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The Regenerative Life: How to be an ergodic pathfinder

Updated: Aug 26, 2023

This article is about managing personal risk and uncertainty as part of our mission to build a more regenerative life. [i] "Personal" is emphasized because how an individual manages risk, mostly, should be managed very differently than group risks or related statistics we are typically taught in school. The ergodicity of the systems in our lives is the lens by which we will explore risk and uncertainty.  Admittedly, ergodicity is a strange word.  This article will give you a confident understanding of ergodicity.

But first, let’s consider the ubiquitous systems of our lives. Some are more nature-made; like trees, the sun, weather, gravity - and even how we defrost dinner. Many systems are people-made; like politics, gambling, investing, companies, markets, and many others. The degree to which a system is nature-made or people-made is essential to understanding risk and uncertainty. Ergodicity brings clarity to the different risks and uncertainties found in:

a) the nature of the system's participants, like individuals versus groups,

b) the nature of our systems, like natural versus people-made, and

c) the time frame relevant to the risks taken, like shorter versus longer time periods.

Many people-made systems are intrinsically non-ergodic. On balance and in isolation, non-ergodic systems are not regenerative. As we discuss in later sections, there are certainly ways to add resilience to non-ergodic systems to blunt their non-ergodic character. But even with added resilience, non-ergodic systems may lead to ruin. It is not a matter of "if," it is a matter of "when." Benjamin Franklin - an American founding leader, inventor, and polymath - intuitively understood the nature of non-ergodic systems when he remarked:

"...nothing can be said to be certain, except death and taxes."

The difference between risk and ruin is significant. Ruin is another way of saying "game over." Game over is when - whatever reoccurring system or game is being engaged - the outcome of the last round prevents you from coming back for future rounds. For example,

  • In gambling, this is when you are out of money.

  • In investing, this is when the company's share price drops and does not recover.

  • In Russian roulette, this is when you are dead.

The difference between risk and ruin is also critical to managing risk, uncertainty, resilience, and regeneration in our lives. N.N. Taleb is an author and mathematician. Taleb is a former risk management professional and securities trader. Dr. Taleb kick's off our ergodicity exploration by observing:

“One may be risk loving yet completely adverse to ruin.”

I hope you enjoy the article and remember - the future is your playing field!

- Jeff Hulett

Summary and Table of Contents:

Essential to understanding the nuances between risk, ruin, resilience, and regeneration is found in the study of this peculiar and not well-known word:


This article explores ergodicity by first providing a framework with helpful examples. We then provide several practical cases. In those use cases, we show the ergodic playing field between customers and businesses, as well as, employees and employers. In many ways, company profits are the difference between:

  1. The company's ability to create a more ergodic environment, and

  2. The company's ability to get its customers and employees to accept a non-ergodic system.

We suggest Definitive Choice to help you achieve a more regenerative life by better managing personal risks. Definitive Choice helps optimize decisions by properly managing ergodicity and knowing when to change to a more ergodic path.

  1. What is Ergodicity?

    1. Ergodic coin flip example

    2. Non-ergodic Russian roulette example

    3. Ergodicity framework

    4. Entropy and Ergodicity

    5. Definitive Choice as a resource to manage ergodic pathways

  2. Ergodicity related to investing

  3. Ergodicity related to employment

  4. Ergodicity related to gambling

  5. Ergodicity related to economics

  6. Ergodicity related to physics

  7. Conclusion and Notes - We provide an example of a famous scientist confusing ergodicity. [ii] It is easy to do!

About the author: Jeff Hulett is a behavioral economist and a decision scientist. He is an executive with the Definitive Companies. Jeff teaches personal finance and the decision sciences at James Madison University. Jeff is an author and his latest book is Making Choices, Making Money: Your Guide to Making Confident Financial Decisions. His experience includes senior leadership roles in banking and bank risk consulting. Jeff holds advanced degrees in finance, mathematics, and economics. Jeff and his family live in the Washington D.C. area.

Thanks to Graham Boyd, Ole Peters, Luca Dellanna, NN Taleb, and many other brilliant researchers and practitioners helping people manage personal risk in their lives via ergodicity principles.

