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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Probability can be a bit confusing.
If you were to ask “If I roll the dice X amount of times, what are the chances I land on 6 one of those times,” your odds of getting a 6 would go up with the number of rolls. This is because you’re asking *what are my odds overall.* This stays consistent as we roll dice, as long as the probability we’re asking about continues to be “if I roll X more rolls, what are my odds of getting a 6.”
However, something being “due,” is **asking a different question**. It’s asking “what are my odds on the *next* roll,” which is completely different. Your odds for the *next* roll will always be 1/6. There’s nothing about your previous roll that can somehow instruct your next roll to be different, so it will always be 1/6.
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