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 issue is independence vs. dependence.
A coin flip is independent. Prior coin flips have no impact on future ones. You cannot be ‘due’ to win a coin flip because there is no memory in the system – the coin doesn’t remember how it landed in the past.
A deck of cards is dependent. If I draw the Ace of Spades, I know that the remaining draws will never contain an Ace of Spades. If our game is won once the Ace of Spades is drawn, the fact that we have not yet drawn it increases the odds of drawing it the deeper we get into the deck.
A large part of the reason people tend to confuse these is the law of large numbers. This states that if you have enough trials, the average will be the odds. People have a great deal of trouble understanding how the coin ‘knows’ to regress to the mean if it doesn’t have memory.
So if I flip a coin and it comes up heads 5 times in a row, people assume that it’s more likely it will come up tails to ‘balance out’ the odds. But this isn’t the case. The reason it isn’t the case is that the coin doesn’t need to ‘know’ anything. Those 5 heads are being ‘washed out’ in the average by subsequent trials – if you flip the coin 1000 times afterwards, the fact that you had 5 heads at the start is trivial even though it seemed significant when it occurred.
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