The law of averages is not very well named, because laws should be true, and this one is false. Coins have no memory. So the next coin you flip has a 50-50 chance of coming up heads, the same as any other. 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.
