The Ergodicity Problem
Ole Peters · 2019
"The average outcome across many people is not the outcome any one person gets over time. When gains and losses compound, a bet can have positive expected value while nearly everyone who keeps playing goes broke — and most of economics quietly assumes the two averages are the same."
Offer a bet: flip a coin, and on heads your wealth rises 50%, on tails it falls 40%. The expected value is +5% per flip, so textbook rationality says take it, and keep taking it. Play a hundred rounds and you will almost certainly end up with a small fraction of what you started with. Nothing is rigged. The average across a million parallel players really does grow 5% a round — because a handful of astronomically lucky ones drag the mean up while the typical player shrinks by about 5% a round. Ole Peters, a physicist at the London Mathematical Laboratory, calls this the ergodicity problem: expectation values describe an ensemble, and you do not live in an ensemble. You live in one trajectory through time.
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Compounding
"Small advantages, repeated, become enormous."