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
I think you grasp the concept that each flip is independent well enough, but a thing to remember is that every distinctive series has the same chance of happening as any other, so HHHHHH is as (un)likely to happen as HTHTHT.
The chances of eventually getting 3 H and 3 T are higher because there are more routes to get that total, but only one route to get 6 H.
It’s just that each flip eliminates all the other routes that had a chance at the beginning.
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