The poster is conflating two different and unrelated things. Determining whether a coin is fair, or putting a probability on it being fair after observing a number of tosses has very little to do with “if I just got three heads in a row with a fair coin, what’s the probability of getting a fourth?”.
Nerdloaf t1_ja9tszy wrote
Reply to comment by johrnjohrn in ELI5: why does/doesn’t probability increase when done multiple times? by Reason-Local
The poster is conflating two different and unrelated things. Determining whether a coin is fair, or putting a probability on it being fair after observing a number of tosses has very little to do with “if I just got three heads in a row with a fair coin, what’s the probability of getting a fourth?”.