That sounds almost like the St. Petersburg Paradox. (But in the paradoxical version, you keep whatever's in the pot; you don't lose everything at the end.)
The St. Petersburg game has an infinite expected payout! But most people would only be willing to wager $20 or so, and it's hard to articulate exactly why.
The St. Petersburg game has an infinite expected payout! But most people would only be willing to wager $20 or so, and it's hard to articulate exactly why.
https://plato.stanford.edu/entries/paradox-stpetersburg/