If you keep flipping a coin you get heads or tails every time. There's no streak-breaking limit where you stop counting consecutive heads after some point. But

If you keep flipping a coin you get heads or tails every time. There's no streak-breaking limit where you stop counting consecutive heads after some point. But here a streak can run into a loss-limiting wall "for this turn, you have $0, so you can't give any more away." That boundary - unless you allow infinite negative balances - breaks the first-glance intuition. As people hit 0, the amount of dollars that are redistributed on the next turn goes down. So the richest will still be losing their dollar a turn, but are less likely to gain a dollar. Which will have the most significant effect on people nearly-broke, since they will still lose, but gain less frequently.