The law of large numbers in a nut shell means that no matter how many trials I use it wont matter because that can be just a small percentage when compared to something like infinity.

Say you take a coin and you flip it not just a few million times but a few billion, no a few trillion times. Well there is nothing stopping the results to end up being 75% heads and 25% tails because when compared to infinity even a few hundred trillion can be considered a small trial.

In other words you can't reliably determine the probability of something just by running trials. If you've ever played a game with a rare item drop you know how gay it can be.. a 1in100 drop might not trigger until the 275+ time or more. Or you might get it on the 1st kill.

put another way, the only way you'll ever truly get a 50% heads and 50% tails result 100% of the time is if you flip the coin an infinite number of times. There is no large number when comparing to infinity.