I don't understand the math here. But, it seems people are saying there is equal probability that any state can arise. Is that correct? If so, I'm unclear why that's true given that the state where one person has all the dollars seems like it can only arise from a much smaller set of states (where only one person, and there would be 99 options, had one dollar and one person had all the rest). In comparison, wouldn't there be lots of times when the next state (say where all the people had similar amounts of money) would be easier to get to from multiple states. I'm saying it simplistically seems like the extreme states are harder to get to than the "middle" states. Is than an erroneous assumption? Is there some technique I can use to reason about this problem in a different way?