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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
by 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 agoI 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 agoThe 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 agoIt'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".