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> everybody's cash goes to zero on step 1008

Surely not in the highly improbable case of everyone starting with 1 dollar, giving money to someone else in a chain that leads back to themselves? Theoretically such a system could continue indefinitely? (a gives to b gives to c gives to.... a)?

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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

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