of this, what would be the probability of the monkey eventually stepping off the precipice over an extended period of time?

Let us approach the problem from an alternative perspective, focusing solely on the initial position (x = 0). In this context, the monkey can potentially fall off the cliff right from the start or navigate to other supposedly “safer” positions, only to find an unfortunate path leading to a fall later on. For the sake of simplicity, we will limit our analysis to the position (x = -1), as any other position with x < -1 would inevitably require passing through (x = -1) (unless the monkey possesses the ability to teleport). In order to maintain simplicity, we will avoid delving into mathematical concepts such as random variables. However, it is worth noting that if the monkey moves randomly with equal probability, denoted as p = 0.5, then it is highly probable that the monkey will eventually fall off the cliff.

If we consider a serial entrepreneur to be taking random steps (where each step denotes the founding of a new venture), then over time, the entrepreneur will eventually fall off the financial cliff and into bankruptcy. Not a happy prospect.

When ensemble and time risk collapse

When analyzing the probabilities of serial entrepreneurs or individuals who repeatedly expose themselves to risk, it is crucial to address the issue of why “ensemble risk” can be equated to “time risk”. To illustrate this distinction, let us consider a game of Russian roulette.

In this game, there are six chambers, one of which contains a bullet. The rules stipulate that if the “house” (or “market”) pulls the trigger and the player survives, they will be awarded a million dollars. If we have 100 participants playing this game, we can calculate the expected payoff for each individual to be $833,333.33. However, it would be misleading to assume that a single person playing this game 100 times will have an expected payoff of $83,333,333.33. Instead, we can reasonably anticipate that the person will meet an untimely demise with a high degree of certainty. Furthermore, if they perish on, say, the second trigger pull, they will not have the opportunity to play the game the remaining 98 times.

This simple yet powerful example effectively demonstrates why gamblers, investors, serial entrepreneurs, and market makers cannot simply expect to achieve the “average“ (I often exacerbate; “most people drown in water that is on average only two feet deep“) return from the game they play. Eventually, the player will reach his uncle point, stopping the game. This highlights the significance of comprehending the distinction between ensemble risk and time risk when evaluating probabilities in the realm of repeated risk exposure.

Serial entrepreneurship as an non-ergodic system?

Now we’ve covered a bit about random walks and the concept of time and ensemble averages, let’s introduce the concept of ergodicity. It is something that people understand intuitively but tend to forget when completing an MBA or taking a statistics class. It is a concept mostly used in mathematical probability theory but originated in thermodynamics. The bottom line of an ergodic system can be viewed as a system that has the same behavior averaged over time as it has averaged over the space of all the system’s states. This means that if you roll a dice 100 times, on average, you will roll a six 1/6 x 100 = 16.6666 times. Now, it doesn’t matter if we have 100 people rolling the dice 1 time or 1 individual rolling the dice 100 times. The average number of times a six will be rolled will not change. We can say that playing a game of dice, in essence, is an ergodic system.

But let’s revisit our analogy of entrepreneurship with playing a game of Russian Roulette. Again, using a gun with six chambers, the odds of someone dying in playing 100 rounds is 16.6666 times. This being the average of the space of all the system’s states. However, if one person is playing 100 rounds of Russian Roulette, the probability of that person dying becomes 1-(5/6)^100 = 0.99999999879. In other words, the player is facing certain death. The big difference with this type of game is there is an absorbing barrier, death, that stops the game. You cannot die and continue playing, as there is no eschatological verification of your state after death. Clearly, playing Russian Roulette is what can be called a non-ergodic system. One could even be brought under the impression that a non-ergodic system is nothing but a random walk with an absorbing barrier.

Riches, ruin and absorbing barriers

In the field of taking steps, or making decisions, Jeff Bezos is someone who proposes that there are reversible and irreversible decisions. If decisions are reversible, we can assume that the consequences of that decision can be erased, and we can return to a zero point. Yet, over a long enough time scale, we are left with no choice but to assume that all decisions, and situations, become irreversible.

Surely, we must recognize the inherent non-ergodic nature of most systems, including entrepreneurship. In 1913, Michel Plancherel provided a compelling proof of the strict impossibility of ergodicity in purely mechanical systems. Another crucial point to consider is the significance of avoiding an absorbing barrier, which presents a mathematical impossibility in terms of exploring state spaces. Additionally, we should be cautious when interpreting normal averages since they solely describe the system’s state averages. Russian Roulette serves as a stark example where one’s life can be jeopardized, whether it be in the first round or the ninety-ninth.

