Everyone starts with $100. Each flip: heads ×1.5 (+50%), tails ×0.6 (−40%). Expected value per flip: +5%. And yet…
The ensemble average (mean across players) grows 5% per flip, but it is propped up by a vanishing minority of extreme outliers. The time average an individual actually experiences is √(1.5 × 0.6) ≈ 0.949 per flip — a 5.1% decay — so almost every single path goes broke. That divergence is non-ergodicity: the average of the group is not the destiny of the individual.