Ergodicity Economics
A bet with a +5% average can still send every single player broke. Here's the math finance hid for 80 years.
Grounded in the research on ergodicity economics
The coin that breaks economics
Flip a fair coin. Heads, your wealth jumps 50%. Tails, it drops 40%. Average the two outcomes and you gain 5% per flip, so textbook economics says play forever. But run it on yourself, flip after flip on the same pile of money, and you go broke. Both statements are true at once. That contradiction is the entire field of ergodicity economics, and physicist Ole Peters built it around resolving it.
Two averages, one mistake
The +5% is the ensemble average: take a million people, each flips once, average their results. The time average is different: take one person and follow their wealth through time. For multiplicative bets these two numbers diverge. The ensemble grows 5% a round; the lone player's wealth compounds at the geometric mean, sqrt(1.5 x 0.6), about minus 5% a round. Classical theory quietly assumed they were equal. They are not.