Probably not. I imagine the likelihood of a fair, properly shuffled deck dealing out 250/250/250/250 in a given run of 1,000 deals is actually pretty low.
I’m saying
you won’t get anywhere near 1,000 hands
And
if you did, it still might not be a big enough sample for any deviations from the expected distribution to be significant,
And
even if you got 10k hands, it might well look like, idk, 2525/2475/2453/2547
I have no idea if that last one I offered would be statistically significant or not, off the top of my head. But my point is to make a robust determination for something like this, you probably just need way more data than you’ll be able to gather. And just because the distribution is fair/even in the long run doesn’t mean the short run (to be clear, 1,000 hands is the short run) will be perfectly evenly distributed.
Humans have a poor intuitive grasp of very large or very small numbers. If I tell you the odds of spades hitting ten times in a row are 1 in 275,000 your brain just files it under “impossibly rare ■■■■ that will never happen.” But there is a big, even infinitely big, difference between 0 and .000000001
Somewhere in Replay today, someone will get aces twice in a row. A table will see 4 hearts come out 6 times in a row. Someone will get dealt JJ while their neighbor has QQ and the next guy has KK. All these events are highly unlikely.
But on 99.9999% of the other tables/hands dealt today, these things won’t happen. More “normal” things will happen instead.
Isolating the 1 table where hearts hit 6 times in a row tells you nothing about the future, or the distribution of hearts more broadly. It doesn’t mean hearts are “hot” at that table, either. It just means we found the outlier for that specific variable. There are thousands of extreme outliers every day. It’s a big corpus.
live shuffling is actually often insufficient to ensure true “randomness.” This is my favorite point to bring up: if anything, online is more true to what stats would lead us to expect. It’s live poker that has randomness issues!
About 1 in 260,000. So it would be rare, but it’s actually slightly more likely than getting AA vs AA in the first place, let alone AA vs AA on a 4 flush board. That’s actually so rare that it’s effectively un-exploitable even if you could perfectly predict exactly when it was going to happen and with which suit.
I think @lihiue’s point about how often the spot even comes up in the first place is the big takeaway here tho.
As players we often fret over the most visually arresting scenarios like losing AA vs. AA to a 4-flush runout. But not only are these configurations exceedingly rare, they also represent very few inflection points in the decision tree. What are ya gonna do, start folding AA depending on the suits?
Better spots to study by far include things like “what should my cbet % be on JT7 two-tone versus A83 rainbow?” We will face these pots far more often, and when we do, there’s a lot more room for our decisions to have a significant impact on our profitability.
Thinking about which AA wins more often across 10k hands might be interesting in a broad number theory sense, but it’s got diddly to do with our winrate.