I love this! If I had to ELIA5 it, I would say: if you get lucky you get rich quickly. If you get unlucky you get poor slowly. So some people will get lucky and some will get unlucky, but the first to get unlucky will get below 100 and the first to get lucky will get above 100, explaining the initial behavior.
Put another way, the key is that for n people and n dollars, you can receive up to n-1 dollars in a given turn, but you can only ever lose 1. Therefore, whoever is lucky early will accumulate faster than they can distribute.