1. What is Ergodicity?

All system outcomes have risk and uncertainty. This occurs because we do not have total control of the outcome at the time we engage a system. Flipping a coin is a simple system example. At the moment we flip a coin, we do not know if the outcome will be a head or a tail. We do understand there is about a 50% chance of the coin landing on either side.

Ergodicity is the degree to which probabilistic outcomes of systems are the same regardless of how the systems are engaged over time. [iii] If a system is perfectly ergodic then the outcome likelihood is the same regardless of whether many system participants engage the system simultaneously or whether one participant engages the same system over time. The degree of ergodicity relates to comparing probabilistic system outcome differences between:

  • Cross-sectional ("CS") distribution - Many participants engage the system at once. A CS distribution is sometimes known as an ensemble.

-- and --

  • Time series ("TS") distribution - One participant engages the system many times over time.

Ergodicity foundation - The order of operations matters!

For Example:

Ergodic: A coin-flipping system (with a fair coin and consistent flipping conditions) is ergodic.

coin flip

Regardless if:

  • 100 people flipped a coin at the same time (an example of a cross-sectional "CS" distribution)

-- or --

  • 1 person flipped a coin 100 times (an example of a time series "TS" distribution),

Then, in either case, the outcome likelihood (or probability) is expected to be approximately 50% heads or tails.

Time is a friend of an ergodic system - like a simple coin-flipping system. Over time, your outcome converges on the CS "best" outcome, represented by heads or tails. Convergence is another way of showing that an ergodic system is regenerative over time. In the case of coin-flipping, gravity is the essential environmental condition of the system. Gravity is expected to persist over a very long time period. As discussed below, other activities less exposed to ruin are how air moves and other natural activities.


(for coin flip 'heads' probabilities, 50% TS = 50% CS)

Graph - Ergodic - converges on best outcome

Source: Author computer simulation. TS = 100 cumulative random coin flips.

CS = 1/2

Please note: This is a simple coin-flipping system example intended to describe key elements leading to an ergodic outcome. However, a coin-flipping system outcome could certainly be non-ergodic. The essential determinant is the transformation function for the expected outcome (or expected value) and how it responds over time. If the transformation function is not sufficiently convex, then the expected value outcome will be non-ergodic. Please see the citation for Jensen's Inequality and how convex functions transform linear inputs. A personal finance example shows how compounding financial returns of a diversified portfolio creates regenerating wealth! This occurs because:

  1. The compounding transformation function of the time value of money is sufficiently convex to lead to an ergodic outcome.

  2. Also, the stochastic nature of the underlying investments is sufficiently diversified to lead to an ergodic outcome. [iv]

Non-ergodic: A Russian roulette system (with a six-bullet chamber) is decidedly non-ergodic.

Order of operations is essential to the Russian roulette outcomes:

  • If 100 people play Russian roulette at once, 1/6th (or 17%) of them will likely die. (CS distribution)

-- or --

  • If I alone try to play Russian roulette 100 times, there is an almost 100% likelihood I will be dead long before I get to 100 attempts. (TS distribution)

Time is an enemy of a non-ergodic system - like a Russian roulette system. Over time, your outcome diverges from the CS "best" outcome. A ruin (death of player) outcome is almost certain to be achieved early on in this time series process. Divergence is another way of showing that a non-ergodic system, on balance, is not regenerative over time. In the case of Russian roulette, the firing gun is the essential environmental condition of the system. Discharging a gun persists over a very short time period. As discussed below, other activities more exposed to ruin are gambling, lottery, stock investing, and most other common human activities.


(for Russian roulette 'death' probabilities, 100% TS > 17% CS)

Source: Author calculation. TS = (1-1/6)^n, where n is the whole number from 1 to 100

CS = 1-1/6. (Please note: The inverse of the death probability is taken to show the chance of living)

Notice the speed at which the lower red line approaches 0%. In the case of Russian roulette, the likelihood of ruin increases dramatically in the first few system engagements. Russian roulette is a VERY non-ergodic system. Other non-ergodic systems could be slower to ruin -- but will still lead to ruin just the same. For example, as we will discuss in Section 2, the average life of a company is about 20 years. While a company's "ruin" is slower, it is still necessary to properly manage the risk and uncertainty of non-ergodic systems. Please do not confuse resilience with regeneration.

