Hi /sci/, please indulge me, I know this is a dumb question but I keep going over it in my head and perhaps another perspective will help.

Say I flip a coin 99 times, each time it comes up as "heads", the probability that it'll come up as "heads" again is tiny.

But is it really? Is it not just 50/50 because the outcome of each individual coin flip is not affected by events which proceeded it.

I know the answer is "well, the likelihood that you made it to 99 flips is what determines the tiny probability" but is there some arbitrary law that I need to know about that really brings down my odds from 50/50 to 1 in 1,267,650,600,228,229,401,496,703,205,376.

Am I making sense here or should I just stop with the answer to my own question and leave it at that?