While it's not a classic pyramid or ponzi scheme, it may well be within the same scope to be illegal.
Unless you could somehow force every participant to pay from start to finish and also factor inflation it's probably going to turn into one of those schemes.
You have to recruit replacement members or later "winners" will get less money and/or less real value once inflation is factored in. It's certainly a legal minefield.
Also the random selection element could also fall foul of being classed as an illegal lottery, even if that isn't the intention.
So yeah lots of problems.