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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The probability of the losing streak continuing is *identical* on the 100th spin as it is on the first.
The probability is only .99^n that, *starting now* you will lose the next n times. But the probability, after n-1 times? Still .99 that the nth spin loses.
You’re conflating “the odds of starting now and experiencing a streak of n losses” with “the odds of continuing a streak for one more spin”. The former is .99^n, the latter is *always* 0.99, regardless of how big the current streak is.
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