So here’s a problem similar to Pascal’s wager. At some points in time, when the powerball is a large dollar amount, the Expected Value of a lottery ticket can potentially be positive.
Say each lottery ticket is worth $1.10, and the time between lottery ticket purchase and payout is 1 month.
A purely rational agent, expecting a 10% 1 month-return, or a 120% annual return - if this was a bot you had programmed to seek optimal investments, it might look at the ROI and invest all of the money it has into lottery tickets.
Say the agent only has 100k and the total amount of lottery tickets purchased is 100 million dollars, and to simplify the math, assume no duplicate tickets.
Then the odds of one of the tickets winning is 1/1000.
So the flaw of the agent is yes, overall, the ROI is positive, but in 999/1000 of the futures the agent is likely to experience, it goes broke.
So this implies a way to not get fooled by Pascal’s wager. Just choose some fraction (I’m not sure how to do this) of the probability distribution. Essentially don’t consider events that have a less than 1% or 0.1% or some arbitrary threshold of likeliness because no matter how bad or good they are, they probably won’t happen to you.
And this is how you could avoid getting mugged by organized religion. A simple analysis of the number of possible (mutually exclusive) religions that exist would indicate that even if “one true religion” exists, backed by a real deity (who is invisible and intangible but is still real), *your *chance of guessing the correct religion is dismally small. Certainly under 1 in 100. So there’s no point in wasting your time and money on one.
Anyways, mathematicians have no doubt proposed this : what’s it called and do they have a better solution?