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
You said it yourself. Each coin flip is independent. The coin doesn’t know about what happened before, it will always give you a 50/50 chance for either heads or tails.
Think about it this way. If you were to toss a coin five times and you get heads every time, then you could give that coin to another person and ask them to toss it for you. It will still be a fair 50/50 for heads or tails. They don’t know the previous result, why should the probability be any different for them?
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