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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 eve

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?"

dfabulich 4y ago
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. https://plato.stanford.edu/entries/paradox-stpetersburg/ https://plato.stanford.edu/entries/paradox-stpetersburg/
- l33t2328 4y ago
  I don’t think it’s hard to articulate why. The reason why is that expected value places too much emphasis on low probability edge cases. With 75% probability, you make at most 4 dollars. There’s almost a 94% chance you make less than 40 dollars. As humans, we evaluate improvable events as not mattering so much.
- ars 4y ago
  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.)
- seebs 4y ago
  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".
grensley 4y ago
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.

dfabulich 4y ago

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. https://plato.stanford.edu/entries/paradox-stpetersburg/ https://plato.stanford.edu/entries/paradox-stpetersburg/

l33t2328 4y ago
I don’t think it’s hard to articulate why. The reason why is that expected value places too much emphasis on low probability edge cases. With 75% probability, you make at most 4 dollars. There’s almost a 94% chance you make less than 40 dollars. As humans, we evaluate improvable events as not mattering so much.
ars 4y ago
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.)
seebs 4y ago
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".

grensley 4y ago

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.