I remember the words of my Six Sigma teacher at Villanova saying this one time. "The sample and analysis you do are only valid for the system you are looking at right now at this moment." That all system will normalize if you continue to add sample size as you diminish the effects of each the data points as you add more and more ( what pattern or trend can you see over a million hands ....none unless it has an assignable cause)
Do a stratified sample and this will yield the best information. That's what we are doing when we analyze 1 game at a time. https://en.wikipedia.org/wiki/Stratified_sampling