correct, if we sample without replacement here https://gist.github.com/kirillseva/961fa1f5b5d64254e0117caf1...

then we'd indeed have a balanced situation where everybody keeps their initial balance. However, we do sample with replacement, and at some point a lucky winner is going to start hoarding cash. Until such time when no one has cash to pay the winner, and he's ultrawealthy... on paper