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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Because each new event in random things is unconnected to the previous event, i.e. “the dice don’t know which roll it is”
Really easy experiment, if you flip a coin a bunch of times you should get a 50/50 distribution of heads and tails. Go flip a coin and then count how often you get the opposite side you did last time. You’ll notice you get the “expected” result only about half the time.
Putting it simply, it’s unlikely you’ll have flipped a coin and gotten 10 heads in a row but once you have you have a 50/50 shot of getting the 11th
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