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 the same way tossing a coin for the 50th time in a row still has 50/50 chances of heads and tails, regardless of what outcomes the previous 49 tosses had. The statistics terms is that these attempts, at coin tossing or playing slots, are independent events. Yes, it becomes more unlikely to keep getting some specific sequence of (non-winning) outcomes, but that’s only true when you step back and do the math for the whole sequence. It doesn’t change your chances of winning on the very next attempt.
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