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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To tie it into your math directly: the chance of it not hitting the jackpot on your first spin is .99^1, as you say, but it’s the chance of you not hitting the jackpot *on your first or second spin* is .99^2. And the .99^n is the chance of not hitting the jackpot *on all n spins put together*. But, if you’ve missed the jackpot 50 times, you aren’t concentrating all the odds of hitting the jackpot in that 51st spin. Rather, you already know the outcomes of those first 50 spins, and they don’t factor into the odds of the next spin, which remains .99.
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