This restatement of the problem might help: "Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, the set of people with mone

This restatement of the problem might help: "Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, the set of people with money each give a dollar to one randomly chosen other person. The set of people with zero dollars simply lose the opportunity to give away a dollar and thus decrease the overall chances that any participant will receive a dollar. After some time progresses, how will the money be distributed?" To me this now seems intuitively obvious. Since the game creator has declared by fiat that the number "0" gets a special branch in the program, it stands to reason that the resulting distribution will change once any participant hits zero and triggers that code-path. For example-- suppose you start with game with one person who has $10,000 and the remaining 99 people have zero. (I don't think you can arrive at that state game organically, but it doesn't matter for the point I'm making.) The first tick through the game all that happens is that the ten-thousandaire gives one dollar to one marginally lucky participant while the other 99 do-- nothing at all. Essentially the 99 all begin by losing a turn. E.g., imagine an implementation where each tick loops through the participants and the ten-thousandaire happens to be the first participant. If you are the last in line, the only opportunity you have to collect a dollar is when the ten-thousandaire gives away a dollar on the very first iteration of the loop. For the rest of the 99 iterations of the loop you have exactly 0% chance of receiving a dollar. That means on the first tick you and all the other zero-aires would have 1 in 99 chance of receiving a dollar. If on the other hand you started out with everyone having a dollar you would have [some immensely larger chance of receiving a dollar that someone who isn't lazy like me can probably calculate here]. But it's actually worse on the first tick of this example for the ten-thousandaire. That player has a 100% chance of losing a dollar and a 0% chance of gaining one. I believe this "problem" essentially describes the conditions of an economic depression. It's also a bit of a visual/conceptual illusion because we're likely to look at that chart and see accumulation of dollars as "winning" and zeros as "losing". But if you instead measure liquidity it should be clear that those who accumulated dollars suffer decreased liquidity even worse than the zero-aires. Also if you remove the special case for zero then the intuition about "more or less equal" distribution should be true. Edit: change "lose a turn" to "lose the opportunity to give away a dollar" to guard against pedantry. Also, changed "tick/turn" to "tick".