Systems generally decay over time. Ergodicity is measured relative to your time standard for decay. While a system may be strictly non-ergodic at some point, ruin may not occur within your standard timeframe. Please see the 'Entropy impact framework' graphic at the end of this section demonstrating how ergodicity is relative to a human life standard. For us individuals, each person's life or time frame standard expectation is personal. This difference is commonly assessed as a risk profile. Your sensitivity to risk may be different than mine. Plus, individual risk sensitivity changes over time and situations. Also, the relative nature of ergodicity extends to the participants of the system. In section 3, employment is explored. We show how the employer can have an ergodic-like relationship with the system, whereas the employees' experience is decidedly more non-ergodic.

Non-ergodic system exceptions There are exceptions to the "systems generally decay over time" rule. As such, in some contexts, non-ergodic systems may lead to desired outcomes. Here is an example from my days as a managing director at KPMG. Let's say we hired 100 "green" associates fresh out of college. The idea is to get them productive as quickly as possible. Let's say, that in their first week, I put all the green associates on challenging and complex projects throughout the world. They would all likely struggle to be successful. So let's say the fail rate of the CS new employee population when put on super challenging projects is 100%. By the way, that is why we would never put green associates on super challenging projects out of the gate.

However, if I took one of those green associates and put them on 100 complex projects over time, they would improve. This improvement results from experience and training. While they would likely start at a 100% fail rate, over time, they would more likely rise toward a 0% fail rate. Let's say their average over time TS is a 50% fail rate. Notice, the TS and CS outcomes are still divergent as expected with a non-ergodic system, just divergent toward a desired outcome instead of ruin.

As such, training and experiential education are the opposite of decay in a medium-term time horizon. Thus, when systems do not decay, non-ergodic systems are more likely to lead to desired outcomes.

Ergodicity summary: Systems in which we participate that could lead to ruin BEFORE the natural end of your life are called non-ergodic. Systems that are more likely to lead to ruin sooner are more non-ergodic than other slower-to-ruin system activities. Ergodicity is a function of:

  1. The system - its rules and how it transforms your inputs into expected outcomes;

  2. How you participate in the system and the degree to which you are CS or TS; and,

  3. The relative entropy-impacted timeframe necessary for the desired outcomes.

Your ability to slow the non-ergodic march toward ruin is called resilience. Engaging in systems that do not lead to ruin is called regenerative. A regenerative system is an ergodic system. At its core, the understanding of ergodicity is understanding the impact of ruin via the systems of your life over time. The future is your playing field.

As a rule of thumb, we cannot rely on a population's (CS) averages when there is a possibility of "game over" ruin when an individual engages a system in an iterating (TS) manner. This is true, even if the individual is a member of the same population. This is because the ruin possibility makes an individual's context non-ergodic. Since many systems are non-ergodic, this means averages are often deceiving. [v]

There are some exceptions to the rule that systems decay over time. In these contexts, non-ergodic systems may lead to desired outcomes. In the main, this article's focus is the "systems decay" context and that non-ergodic systems may lead to ruin.

Next, ergodicity is explained in a 4 step graphic. We introduce the universal uncertainty driver underlying ergodicity, called "entropy." We discuss entropy in the following section.

Ergodicity - explained in 4 steps

In section 6, Birkhoff’s Ergodicity equation is presented as a compact way to specify this graphic.

Entropy is the universal uncertainty driver underlying ergodicity

Ergodicity is best understood as a matter of degree. Ergodicity also relates to a system's entropy. The human life span is the standard when relating entropy to ergodicity. We manage entropy as a means to reduce the chance of ruin that may take away from our lives. Luca Dellanna, in his book about Ergodicity [vi], mentions: "all our decisions are underpinned by an implicit assumption of a time frame to optimize for." As such, deciding to do something today that may hurt us today (like playing Russian roulette) is perceived as much worse than deciding to do something today that may hurt us in 20 years. (like investing in the wrong company) Then, any system that may hurt us, conceptually, after our expected lifespan is generally not even considered as something that could hurt us.

