> Bro just assume there's been a billion flips right before my example indicating it's close to perfectly fair, the only point of my comment was to illustrate that previous flips don't influence future flips.

I agree: the events are independent in probability, which was never under debate, and is a separate matter to whether or not the coin is fair.

As for your edit:

> Pretend I said 5 instead of 500 if it makes you feel better.

At this point, wouldn’t you say that’s a bridge too far? It’s uncharitable to ask of your interlocutor as that changes the entire context and implications of what you originally said upthread.

Asking me to just pretend that you made a different argument than you originally made, when the mathematical implications of your original argument are the context under question, is literally moving the goalposts.

If you had said it was 5 flips in a row instead of 500 flips, then I wouldn’t have said what I said, because there’s a difference so wide between the two statements in their degree of probability as to be different arguments entirely. You didn’t say that though, and so I don’t know what you’re trying to say now.