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
Imagine you had 6 different people flip a coin at the same time, and they wrote down the result. You read the results one at a time. After you read the first 5 results and they’re all heads, do you feel the 6th one should be tails? Would it feel wrong if you read it and it said heads as well? What if I told you that all of the people flipped their coins on different continents? Do you feel like someone flipping a coin in Paris would change your chances?
What I am trying to show is that there is no link between the flips, no way they could influence each other. It’s the same even if it’s the same person flipping the same coin, there is no link between flips, not in any way that has any effect on a flip.
The reason you “feel” it should is because humans evolved to notice patterns. Specifically in this case you are noticing the flips are not making the pattern you expect, so you feel that it should overcorrect to make it look like your expected pattern, like it’s “due”, so that the pattern will be more like you expect.
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