Ergodicity is dynamic - an environmental example

Our ergodic-impacted (mis)perceptions are an important reason why global warming has been a difficult challenge... its relative entropy and ergodic nature were thought to be "low and long." Our collective environmental inattention is quickly changing global warming to a non-ergodic "high and short" system outcome. In effect, humanity, through its own environmental-neglecting transformative actions, has converted a once ergodic system (our environment) to a "risk of ruin" non-ergodic system. This example demonstrates the ergodic scale is dynamic. It is possible to move systems to either side of the entropy scale. This may be done by changing one or more of the 3 ergodicity factors mentioned earlier - participants, system, or timeframe.

This means the relative speed of entropy between systems and the resulting decisions about those systems is central to an objective comparison of risk and uncertainty. Also, like in the case of the environment, human systems may dynamically impact and transform natural systems. Thus, the speed of entropy may change over time.

How quickly a system is subject to entropy defines the degree of ergodicity. The slower the entropy, the higher the degree of ergodicity. Given our lifespan is about 80 years, activities like Russian roulette may quickly and dramatically impact our standard entropy. Thus, Russian roulette is at the far end of the non-ergodic entropy scale. Slower entropy systems like the solar system are at the far other end of the ergodic entropy scale. The sun is on a much slower decay cycle than us humans. In the next graphic, please notice the "Entropy scale" from the last graphic is turned on its side.

A deeper dive into Entropy:

Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. In physics, entropy is also known as the Second Law of Thermodynamics. The law tells us the universe is inexorably moving toward higher entropy. Higher disorder is not a matter of "if" it is a matter of "when." Much of the structure we surround ourselves with, whether homes, jobs, cars, roads, cities, medical services, etc is humanity's attempt to reduce entropy. Aristotle said, "Nature abhors a vacuum." Aristotle suggests the universe is moving toward higher entropy by moving away from a structure that maintains a vacuum. Thus, the universe considers human life, or any structured life for that matter, a vacuum it is trying to move away from. (Yikes!)

The entropy principle can also be found in the Bible - “By the sweat of your face you shall eat bread, till you return to the ground, for out of it you were taken; for you are dust, and to dust you shall return." - Genesis 3:19. This biblical reference is a declaration of the entropy principle. We are born from dust via an explosion of negative entropy -- thanks, Mom! We work and nourish ourselves to delay entropy. The universe inevitably works us back to the dust of our higher entropy beginnings. Extending from this entropy-like biblical reference, ergodicity initially describes the systems of our lives. Ergodicity further describes how we participate in those systems over the time between our dust beginnings and our dust endings. [vii]

In the later physics section 6, we explore how ergodicity is a descriptive feature of entropy.


Reader Resource: Apps and related tools help you achieve a more regenerative life. This occurs by assessing value and utility in the service of properly managing exposure to the ergodicity of systems. Objectively identify, weighing, and assessing your ergodic-based criteria and alternatives is central to making the best decision. Especially, before making any purchase or important decision, such as a job change. See the following app:


2. Ergodicity related to investing

Investing is a good example of where ergodicity confusion may create undesired risks.

Most companies eventually fail. Credit Suisse and CNBC demonstrate the average life of companies is shortening, down from an average of 60 years in 1958 to an average of 20 years in 2012. The average life trend shortens as technology disrupts older companies. The scaffolding needed to support companies as they grow from small to large may become a source of fragility. Thus, disruption reveals a company’s lack of adaptability to changing markets. So investing in one company, no matter how good it is today, may at some point lead to a loss of value. Statistically, a good company is likely to become a victim of its own success as it grows and builds structure to support that growth. To manage this risk, a best practice is to invest in portfolios of companies and periodically rebalance holdings. If investing was ergodic, we would only need to invest in one company. This recognizes that investing, by its very nature, is a non-ergodic activity. Rebalancing is how less ergodic companies are culled from the portfolio. This approach assumes business activity is an ergodic signal.

It is possible individual companies could be more ergodic than others. Entrepreneur and ergodicity expert Graham Boyd said [viii],

"All of us, and our children, can thrive in the coming decades, because we can build a regenerative global economy by using ergodic finance and investment."

Dr. Boyd is suggesting investment portfolio construction benefits from identifying companies with higher ergodicity. Perhaps, someday, there will be an index to help identify company ergodicity.

