system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Gambler's Fallacy

Suppose a fair coin is flipped 10,000 times in a row and landed heads every single time. We would say that this is improbable. However, if a fair coin is flipped 9,999 times in a row and then is flipped--landing on heads one more time--that is more or less probable. I can't seem to wrap my head around this. If the gambler's fallacy is a fallacy, then why would we be surprised if a fair coin always landed on heads? Any help is appreciated.
gpt
Gambler's fallacy is basically an incorrect line of thinking that previous outcomes somehow affect the next outcome.  So if you just flipped tails 9 times in a row, then the "gambler" would be thinking *this next one has GOT to be heads because 10 tails in a row is just ridiculous!* and he bets heads.


It's a fallacy because the odds were still 50/50 on that coin, yet he *thought* heads had a higher chance.