Ok right. It just seemed like the article and jordigh were making contrasting points. Although neither make an explicit broad claim (in which case, what are we doing here other than running an arbitrary MCMC and then stating a Markov property), the article is saying hey look, rich people get richer, while jordigh is saying, nah "you should eventually see each person hoard all of the money in turn.".

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.