Companies promoting their own employee stock ownership plans may expose their employees to undesired risks. A company, because it is likely to fail at some point, is non-ergodic. As such, stock ownership plans are very risky. Just look at what happened to the GSEs (the Government Sponsored Enterprises, Fannie Mae and Freddie Mac), resulting from the Financial Crisis and Great Recession.

After they went bankrupt and were ordered into conservatorship, the employees lost their company stock value. The employees of the GSEs had accumulated stock via various company stock ownership plans. At the time, the GSEs were backed by an implied guarantee from the U.S. Government. So if GSE employees and retirees lost value in their company stock ownership plans, imagine the risk of companies without the backing of the U.S. Government!

Fannie Mae’s workers had $116 million in the employee stock ownership plan at the end of 2006. [In 2008], it’s more like $17.5 million. Ouch.

- New York Times article and this was before they went bankrupt!

Company stock ownership plans expose employees to diversification risk. If a company fails and its employees are deeply invested in the company stock, then they lose both income and wealth. It is a best practice to diversify that risk by separating sources of income and wealth.

To be clear, I’m certainly not suggesting company stock ownership plans are intrinsically bad. Like any other tool, my concern relates to usage. In this case, my concern relates to a potential lack of diversification. Single-company stock ownership should only be considered in the context of a well-diversified investment portfolio. Complicating the considerations, some companies provide significant incentives for their employees, especially executives, to participate in employee stock ownership plans. For executives, SEC public disclosure requirements and tax liabilities may create a disincentive to divest employee stock.

For a deeper dive into ergodicity-sensitive investing, please see the article:

Ergodicity and personal risk management rule of thumb:

Individually, it is a best practice to simulate our long-term outcomes after repeated engagement with the same system. Relying upon system averages across a population, even if we are a member of that population, is often radically different than our realized lifetime experience.

An ergodic v. nonergodic investment example:

Let's say you have $100,000 to invest. You saved this early in your career. You have a 25-year time frame for when you will need it for retirement. You expect this investment will be a significant contributor to your retirement. You have 2 options.

  1. Invest it in a highly diversified fund expected to earn 10% annually. Because of the diversification, there is no chance of ruin.

  2. Invest it in an undiversified single company on the cusp of a big breakthrough. The prospectus suggests the return should be 20% annually. But also, there is a 10% chance the company will face ruin at some point over the 25 years.

Your first response is, let's estimate what the returns will be in 25 years, assuming both investments are not ruined. Then we can figure out our margin of error to offset the ruin risk. The standard future value formula reveals investment A is expected to earn $1.1 million. However, investment B is expected to earn over $9.5 million!

Your initial response is "WOW, there is an over $8 million margin of error. B seems like the best choice. There is only a 10% chance of ruin... that seems worth it for $8 million of upside."

But is it?

Next, your newly acquired ergodic thinking kicks in. You decide to simulate the impact of ruin. The next graph shows such a simulation.

difference between ergodic and non-ergodic investments

It turns out, when you include the chance of ruin, investment B is only worth about $700k (bottom solid yellow line). The top blue line demonstrates the ruin magnification that decreases the expected return on investment B. Just like the Russian roulette example, ruin is geometric over time in non-ergodic systems. Time is NOT a friend of non-ergodic systems. The $9.5mm is just an unrealistic teaser. However, the EV when you overlay the risk of ruin on the investment is subject to HUGE uncertainty. You do not know when the ruin will occur. Thus, for investment B, the expected value is lower when considering ruin AND the uncertainty of receiving that lower value is higher. A "lose/lose!"

Then you reconsider investment A. The $1.1 million is practically guaranteed. The diversification and rebalancing eliminated the chance of ruin.

So, doesn't a guarantee of being a millionaire sound better?

Another consideration is the awareness of how you engage the system. You may gain awareness by answering the question:

Am I the gamble or the gambler?

This is an important distinction. In this example, you are "the gamble." This means this money is for a single important use, like retirement. Without it, your retirement will fail.

