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Ergodicity is the study of how payoffs scale over time and space. It concerns business, relationships, sports, traveling, and many more aspects of our life.

Take the example of sports. My cousin was a promising competitive skier. However, one day, he skied too fast. He fell, broke a leg, and prematurely ended his career. It turns out that it’s not the fastest skier that wins championships but the fastest of those who get to the finish line. What’s best to win a race is not what’s best to win a championship. The long term isn’t made of a succession of short terms, each optimizable in a vacuum. Instead, payoffs change as time horizons change.

A skier

Let me clarify this by running some numbers. Take two skiers. The first one has a 20% chance of winning each race and a 10% chance of breaking his leg during that race. The second one takes fewer risks; as a result, he has a 15% chance of winning each race but only a 1% chance of breaking his leg. Which skier will win more races during a championship?

The answer is that it depends on how long the championship is. If it comprises a single race, the first skier – the risk-taking one – has a higher number of expected wins: 0.18 vs. 0.15 (each is the product of the chances of finishing a race times the chances of winning it; for example, 90% times 20% makes 0.18). However, the more races in the championship, the higher the chances that the first skier will break his leg and has to forfeit the remaining races. In fact, if we run the numbers (see the table below), we can see that the risk-taking skier wins more races than the conservative one in championships up to five races long. Any longer than that, and the conservative approach pays more. What’s the take-away? That payoffs depend on time horizons. And what’s the practical implication? That you cannot base your decisions on a payoff computed on a time horizon that isn’t yours. This is one of the big lessons of ergodicity: the study of how payoffs scale over time and space.

In the rest of this article, I will make more examples of how the strategies to win in life should consider uncertainty and time horizons. (By the way, I also wrote a book on the subject.)

Winning in Life

In the previous example, we’ve seen how it’s not the fastest skier who wins championships but the fastest one of those who make it to the finish line. Performance is subordinate to survival.

This is not just a banal argument that survival matters. It’s an argument that it matters more than performance when time horizons are long enough. We’ve seen it with the comparison between the two skiers – over a championship, the property that matters the most is not speed but resilience.

Hence the lesson for all of us: seek performance only after having assured survival. Don’t work as hard as possible; instead, work as hard as you can without risking burning out. Don’t maximize sales; instead, aim to sell as much as possible without risking your reputation and your brand’s. Don’t train as hard as you can; instead, train as hard as you can without risking major injuries. And so on.

Irreversible losses

Imagine two horses participating in a series of ten races. The black horse has a 60% chance of winning each race, whereas the white horse has a 40% chance. If you bet on a horse and it wins, you double your bet; otherwise, you lose it. You start with $10; each race, you must allocate all of your money as a bet on either or both horses. What’s the best gambling strategy?

A naive answer would be to always bet on the black horse. After all, it’s the one with the highest expected winnings. For each $10 bet, you will usually net $2 (a 60% chance of winning $20 means you will get $12 back, minus the $10 bet, which makes it a $2 gain). Conversely, for each $10 bet on the white horse, you are expected to lose $2 (a 40% chance of winning $20 means you get back on average only $8 and thus lose $2 each bet).

However, if you went all-in on the black horse and he lost, you would be left with $0. You wouldn’t have anything to bet again during the next race. You would lose the possibility to profit from the black horse’s advantage.

Here is another learning from ergodicity: irreversible losses absorb future gains. Maximizing gains requires avoiding irreversible losses.

A better strategy is to favor betting on the black horse but never go all in. If you can, keep some cash; and if you cannot, bet it on the other horses, even if their expected winnings are negative. This way, you guarantee that you will never go bankrupt, and you will always have funds to profit from bets that are profitable on average.

Again, we see that performance is subordinate to survival (in this case, survival means being able to benefit from future payoffs).

Russian Roulette and ergodicity

Russian Roulette

A simplified definition of ergodicity is as follows. An activity is ergodic if the outcome of many people completing it once is the same as one person completing it many times.

For example, Russian Roulette is non-ergodic. It is a gambler’s game of the riskiest kind. The player takes a gun, empties the cylinder, and puts back a single bullet. Then, he spins the cylinder to randomize the position of the bullet. Finally, he takes the gun to his head. After staring at death for a few seconds, he pulls the trigger. If he survives, he collects a prize, usually in the tens of thousands of dollars. (Obviously, do not try this at home or anywhere else.)

