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Ergodicity
Systems / Concepts
The average across many people is not the average across one person's life.
What It Means
An ergodic system's time-average equals its population-average. A non-ergodic one doesn't. Most real-world systems — especially ones with ruin or path-dependence — are non-ergodic. Playing Russian roulette once with a hundred people produces different outcomes than a hundred times with one person.
Why It Matters
- Expected value is misleading when outcomes can wipe you out.
- "On average, investors do X" tells you nothing about the investor who went bankrupt in year two.
- Path-dependence means the sequence of events matters, not just the statistics.
How to Apply
- For any strategy, ask: what happens if I lose badly early?
- Avoid bets with ruin built in, even with positive expected value.
- Separate population statistics from individual trajectories.
Example
A coin flip that doubles your money on heads and halves it on tails has positive expected value across people but loses money over time for any single person.
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