Scenario: there is a machine at a casino that hits jackpot 1/100 times it is used. The probability that one does NOT hit jackpot on their first spin is .99^1, the second .99^2, and on their nth .99^n (hoping my math is right). As the number of non-winning spins increases, many people would say the machine is “due” because the probability of the losing streak continuing gets lower and lower, but AFAIK that is not valid. Why is that?
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It’s called the gambler’s fallacy for quite obvious reasons. Basically there is no reason it should be “due” from the results of a previous attempt, because the next result is completely independent of all others.
If I flip a fair coin and it gets heads 100 times in a row, there’s no reason that the next flip isn’t still a 50/50
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