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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What you said is mostly true. Slot machines won’t pay out jackpots more often than a pre-programmed setpoint, but once that limit is reached the probability doesn’t increase over time. It basically just “unlocks” the jackpot.
Anyway, for any game of chance with a set probability of success, previous results **do not matter**. If you’ve played 1000 games and lost 1000, you have the same probability of winning after that point as someone who just walked in the door. You aren’t “owed” a win or anything like that. Now the overall probability of going that dry may be low, but that has no bearing on future results.
The longer you gamble, the more likely you are to lose. In every game (excluding skill) the house is more likely to win than you are.
Aside: look up sunk cost fallacy, conditional probability, and binomial distributions
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