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
The probability of flipping six tails in a row is completely different than the probability of the next flip being tails. You can’t mix up the two calculations. If you’ve already flipped five in a row, those flips are in the past and do not influence your next flip’s probability, which will always be 50/50. But if you’re about to make 6 flips, the chances of all 6 being tails )or heads) are indeed 1/64. You have to separate past from future. Same with the lottery. Playing yesterday’s winning number in tomorrow’s lottery gives you the same odds (low) as playing any other number, but the odds of the same number winning twice in a row in two future drawings are low*low. In one case you’re calculating the odds of a single drawing, and in another case you’re calculating the odds of a sequence of drawings. Not the same.
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