I had something like this too for a quant trading interview. It was one of those problems about flipping a coin, heads doubles your money and tails you lose everything, "how much would you pay to play the game?" If forget the nuance of the question but when I did the math on the whiteboard, the expected value was 1 i.e. the same amount one wagers. At that point I said, "Well, I guess I could pay for the entertainment value... how much do I owe you for this interview?"
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.
It's not hard to articulate why: Nearly all the large numbers are beyond what anyone can actually pay. If you assume that the bet pays out at most 4 billion dollars, and simply can't pay more than that, suddenly the expected value is $32, instead of "infinite".
The math and discussion of infinity in the problem unnecessarily complicate it.
You could ask: You have a 10^-30 chance of winning $10^40, otherwise you'll win $1.
Based on expected utility you should pay a huge sum to play, based on the real world you should pay $1. (Adjust the large numbers as needed if you have an issue that that much money doesn't exist.)
I suspect they were looking for you to do some risk/reward analysis.
Personally, I would play one time, bet an amount of money I wouldn't be unhappy to lose and continue flipping until I were into 5 digits. On a $10 bet, that would be 10 flips, and I'd have a 1/1024 chance of pulling it off.