Another practical illustration is the concept of the “gambler’s ruin.” Here, a player begins with $3 and engages in a fair coin flipping game. With each instance of heads, the player loses $1, and with each instance of tails, they win $1. If the player participates in 100 rounds of this game, it becomes evident that the player will neither lose nor gain any money on average. However, it is crucial to understand that this average only holds true for ergodic systems, not non-ergodic ones. Unfortunately, this game of coin tossing does not fall under the category of ergodic systems due to the presence of an absorbing barrier at $0. It is clear that the expected outcome of playing this game 100 times is bankruptcy, ultimately resulting in the gambler’s ruin as depicted in the gambler’s ruin problem.

It seems that in a random walk in one dimension, one will always hit the absorbing barrier if you walk long enough. So, playing the game of serial entrepreneurship in an infinite number of rounds means you will hit the absorbing barrier of personal bankruptcy at some point.

A caveat and a pondering

In case of entrepreneurship, one might notice that founders who went bankrupt often bounce back to enter the game again. That’s indeed a correct observation, and in order to correctly interpret the importance of an absorbing barrier and the concept of ergodicity, it is that it describes the system, not the player. We simply assess if a system is ergodic or not, not the actor. So when we state how a game stops, we mean the player can no longer play the game he was playing. It doesn’t mean he can’t play another game, although the damage incurred by crossing the absorbing barrier might make it considerably more difficult. Without divine intervention, it has been incredibly hard to make it back alive after a lost round of Russian Roulette.

Another remark is that we generally have no idea in what system state you will hit the absorbing barrier (remember the Russian Roulette), you could blow your brains out on your first round. While it is certain you will hit bancrupcy at some point. This means that time plays an important concept in life, and specially the direction of time. You want to exit your company and die 50 years later, not the other way around. In ergodic systems, sequence trumps time. Warren Buffett once stated that, literally, anyone who survived in the risk taking business has a version of “in order to succeed, you must first survive.”

Prolonging ruin by adopting the Kelly Criterion

If entrepreneurship involves a non-ergodic system, with a high probability of financial ruin and facing ruin early on, it becomes crucial to find ways to optimize our chances. However, answering this question is a formidable task due to the complex nature of entrepreneurship in real-life, which encompasses numerous intricate factors that are hard to model accurately. In reality, founders are involved in multiple non-ergodic games simultaneously, not just the game of entrepreneurship. Therefore, we should avoid falling into the trap of the Ludic fallacy, as coined by Nassim Nicholas Taleb, which involves basing our understanding of chance solely on the limited world of controlled games and dice.

Given the realities of everyday life, it is prudent to adopt a risk-averse attitude in order to avoid encountering overwhelming obstacles prematurely. In this context, engaging in mental accounting is not only a logical choice but a crucial one for our survival. Any other approach would indeed be considered irrational. This leads us to question whether there could be an “irrational” strategy that we can exploit to our benefit.

Perhaps we can draw lessons once again from market traders. The financial markets are a game where the threat of financial ruin looms at every turn. Every surviving trader follows the principles of the Kelly Criterion, which, from an entrepreneurial perspective, can be interpreted as playing with the funds provided by the market. It entails increasing your investments when you are profitable and reducing your bets, or even refraining from placing any, when you experience losses. In the realm of entrepreneurship, it is likely that you don’t have the luxury of “house money” during the initial years. Therefore, raising capital from investors can be seen as acquiring market money or, in other words, money to be used strategically by founders to prolong their journey in the non-ergodic game of entrepreneurship. By utilising funds from the market, a founder can effectively delay reaching its absorbing barrier.

Perhaps a more recent example illustrating how humans tend to exhibit diminished loss aversion when operating with “house money” occurred during the COVID pandemic. Governments worldwide initiated grants to support distressed business owners and implemented various financial incentives. Consequently, there was a notable surge in cryptocurrency and stock trading activities. This exemplifies how governments can leverage the house-money effect to their advantage. As an illustration of this concept, during President Bush’s 2001 tax reform, every American taxpayer received a $600 tax credit. Individuals who perceived this credit as a government-provided gift demonstrated a propensity to spend more than three times the amount compared to those who regarded it as their own money. Thus, the utilisation of “house money” in the form of tax credits can potentially serve as a stimulus for an economy.

Conclusion

Through the narrow perspective of serial entrepreneurship, one can argue that blindly exposing oneself to repeated risks is a sure path to eventual ruin. This ruin may manifest in various forms, not limited to financial consequences but also encompassing reputational, social, or even physical repercussions. As a constant reminder of mortality, I keep a skull on my desk, serving as a memento mori. Observing this haunting symbol while engaged in work serves as a solemn reminder that each of us will inevitably face our own day of ruin. As a serial entrepreneur, this sobering incentive prompts me to cautiously allocate resources (thus, play with house money), seize profitable opportunities early (thus, sell too soon), and pursue frequent transactions (thus, sell often). This approach has enabled me to transition from serial entrepreneurship to portfolio entrepreneurship which is, in a way, also a risk management approach.