Random Rant (@math

I was arguing with my friend about this and we need a mathematician to settle it.

I flipped a coin 10 times and got heads every single time. My friend says "the next flip is MORE likely to be tails because its due."

If I flip a fair coin 9 times and get heads EVERY time, whats the probability the 10th flip is tails?

My gut says "tails is due" because theres the law of averages right? After 9 heads in a row, tails has to come to balance things out.

If $0.\overline{9} = 1$, then does $0.\overline{8} = 0.\overline{9}$? Wait no thats dumb. But hear me out:

I was arguing with my friend about this and we need a mathematician to settle it.

I flipped a coin 10 times and got heads every single time. My friend says "the next flip is MORE likely to be tails because its due."

If I flip a fair coin 9 times and get heads EVERY time, whats the probability the 10th flip is tails?

My gut says "tails is due" because theres the law of averages right? After 9 heads in a row, tails has to come to balance things out.

If $0.\overline{9} = 1$, then does $0.\overline{8} = 0.\overline{9}$? Wait no thats dumb. But hear me out:

Random Rant