Imagine that the prize is $6000. If a hundred people play Russian Roulette once, the average outcome is $5000 in winnings (each person has a five-in-six chance of winning). If one person plays Russian Roulette a hundred times, the average outcome is a dead person.

The expected returns of playing Russian Roulette

This was an extreme example, of course, but it shows that if we play Russian Roulette once, losing means that we lost the prize; if we play Russian Roulette more than once, losing means that we lost the prize and all future chances of winning. This last part is a “phantom consequence” that cannot be neglected. If you participate in a non-ergodic activity, you do not just care about the average; you care about phantom consequences too.

Baking cakes and ergodicity

Baking a cake

Baking cakes is also a non-ergodic activity. If 10 beginners bake a cake once, the outcome is 10 bad cakes. If one person bakes 10 cakes, the outcome is 2 bad cakes and 8 good ones (after some learning) – the phantom consequence).

What’s the expected outcome of baking a cake? A bad one (as in the first case)? Or almost a good one (as in the second case)? It depends on how long one participates in the activity. This is true of endeavors other than baking cakes. For example, dating a person ten times results in a very different relationship than dating ten people once.

One of the lessons of ergodicity is that when there is a phantom consequence (a form of irreversibility), averages do not tell the full story.

Why do we have moods?

In our society, many see being moody as a problem. This is true to some extent, but moods are generally beneficial. For example, consider two hunter-gatherers, Alice and Bob. They live in a territory where the primary source of food is berries growing under bushes. Some bushes have no berries, whereas others are full of them. Gathering them is tiring, for one has to walk close to a bush and lift some of its leaves to know whether it contains any berry. Bob is moody, whereas Alice cannot feel any mood. Who do you think is a better gatherer, all other things equal?

The answer is Bob. He is likelier to check the bushes with berries and not check those without berries. Why is that?

Well, Alice does not feel any mood, so she tends to sample every bush she walks by – an inefficient method. Conversely, Bob checks the first bush; if empty, he becomes discouraged (a mood) and walks for a bit before checking another bush. Once he finds some berries, he gets excited (another mood) and checks all the bushes nearby. This strategy is advantageous because, in nature, resources tend to cluster together. If a bush is particularly fruitful, the chances are that the ones around it are also fruitful because they grow on the same fertile soil; and if a bush doesn’t carry fruits, those around it probably don’t either. Better to focus your efforts where resources cluster.

Moods are adaptations to environments with clustered resources.

As the hunter-gatherers’ example showed, moderately moody people tend to be more efficient than moodless ones. (The keyword being “moderately” – as with most things, excesses are bad.)

Moods improve effectiveness by making people spend more time on what looks promising and less time on what is likely to be a waste of time. Moreover, they reduce exposition to what is dangerous (wasting time and energy), thereby improving survival. They allow us to adapt to a world where threats and resources are not uniformly distributed.

This is another example of how, when measurements and strategies do not scale homogeneously, the study of ergodicity comes in handy. What seems irrational – moods – is actually rational after accounting for inhomogeneities.

More on ergodicity

Over the previous paragraphs, I barely scratched the surface of ergodicity, ergodicity economics, and its applications.

In my book “Ergodicity” (ebookpaperbackhardcover), I examine more aspects and applications of ergodicity, including:

  • What ergodicity means for relationships, careers, and companies.
  • Three strategies to manage the problems of non-ergodicity
  • More definitions of ergodicity and more interpretations of the concept.
  • How payoffs and measurements scale across dimensions other than time (e.g., space)

I answer questions such as:

  • How can you make your businesses, investments, relationships, and yourself more resilient to the passage of time?
  • How can you balance between short-term and long-term while making decisions?
  • Does sharing make one stronger or weaker?

There is currently an eBook discount for the readers of this article (use this link). You can also purchase the paperback from Amazon but there is no special discount there.

Ergodicity: Definition, Examples, And Implications, As Simple As Possible

The video on What Is Ergodicity

In 2021, I also recorded a short introductory video I made about ergodicity. There’s a lot of overlap with what I wrote here, but it’s only 22-minutes long. Enjoy!

Interested in me giving a talk on ergodicity (to your organization, on your podcast, etc.)?

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