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Before I can tell about the reasons, we have to consider what ponzi is. What is ponzi?
I like a simple fact that says "ponzi is a scheme in which Peter money is used to pay Paul. I believe that example is a good definition on its own, in ponzi scheme, the people that started it gain the most, people that first invested are the second that gained in such a way that the people that invested late are the ones that lose.
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Unfortunately, your definition is wrong. You are describing a "pyramid scheme".
A ponzi scam is investment fraud. The operator claims to invest the victim's money, but instead keeps it. The operator can maintain the illusion by using the victim's own money to pay out "profits", but that is not necessarily a requirement.