This is essentially an explanation of "absorbing barriers" [1] from ergodicity economics [2]. In ergodic systems, the ensemble average and time average are equ

This is essentially an explanation of "absorbing barriers" [1] from ergodicity economics [2]. In ergodic systems, the ensemble average and time average are equivalent, but in non-ergodic systems (most of real life) they aren't. In non-ergodic systems, E[X] [3] is path-dependent. An absorbing barrier is like going all-in on a hand in poker and losing - you lose your entire bankroll, are out of the game, you stop progressing and have no more iterations. Your E[X] no longer incorporates the set of all possible steps or outcomes (ensemble average), but only the ones you actually experienced before incurring the absorbing barrier (time/path dependent average). As a result your real-life E[X] materially differs from your theoretical one. The lesson is that long-term survival should anticipate absorbing barriers, prioritize avoiding them, and build deep buffers against them (cash on hand, etc). [1]:https://en.wikipedia.org/wiki/Absorbing_barrier_(finance) https://en.wikipedia.org/wiki/Absorbing_barrier_(finance) [2]:https://ergodicityeconomics.com/ https://ergodicityeconomics.com/ [3]:https://en.wikipedia.org/wiki/Expected_value https://en.wikipedia.org/wiki/Expected_value [4]:https://www.nature.com/articles/s41567-019-0732-0 https://www.nature.com/articles/s41567-019-0732-0