I'm not wanting to ruffle anyone's feathers, but just curious.

If I understand correctly, the standard error of the mean describes how well my sample of Blackjack hand outcomes represents the population of all Blackjack hand outcomes. As such, if my sample contains less than a certain number of hands, it is considered inaccurate.

I know the following practical application has been discussed before, but when I play 1000 hands in Las Vegas, my wallet surely feels the impact - either way. So in a 'real world' sense, the results of my play in Las Vegas are extremely real or 'accurate' to me.

The best we can do to bridge the gap between the results of a weekend trip and a billion hand simulator is to use, for example, one of Norm's awesome 12 calculators to estimate how closely our weekend result matches up with long term expectation.

But yet if I mimic this same practice and report my at-home, manually dealt sample of 1000 hands to only be expected to occur, say, one out of 200 times, this sample is said to be way too small.

1) Is there really no standardized, respected metric that accurately compares my sample not to the population but to other similarly-sized samples?

2) I find the following interesting:
250,000,000 hands is deemed to be inaccurate
250,000,000 hands is deemed to be inaccurate
250,000,000 hands is deemed to be inaccurate
250,000,000 hands is deemed to be inaccurate,

but yet when I add up these 4 sets of inaccurate sims, I suddenly have an accurate sim or sample or representation of the population?

Finally, this brings me to the following:

3) Norm and others, what do you say to those that say, "One billion rounds are TOO accurate and can be considered to be overfitting because they take into account the possibilities of all of the rarely occuring, outlying possibilities of dealt hands (?that mostly work to the player's disadvantage?)?"

Again, I am not wanting to start an embroiled debate. I do understand how simulations are awesome, but are there limitations to their application, and, if so, alternatives?