However, what if the example was set up differently? What if the $100k was only a small portion of a much larger retirement portfolio? In this recast example, you are now "the gambler." In the appropriate investment strategy, you may decide to accept investment A. Effectively, by accepting investment A, you are knowingly accepting a relatively small nonergodic risk in the context of a (presumably) much larger ergodic portfolio. The small chance of receiving a large, $9 million+ payoff if the company breaks through is more likely to be worth it. But only in the context of an otherwise ergodic portfolio.

Please see our article for our investment strategy to achieve an ergodic investment portfolio.

3. Ergodicity related to employment

I am a former Managing Director for KPMG. KPMG is a global professional services firm providing accounting, tax, and consulting services. The firm has been around since 1891. Clearly, they have stood the test of time and are an extreme outlier to how long companies typically stay in business. Next, I share my employment experience at KPMG, though, there are many similarities to other large firms.

KPMG creates structures to enable ergodic-like outcomes within a non-ergodic business environment. Their ergodic-like structures include risk management, legal, compliance, resource management, technology, and other ergodic-enabling internal organizations. An essential way by which they enable ergodic-like outcomes is via their pay and incentive structure.

A partnership like KPMG has significant expenses related to retired partners. It is the job of the current workers to “pay it forward” with a portion of current revenue going toward a significant retired partner fixed cost. The idea is, someday, the current workers will graduate to a retired partner or other retirees with benefits. Then, the people that come after them will keep the forward retirement fixed payment cycle going.

Firm leadership's priority is to incentivize consistent results to pay those significant fixed costs. As such, the most important revenue goal is consistency. Certainly, firm leadership does not mind if someone hits their revenue goals out of the park. But they do not incent those results. Most firm incentives are protective. That is, an employee missing their revenue goals is at high risk of being shown the door. In keeping with a consistent, ergodic-like environment, consistency of delivery is valued much more than more volatile but value-creating revenue delivery. This consistent delivery value is sought even if larger, but less consistent results are likely. As such, the firm attracts people that are good at protecting more modest but predictable revenue streams. The firm also attracts people willing to accept a concave or nonergodic employee compensation plan.

Concave compensation plan explained: During the annual performance cycle, the typical concave comp plan includes a high downside for missing expectations (downside = getting fired) vs. a low upside for hitting revenue goals out of the park (upside = modest % bonus based on the employee’s current salary and their individual revenue is diluted by the average revenue of the firm.)

Additionally, the firm creates an ergodic-like structure via a portfolio of professional services practice areas. That way, if one practice area is doing well and another is not, they can shut down the underperforming practice area and gear up the higher-demand practice area.

Professional services employee employer relationship.  Convex, Ergodic, Concave, Nonergodic

Professional services firms like KPMG create ergodic-like resilience by putting their non-ergodic ruin potential on their employees.

Employer: To a professional services firm, people are factor inputs. If one does not work out they can be replaced with another with potentially unlimited revenue generation upside.

This is ergodic and convex.

Employee: However, to an employee, all their eggs are in one basket. They likely only have one job. The downside is employment existential. They can get fired.

This is nonergodic and concave.

As an aside, in the United States, the Fair Labor Standards Act ("FLSA") permits professional services firms to "exempt" their employees from protections. In the case of a "non-exempt" employee, those protections reduce potential non-ergodic employee outcomes (burn-out, chronic health problems, etc) Thus, typically, the FLSA protections, like time and half pay for over 40 hours of work per week, do NOT extend to consultant professional service workers. It is certainly ironic that the law enacted to help employees is actually enabling professional services firms to put potential non-ergodic outcomes on their employees. In many ways, today's information age consultants are like the factory workers protected by the "non-exempt" status of the industrial era implemented FLSA. As such, at some point, it would not surprise if FLSA protections are extended to consultants and other professional services workers.

For a deeper dive into employment economics and what is called the "Greedy Work" professional services employment environment, please see section 4 and the appendix of the article:

Finally, as an employee or worker, you may wonder, "How do I manage my personal employment risk so as not to be a non-ergodic sink for those ergodic-seeking firms?" Good question! One possible answer is to become the gambler and not the gamble when it comes to your relationship with work. That is, seek a portfolio of work across many companies as either a labor provider or a small business owner. This way, you are diversifying your employment (labor supply) risks across many companies (labor demand). If one company does not work out, you have other work to rely upon. Also, if one company works particularly well, you could scale up your time or bring in others to leverage your time and help grow your relationship with a successful venture.

