Let's say I'm organizing a transparent Ponzi scheme for gambling purposes.
It's a game of doubles. Each player's goal is to double their deposit. Each new entree pays for the players before him in equal parts. 2nd deposit pays for the 1st deposit, 3rd for the 2nd and the 1st, 4th for the 3rd, 2nd and 1st and so on. Once the player's deposit is doubled, he no longer receives payments from the new entrees. He can withdraw at any time, but it's unlikely he will until his deposit is at least matched.
There are no limitations on how much one would deposit, but players are expected to be cautious because they are aware that this is a Ponzi scheme.
I need to establish additional rules/guidelines for the game for it to be more efficient. The goal is for the game to be as efficient as possible and double the money for as many people as possible before it gets too big for the diminishing returns to cover the remaining players.
I need an estimation of how many players could join before it gets too big to double the deposits for everyone.
What are the viable solutions for this problem?