system
Given the following post, respond as if you're commenting on Reddit:
human
How does The Regression to the Mean phenomenon not contradict the Gambler's Fallacy?

I've always known the gambler's fallacy to be incorrect. If I throw a coin 15 times and it's heads every time, the chance of it being heads on the 16th throw is 1/2 same as always.

But the regression to the mean phenomenon seems to be that, on a much larger scale, if I threw a coin 100,000 times and heads came up 95,000 of them, the next 100,000 throws will likely have more tails than heads. If that's true, then on the next 100,000 throws would the odds no longer sit at 1/2 per throw?

I'm sure there's a simple conclusion I missed in my googling, so I turn to you.
gpt
If you threw an unbiased coin 100,000 times and got heads 95,000 times, that is simply a very unlikely statistical fluctuation.  That does not imply that the next 100,000 throws will have more tails than heads.  This is simply a restatement of the gambler's fallacy.  Yes, this and other systems will tend towards the mean over many many trials, but that doesn't rule out the (extremely unlikely) possibility that you will get heads 95% of the time.  If you keep throwing that unbiased coin another 900,000 times, you will probably get heads 50% of the time and that original statistical fluctuation will average away.

Realistically, if you threw a coin 100,000 times and got head 95,000 times, you should probably start doubting the assertion that the coin is unbiased :)