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You're absolutely right, the thing to look at here is the St Petersburg problem. You have a coin, and each time you don't get heads the payout doubles. Get hea
by lordnacho 5y ago
You're absolutely right, the thing to look at here is the St Petersburg problem.
You have a coin, and each time you don't get heads the payout doubles. Get heads and get the payout. What do you pay to play this?
It turns out that you can't work out an E[X] for this, as it's a series that doesn't converge. But also if you go around and ask people what they'd pay, surprisingly they don't say infinity. Expectation is thus not the last word in decision making.
Turns out utility is a thing that matters, and we can come up with some thoughts on it (von Neumann-Morgenstern etc).
- portent 5y agore: surprisingly they don't say infinity I'm not sure it's that surprising, the expectation is only infinity if you think the person making the payout has the capacity to pay an infinite amount. The second you think this amount is finite (which must always be the case in reality), then the expectation becomes finite and probably quite small. I agree in the more general point, expectation is not always the best tool for extremely rare / extremely significant scenarios.
- Tomminn 5y agoThe parent is correct, and shouldn't be downvoted IMO. If you set the max payout to world gdp of ~$100 trillion, you get an expected value of ~$50 for the game. So people are actually calculating expected value correctly with their intuition. It's just that in their instinctive calculation they're also making better assumptions about reality than mathematicians do.
- plmu 5y agoIndeed, it is one of the proposed solutions as listed in the corresponding wikipedia article on the St. Petersburg paradox. There is a table with quite low expected values, mapping the wealth of the bank to the expected value.