But if you are an employee in a single firm, you may manage your work as a portfolio series. This approach puts a premium on knowing when to change jobs. The app resource suggested earlier helps you know when it is time to change jobs.

For a deeper dive into job change processes, please see the article::

Please note: I am careful to use the word “Ergodic-like.” The firm cannot achieve natural ergodicity because of its size and existence within a non-ergodic marketplace. A firm like KPMG is a resilient, but still a non-ergodic firm. Recall the 2 earlier graphs:

  1. The first is an ergodic coin-flipping system - it naturally converges on the best outcome over time.

  2. The other is a non-ergodic Russian roulette system - it naturally diverges from the best outcome over time.

The firm implements resilient processes to guide a naturally diverging non-ergodic system toward the outcome of a more ergodic system. But, the firm is still swimming against the ergodicity tide.

For a deeper dive into ergodicity, concavity, and convexity in employment relationships, please see the article:

We suggest ways to have a more regenerative relationship with work.

When is it time to change jobs? Please see the article:

4. Ergodicity related to gambling

Ergodicity in gambling has similarities to investing. However, gambling has a “staying power” characteristic that helps us understand the degrees of ergodicity. Gambling generally has two primary agents, the bettor and the house. The bettor places the bet, the house makes the bet. The odds are the chances the bet will pay off, once the bet is made. Both agents are aware of the odds. However, in most cases, the house's system is more ergodic than the bettor's system. This means the house can absorb more losses until the payoff makes them whole. On the other hand, the bettor has much lower staying power. The bettor is more likely to run out of money before the house. Thus, the bettor’s ability to absorb risk is lower, even though they are operating under the same odds as the house. Keep in mind, losses and gains are inversely related between the house and the bettor. That is, the bettor’s loss is the house’s gain and vice versa.

In fact, the house depends on this relative ergodicity principle as the source of revenue. There is a higher chance a bettor will leave before they realize a payoff than the house will not be able to absorb additional losses before the payoff. The house, like a bank, is much better capitalized than the bettor. That difference is how the house makes money.

Gambling can be compared to the risks from wildlife, like bears. There is an old saying when fleeing from a bear, "You do not have to be faster than the bear, just faster than the next faster person running from the bear!" In the case of gambling, the odds are the bear, the house is the faster runner, and the bettors are more likely to be the slower-running bear snacks.

For a deeper dive into gambling and decision-making, please see the article:

5. Ergodicity related to economics

In the last couple of decades, the economics profession has evolved. Underlying this change is the impact of ergodicity. [ix]

“Much of classical economics assumes that human behaviour is founded on the expected average outcome of the group (see Expected Utility Theory). This works under the assumption that most environments or situations are ergodic, when in fact this is not the case.”

- Joe Wiggins, CFA and portfolio manager

This statistical mechanics approach works well when describing gases and entropic behavior. However, in the world of human affairs, very few activities are ergodic. Paul Samuelson was a Neoclassical economist who led a mathematical revolution in the economics profession in the second half of the 20th century. The underlying assumption of ergodicity in the Samuelson-influenced branch of economics is problematic. (E.g., Expected Utility Theory, Efficient Market Hypothesis) It was a convenient assumption to enable mathematical rigor. But the non-ergodic nature of humanity proved to be incompatible. In the 21st century, the behavioral economics revolution improved economic formulations with more realistic ergodicity assumptions.

6. Ergodicity related to physics

Given entropy is the ultimate definition of ruin, then the human struggle against entropy is equivalent to our search for ergodic systems. At least, the human struggle against entropy relates to building resilience in known non-ergodic systems.

See the following link for a nice article on ergodic systems and economics in Nature:

In the late 1800s, Ludwig Boltzmann developed the statistical mechanic's rigor to entropy. Boltzmann also developed the initial ergodicity conjecture, flowing from his work on entropy. Ultimately, in 1931, George Birkhoff and John von Neumann are credited with formalizing ergodicity mathematics.

Birkhoff’s Ergodicity equation:

This is the compact mathematical formulation for the 4-step graphic presented at the beginning of the article.

