[KK7NIL]

Some math/finance nerds made a whole YouTube channel about ergodicity, which I've been really enjoying: https://youtu.be/VCb2AMN87cg

Nassim Taleb also talks about this quite a lot: https://youtu.be/91IOwS0gf3g

TL;DR: while a single investment may be ergodic, portfolio management (the math behind weighting successive and concurrent investments/bets) is not, as it has a strong dependence on all prior states.

[uoaei]

this comment may be confusing and I doubt this will help much but:

Ergodicity is less about memorylessness and more about the constraints on transitions into this or that state. A system is ergodic if "anything that can be an outcome, eventually will happen".