Okay, so aside from the cool terms (ergodicity, which... well whatever), what I think is really going on here is that the results of the iterative system, which

Okay, so aside from the cool terms (ergodicity, which... well whatever), what I think is really going on here is that the results of the iterative system, which intuitively appear to be a normally distributed value distribution for "not large" iterations, actually is NOT. Since it is actually a very not-normal distribution, the typical concepts of "mean", "median", and "std deviation" (which AFAIK isn't even really mentioned and would be meaningful) are warped to the point of meaninglessness. Of course economics being essentially a social science with some math and therefore defaults to thinking in typical normal distribution assumptions, won't naturally deal with that sort of pattern. And while I agree game theory (and this is a game) is relevant to economic study, the fact is that real world "games" like wealth distribution has a vast chasm of chaos/randomness/nonlinearity that blocks things like this or the "pirate distribution" game and others. Distrubingly, the games are parroted in some either overt or subvert manner to justify the distribution of wealth in the current 30 year era. "It's the natural way of economics and mathematics, how dare you chop off my head in the guillotine!" And yet "Some men want to watch the world burn". The elite also love the "great man" theory of history, because they are, of course, great men. But bring up the revolutionaries, and suddenly they don't like those pet ideas.