The way the overall proportion settles down to 50% isn’t that fate favors tails to compensate for the heads that have already landed; it’s that those first ten flips become less and less important the more flips we make. If I flip the coin a thousand more times, and get about half heads, then the proportion of heads in the first 1,010 flips is also going to be close to 50%. That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.
