How is it that when you flip a coin 10 times, the likely hood that it’ll land on heads 10 times in a row is extremely small but the likely hood that it’ll land on heads is 50/50 if it already landed on heads 9 times? I get that it’s a closed system and its roughly 50/50 for every coin flip but my brain is just telling me that it should be a higher chance that it would land on tails instead of heads. How does this work?
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The odds of 10 coin flips in a row being heads is 0.5^(10), or 0.09765625%. Incredibly low. So the gambler thinks, well there’s already been 9 heads so far, surely it must be time for a tails. The odds of 10 heads is so small!
You know what the odds of 9 heads and then a tails is? 0.5^(10) or 0.09765625%. Yep, exactly the same. The coin doesn’t care that the last 9 flips were heads. The next one is still either heads or tails, 50/50.
It’s pure psychology. Humans are pattern recognition machines. We’ve assigned special meaning to 10 heads in a row, thinking it’s unlikely to occur by chance, assuming a fair game. You can’t get it out of your head because your head is wired to give such outcomes significance. You think 10 heads is special. But you don’t care about 9 heads and a tail. Or 1 tail then 9 heads. Or if the 5th one was a tail and the rest were heads. Those are just normal random occurrences. But statistically all these outcomes have exactly the same chance.
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