A coin flip pays +80 % on heads and costs −50 % on tails. That is +15 % expected value, a bet every poker player should take. Bet your whole roll on it, flip after flip, and $10,000 becomes $52 after 100 flips with exactly 50 wins and 50 losses. Under one cent after 264.
Both numbers are true. Expected value averages one flip's outcomes; your bankroll multiplies them. Averaged over a crowd, the bet wins. Lived through by one person with one bankroll, it loses. That gap is called non-ergodicity, and it is why "maximise EV" is the wrong objective for anyone with finite money. The right one is the growth rate of your bankroll. How much of your bankroll to bet is the next video: Kelly.
In the video
0:00 The bet
1:01 The same bet, with your whole roll
2:05 Two numbers: +15% and −5.1%
3:16 Two averages: non-ergodic
4:17 What it means for you
5:11 The fix: bet a fraction
6:03 Where this series is going
Sources
Daniel Bernoulli (1738), "Specimen theoriae novae de mensura sortis". English translation: "Exposition of a New Theory on the Measurement of Risk", Econometrica 22(1), 23–36 (1954). https://doi.org/10.2307/1909829
John L. Kelly Jr. (1956), "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 917–926. https://doi.org/10.1002/j.1538-7305.1956.tb03809.x
Harry Markowitz (1952), "Portfolio Selection", Journal of Finance 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Ole Peters & Murray Gell-Mann (2016), "Evaluating gambles using dynamics", Chaos 26, 023103. https://doi.org/10.1063/1.4940236
Ole Peters (2019), "The ergodicity problem in economics", Nature Physics 15, 1216–1221. https://doi.org/10.1038/s41567-019-0732-0
A note for readers of the paper: Part 2 gives the 100-flip figure as about $0.0002. The correct figure is 10,000 × 0.9⁵⁰ = $51.54. This video uses the correct figure.
The series
Next, on 2026-10-30: Kelly: why it sometimes says "not at this bankroll"
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