Ergodicity: The Hidden Tax on Risk
Why the average return on paper is never the return you actually get.
Grounded in the research on ergodicity economics
Not What You Think
A coin flip: heads you gain 50%, tails you lose 40%. The ensemble average across many people looks positive — run the math, it's +5% per flip. So you play. But over time, YOUR outcome compounds differently. One bad run and you're down a hole you can't climb out of. The long-run average for a single player is -5% per flip. Two totally different numbers. That gap is ergodicity — and most financial advice ignores it.
Peters Named It
Ole Peters, a physicist at the London Mathematical Laboratory, laid this out rigorously in a 2019 Nature Physics paper. His argument: classical expected utility theory (going back to Bernoulli in 1738) averages outcomes across imaginary parallel universes, not across time. You only live one sequence. Peters called this the 'ergodicity problem' and argued it resolves the St. Petersburg paradox and explains why rational people avoid positive expected-value bets.