Individual flips stay unpredictable. Their running proportion tends to stabilize near the coin’s probability.
For independent flips with the same head probability p, the sample proportion converges to p with probability one. A finite run can fluctuate and does not need to get closer after every flip. Each simulation here uses pseudorandom independent draws.
The law of large numbers does not promise short runs will balance out.
Results are empirical pseudorandom simulations. A finite sample need not get closer to p on every flip. Changing p starts a new experiment.