Flipping a tail is a 1/2 chance, but flipping 6 tails in a row is a 1/64, so if after flipping 5 tails, why is it incorrect to say that your chance of flipping another tail is now lower, like you’re “bound” to get a head? I know this is the gambler’s fallacy, but why is it a fallacy? I get that each coin flip is independent, but it feels right (as fallacies often do) that in consecutive flips the previous events matter? Please, help me see it in a different way.
In: Mathematics
Before you start flipping the coin, flipping 6 tails in a row is indeed pretty unlikely. However, by the time you’ve flipped it 5 times, the “unlikely” part has already happened. Taken as a whole, the sequence is unlikely, but the fallacy comes from the fact that at the 5th flip you’re not dealing with the whole sequence anymore, but just that single 50-50.
Think of it another way: if I showed you two (perfectly ordinary) coins and told you that one of them just flipped 6 heads in a row, what could you possibly do to determine which one of them is more likely to land tails on the next flip? None of the flips you do change the coin in any way to make one outcome more or less likely.
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