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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You’re describing the gamblers fallacy.
Think of flipping a coin. If you flip a coin 50 times and it comes up heads every single time. On the 51st flip there’s a still a 50% chance of heads and a 50% chance it’s tails. The previous flips are not relevant to those odds.
For your slot machine, each spin has a 1/100 chance to hit the jackpot, that’s not going to change no matter how many times you play. Every play has the same odds of hitting the jackpot irrelevant of the number of times you play or the results of previous plays
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