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
Lot’s of good answers, but I’ll try to explain it more like you’re 5.
Every single time you flip a coin write the result on a piece of paper, and imagine everybody in the world is doing the exact some thing, and if they don’t get the same result as you the stop. After one flip, half of the world just stopped. After two flips, half of the people still flipping stop. After three flips, another half, and so on. This is true no matter what you get on each flip. If you wrote heads on that paper five times and you flipped tails, half of people flipping would stop because they got heads. Those people just flipped heads six times in a row and on the last flip their odds were 50/50
Or
If i hand you a fair coin, the odds of getting heads or tails is 50/50. No matter how many times i flipped it in the other room and what the coin landed on each time it’s still a new coin for you and you have 50/50 odds.
Each flip you make no matter what you get, the next flip is still just taking a new coin and flipping that new coin which has 50/50 chance of landing heads or tails.
The odds of one flip never change, only trying to predict more than 1 flip ahead of time changes how likely that is to be right.
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