Published: 2025-12-21 by Luca Dellanna
What is ergodicity and why does it matter? Learn how irreversible outcomes affect long-term performance in investing, business, and life decisions.
"One of the most important books I've read, period. It's short, articulate, and expansive on a singular subject matter — ergodicity, which is really the key ingredient to success in life, marriage, business, family, happiness, health, etc."
Blake Janover
CEO, Janover Inc.
"One of the most important books for everyone to read. Ergodicity should be taught in school and it should be a common metric in businesses that leaders pay attention to and are deliberate about."
Matt Cannon
"A fascinating book […] Once I started, I couldn't put it down […] the math is minimal, and Luca treats the subject well. I wish I had read it two years earlier"
Robert Matthews
VP of Engineering, Equifax
"One of the very best books I read about risk management. A must read."
Alessandro Francescotto
Partner, Excellence Consulting
"Profoundly insightful [...] If you are someone who often needs to make decisions under uncertainty and using incomplete information (which I think applies to most of us), then Ergodicity is a must-read."
Dev Ashish
StableInvestor Founder
"Brilliant. Must read."
N. S. Ramnath
Journalist & Author
"A brilliant, concise, thought-provoking gem. A must-read for investors."
Rakesh
Investor
"A great book for those who quickly want to familiarize themselves with the concept of ergodicity. The author goes to great lengths explaining the concept in easily understandable terms. Highly recommended!"
Auke Hunneman
BI Norwegian Business School
"It helped clarify several longstanding pragmatic questions I had about uncertainty and risk [...] a lucid explanation, accessible for a general audience."
Pankaj Saikia
Datafarer co-founder.
"Excellent book. Highly recommended. Luca compresses a lot of wisdom and actionable guidance into few words. No fluff, no fillers, only thought through foundational ideas."
Eleanor Berger
AI consultant
One of the most dangerous misconceptions in decision-making is that maximizing expected value always leads to optimal outcomes. This belief has led countless investors, entrepreneurs, and professionals to financial ruin despite making “mathematically correct” decisions.
The missing piece? Ergodicity.
Consider this bet: flip a coin. Heads, you gain 50% of your wealth. Tails, you lose 40%.
The expected value is positive:
(0.5 × 50%) + (0.5 × -40%) = +5% per flip
Traditional economics says: take this bet every time. The expected value is positive!
But let’s see what actually happens. With $100, after one heads and one tails (in any order):
Either way, you end up with $90 - a 10% loss.
After 10 flips, your expected wealth taking into account the +5% per flip average is about $163. But what happens in practice, is that you’re more likely to find yourself with a loss.
This is not a paradox: it’s the difference between what happens to the average of a population versus what happens to an individual over time.
To further understand this phenomenon, let’s consider the gambler’s game of Russian Roulette. 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.)
If the prize of winning one round of Russian Roulette is $10,000, its “expected value” is:
(5/6 × $10,000) + (1/6 × $0) = $8,333
What if you play it 10 times? The average outcome is not 10 times the average returns of playing it once, but death.
That’s because your probabilities of survival decrease with each round played.
This reveals the fundamental flaw in expected value thinking: it assumes you can somehow experience the average across all possible outcomes. But you only live one life, experiencing one timeline.
In ergodic systems, time averages and ensemble averages converge. In non-ergodic systems, they diverge, often dramatically.
What makes a system non-ergodic? Irreversibility.
When losses are irreversible, losing a bet doesn’t just mean losing that bet but also all future ones (and thus, missing their returns).
Most important decisions in life are non-ergodic:
There is a common belief that people are irrationally risk averse. It’s the result of experiments such as the following:
“Here is a game. You flip a coin. If it’s heads, I give you $1000. If it’s tails, you give me $950. Do you want to participate?”
From a naive point of view, the expected return of playing the bet is $1000 times 50% (the chances of winning) minus $950 times 50% (the chances of losing). That would be $500 - $475 = $25. On average, every time you play the game, you’re expected to win $25. This makes the gamble apparently desirable. And yet, if researchers go around asking the question to real people, most decline. This led behavioral economists to conclude that people are irrationally risk-averse.
Are they, though?
If people had infinite cash, they could play the game as long as they wanted. The law of large numbers would kick in, their lifetime outcome would converge to their expected outcome, and they would realize the expected win of $25 per coin flipped.
However, real people do not have infinite cash. They can only play this game a few times before emptying their bank accounts or having to quit the game. Some cannot even afford to lose once.
For real people, the limitation on the number of times they can play can transform their lifetime outcome of a gamble into negative.
Imagine that you have a sum of $1000 in your pocket.
After one iteration of the game:
The average is a win of $25, as expected. However, if you are offered to play a second time, you can only afford to play if you won the first toss. Therefore, you can expect to win $25 from the second toss only if you won the first one.
This means that in four parallel universes:
After two iterations of the game, you have won an average of just:
($2000 + $50 - $950 - $950) / 4 = $37.5
This is surprising! If you had infinite wealth, you would have won an average of $25 per bet times two equals $50. But because your wealth is finite, your average win is lower: only $37.5.
More importantly, you have a one-in-four chance of winning a lot of money, one-in-four chance of winning a modest amount, and one-in-two chance of losing a significant amount.
Further readings: Ole Peters’s and Alexander Adamou’s papers discuss this problem and contain additional examples of how (non-)ergodicity explains the hidden rationality of some risk aversion and of other behaviors that would be irrational in an ideal ergodic world. As far as I know, he was the first to propose ergodicity as the solution to many otherwise puzzling behaviors.
Before making any risky decision, ask yourself:
Understanding the difference between ergodicity and expected value is one of the most valuable mental models for long-term success. If you want to go deeper:
