I guess this is off topic a bit, but what if they had a provably fair system that determined when the ponzi would collapse, each investment was x% less likely to trigger the collapse and the owner always profited x% of total investments.
Would it still be a ponzi scheme? It sounds kind of fun.
You use the "if" word twice there in important contexts.
The idea of "Ponzi Games" is not new, it's always been a half hearted (false) defense by the HYIP industry that everybody knew what these schemes were about and that there were no deceived victims, only winners and losers.
It was a lie of course, admin could pack the pyramid and rig the payouts in their own favor. They were not 'provably fair'.
The advent of smart contracts may have changed that and, if the player is competent enough to "audit the code" and make an informed decision, it could be argued that there is no deception and that it is just a form of provably fair gambling.
With no deception involved, i.e. no imaginary forex, arbitrage, mining, etc. context, then they can be called "Ponzi Games" as opposed to "Ponzi Schemes."
Sounds pretty dull to me, but whatever floats your boat.