To my understanding:
Flipping a coin has a discrete 1/2 probability to be heads or tails, and every iteration of that trial resets the probability back to 1/2. So, it could be heads every time, or, heads 20% of the time. Both of these outcomes are perfectly valid. Yet, the more you do the experiment, the more the results tend to normalize into 50% heads and 50% tails as you approach infinity.
So my question is: what governs these outcomes and causes distributions to equalize/find equilibrium?
Edit: To clarify, I am not looking for mathematical proofs or theorems, I am simply looking for intuition regarding the ontology of this matter as it applies to our reality and the law of large numbers. I'm simply demonstrating my question in the context of a coin toss experiment.