Also, while I agree this is theoretically possible to "see everyone hit the maximum amount of money possible for one individual"... given enough individuals the possibility of someone ending up with nearly all the money is close to zero. I've run a simulation with 500 individuals (here: https://github.com/subroutines/DollaBillz ) and it seems like the distribution of money reaches a steady-state. What should we make of that?

We're they trying to imply that people should assume the distribution would remain uniform?. That strikes me as more "insane" than intuitive.

It's simply a function of how the tokens are being exchanged that would almost require some actors get the short straw, and since this is happening 100 times per round, that randomness ensure some actors get progressively shorter straws over time, because randomness is neither fair, not even. It's randomness.

If you want an even more insanely staggered distribution, let people with resources increase their chances of being given a dollar. This establishes that even in the complete absence of merit, a striking distribution will arise and stably persist, and it's created out of the mechanical behavior constraint of 'possibly being broke and having no dollar to give'. That alone creates what looks like a 'meritocracy' with 'high performers'.

Add literally any form of actual merit, and this gets more extreme still. The funny thing is, the merit-less distribution is not wildly out of line with what people think the distribution should be WITH merit.

So which is it, probably? I think this might be more complex than "everyone will hord all the money eventually", given that the most probable number of sign changes in a 1D random walk is zero.

To make things worse, quantum mechanics is intrinsically random (at least as far as we know) and having a detailed knowledge of the state of the system allowing for certain prediction of its evolution is impossible in principle (and not just in practice).

Not to demonize accumulation of wealth but just to model reality where rules can sometimes be changed by those with enough wealth accumulated.

The way I interpreted the solution was that every individual will at some point have the max possible amount of money (which is roughly $100).

I don't think jordigh is trying to imply that a single individual will have a majority of the total wealth

(minus 1 because you give away $1 on every turn).

For a more interesting example, suppose that on each round, everyone with money picked a random person and gave them 2 dollars (and take N even). Now you'd have a Markov chain that is reducible in a nontrivial manner -- think about the parity constraints.

here's how that looks in a 100 person with 100 bucks game (10,000 money supply)

https://github.com/un1crom/givemoneyaway/blob/master/qqplots...

but no you cannot get back to that initial condition.

but in the real world you most definitely can start that way.

chess is like that too... the initial condition can never be regained.

Because both players have already taken two turns, a player can claim a draw after only 48 moves. If the movement of the knights was repeated 25 times, for instance, then either player could claim a draw. However, this is not possible at the beginning of the game, so simply moving the knights back does not actually restore the game state.

It's just built into the rules: 50 moves without a capture results in a stalemate (https://en.wikipedia.org/wiki/Fifty-move_rule). I guess you could say that the two moves 'go' into the implicit state counter that keeps track of the number of moves without capture.