Once a lottery like Mega Millions has a high enough jackpot so that the expected value of the ticket is higher than the cost, why does it still feel like it’s a bad investment to buy a ticket?
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The problem is in using expected value as a measurement for success. You can find a similar issue proposed by the St. Petersburg paradox where the expected payout of a proposed lottery is infinite, but literally no one would agree to play it.
The paradox comes from the fact that maximizing expected value as a guiding principle in selecting outcomes of chance doesn’t actually seem universally applicable.
Some statisticians outright reject expectation while others have created modifications called expected utility.
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