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
Lets just imagine that all previous flips matter. Wouldn’t that mean that you would have to know ALL its previous flips to be able to determine if its “bound” to flip heads?
Eg. You pick up the coin and it flips 5 tails, but if before that someone else had flipped 20 heads its still “bound” to flip tails. Even if you knew all the flips a coin has made it wouldnt really make a difference that you had flipped 5 tails since its probably been flipped thousands of times 5 flips in a row is nothing in a ever expanding dataset.
But since all the other flips already happened it doesnt really influence the next flip. If we exaggerate the example its easier to see.
Lets say you and I make a bet, I say: “Ok, If I win the lottery and lightning strikes me and I roll at least one head in ten coin flips you give me 50 bucks otherwise I give you 50 bucks”
Sounds like a great gamble for you right? So you accept.
Then I say “Ok well it turns out I already won a small lottery 15 years ago and I was hit by lightning 20 years ago”, so now the gamble is terrible and logically you lose as I dont flip ten tails in a row.
But nothing changed really, why did the gamble go for good to bad after revealing that something already happened? Well, because if it has already happened you aren’t working with the probability of that happening or not since its 100% happened so you only work with what has not happened yet.
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