After the game

This isn't the answer. It's where to look.

The game was not a lesson and this page is not a set of answers. It is a list of places to go digging, if any of those six questions has stayed with you.

One thing worth knowing before you start: what you watched — the crowd's average climbing while your own money sank — is called non-ergodicity. The average across many people and the average across one person's lifetime are different numbers, and most calculations you will ever meet quietly assume they are the same. That single word will open every door below.

WORDS TO SEARCH

If you only take one thing away, take these. Any of them will open the door.

ergodicity economicstime average vs ensemble average non-ergodicKelly criteriongeometric mean volatility dragJensen's inequalitygambler's ruin Gibrat's lawthe flaw of averages

IF YOU'D RATHER READ A BOOK

Skin in the Game
Nassim Nicholas Taleb, 2018
The chapter on ergodicity is the clearest short statement of why surviving matters more than averaging. The rest of the Incerto — Fooled by Randomness, The Black Swan, Antifragile — circles the same idea.
Safe Haven: Investing for Financial Storms
Mark Spitznagel, 2021
What to actually do about it. Why something that loses money on average can still make you richer over time — the insurance question, worked out properly.
The Flaw of Averages
Sam Savage, 2009
The river three feet deep is his. The most readable book on the list, and the least mathematical.

IF YOU WANT THE PAPERS

The ergodicity problem in economics
Ole Peters · Nature Physics 15, 1216–1221 (2019)
Start here. The argument in full, by the person who made it.
Evaluating gambles using dynamics
Ole Peters & Murray Gell-Mann · Chaos 26, 023103 (2016)
The coin flip you just played is in this one. Free to read on arXiv.
A New Interpretation of Information Rate
J. L. Kelly Jr. · Bell System Technical Journal, 1956
Where the answer to "how much should I bet?" comes from. Sixty years before anyone called it ergodicity.
Ergodicity Economics — lecture notes
London Mathematical Laboratory
Free, book-length, and updated. The technical route if you want to work through it properly.

None of this is settled. Plenty of economists argue that this is expected utility theory restated, and that the maths was always there in Bernoulli and Kelly. They have a point worth hearing. What isn't in dispute is the arithmetic you just watched happen.

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