The question on the table wold seem to why about 1 million hands is considered "the long term" in video poker. As Kaypea and Snidely have already answered this I'd just like to add something.
It is a complex mathematical equation, nothing more nothing less. If you don't know it, explaining it here won't solve anything because of demographic exclusion. The people that know it, don't need it explained, and the people that would need it explained, would never understand it. It would have been covered in high-school statistics class, and if you've forgotten it then several months of study would be required to bring a person up to speed on just the concepts required to comprehend the equations.
Basically, if you even have to ask the question of why at 1 million hands one has about a 99% chance of being within + or - 1% of expectancy, we can't answer it in a way you'll understand. If you play VP seriously you shouldn't have to ask. And if you play VP seriously and still have to ask, you shouldn't be playing VP seriously.
Just know that when you see math savvy APs referring to "the long term" that's what they mean.
I tried to paste some of the functions into this post to illustrate, but apparently LVA can't handle the symbols. Here's an image of the function for statistical significance and error rate:


For anyone that wants this answered try wizardofodds. Michael may have some template responses ready to go. It's far too much to post here anyway.
The issue as Kaypea and Snidely stated is one of variance, not getting dealt every possible hand to which one would then need to get dealt every possible draw. A coin only has two sides, but how many sides it has does not determine how many times you need to flip it to be within 1% of the expected 50/50 ratio 99% of the time. This is done with a mathematical equation and is not subject to personal interpretation.
Here this might help: https://people.ccmr.cornell.edu/~ginsparg/INFO295/mh.pdf (or not!)