To interpret Birkhoff's equation - an individual performing the same activity over time (left side of the equation) has the same probabilistic outcome as many individuals performing the same activity at the same time. (Right side of the equation). This is a perfectly ergodic system.

Also, a gas being released from a closed container would have an ergodic relationship to its surroundings. Meaning the gas would have an equal distribution across the new container. In effect, time becomes meaningless as a descriptor of the gas distribution in the new space. The gas would have a uniform distribution after the initial transition.

The key here is the gas movement to the new space is aligned with the Second Law of Thermodynamics (entropy). The gas outcome (I.e., a uniform distribution in the new space) is the expected entropic outcome.

Most people want to avoid ruin. (that is, entropy) As such, many human activities that are non-ergodic, if properly managed, may avoid ruin.

For a deeper dive into time and entropy, please see the article:

7. Conclusion

It is easy to confuse risk and ruin. The degree of system ergodicity is a key determinant of system outcomes and their potential for "game over" ruin. As our examples showed, ergodicity differences are critical to understanding and appropriately managing personal risk. We showed the ergodic playing field between customers and businesses, as well as, employees and employers. In many ways, company profits are the difference between:

  1. The company's ability to create a more ergodic environment, and

  2. The company's ability to get their customers and employees to accept a non-ergodic system.

Most systems impacting our lives are non-ergodic. This means we must consistently manage our risk of ruin while accepting reasonable risks. This may seem obvious but requires a decision process to help separate risk from ruin. People could significantly improve personal life decisions by managing risks via a non-ergodic lens. Warren Buffett is the chairman of Berkshire Hathaway, an investment firm. Buffett is also one of the richest people in the world. Mr. Buffett demonstrates his intuitive ergodicity understanding with the following comment:

"Never test the depth of the river with both feet."

Please see the article Our investment barbell strategy for an investment strategy that implements ergodicity principles. The strategy embraces risk and avoids ruin. The app mentioned earlier provides easy-to-use tools to help manage ergodicity in your life.



[i] There are nuanced but important differences between risk ("the known unknown") and uncertainty (the unknown unknown). The differences are explored in the following article:

[ii] In Richard Dawkins’ book, The Selfish Gene, the author uses a probability-based evolution comparison example that misses the mark from an ergodicity standpoint.

"At some point a particularly remarkable molecule was formed by accident. We will call it the replicator. It may not necessarily have been the biggest or the most complex molecule around, but it had the extraordinary property of being able to create copies of itself. This may seem a very unlikely sort of accident to happen. So it was. It was exceedingly improbable. In the lifetime of a man, things that are that improbable can be treated for practical purposes as impossible. That is why you will never win a big prize on the football pools. But in our human estimates of what is probable and what is not, we are not used to dealing in hundreds of millions of years. If you filled in pools coupons every week for a hundred million years you would very likely win several jackpots."

As it relates to ergodicity, the football pool/evolution probability comparison is like comparing apples and oranges:

  • A football pool is non ergodic. Eventually, the pool player will run out of money. Thus, there is a different probability of ruin the longer the game is played.

  • A natural system like the earth and evolution is ergodic. In effect, the probabilistic evolution game can be played forever with little impact on probability.

[iii] Physicist Ludwig Boltzmann first theorized ergodicity in the 1870s. His theory related to the equalizing atomic nature of gases over time and across space. In the 1930s, John Von Neumann, along with George Birkhoff, proved Boltzmann’s ergodicity conjecture.

As a suggested reading: NN Taleb, in his book Skin In The Game, does a nice job applying Ergodicity principles across a number of disciplines.

[v] The potentially deceiving nature of averages is explored in the following article. We show how averages across arithmetic and geometric transformations, within the same system, can lead to very different results. The moments of statistics are explored, to help reveal the nature of different populations. The 1st moment (average) is shown as often very deceiving without its more fulsome descriptive moment compliments (2nd - variance, 3rd - skewness, and 4th - kurtosis)

[viii] Boyd, Reardon, The Ergodic Investor and Entrepreneur, 2023

[ix] The following article provides a good explanation concerning ergodicity in the context of economics.

Wiggins, We Need To Talk About Ergodicity, Behavioural Investment, 2020

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