Originally Posted by vapandrei
Is there a mathematical thingy that I'm missing or I'm seeing a pattern which isn't there?
I'm asking because I end up folding high pairs (except AA) right from the flop if some moderately tight player 3xes me or shoves. And most of the times I'm right.. he's got the set.


The probability of getting a pocket pair is around 1/17 (or ~5%). The probability of hitting a set with your pocket pair is around ~12%. Therefore, the probability of getting a set is in theory 12% * 5% = 0.6%. Or let's just say 1% for simplicity's sake. So, you would think that 99% of the time, someone doesn't have a set on the flop, which is actually correct.
How can this be correct? Well, what you're missing is a mathematical concept called
conditional probability. It is only 99% of the time that someone doesn't have a set
if they would play every single hand. In reality, nobody plays every hand  not even the biggest maniac in the world. So, given that we get to the flop with the villain, we can already drop a significant portion of hands (trash such as unsuited, unconnected, low rank hands). This is the conditional part that you're leaving out.
We also know that most people will play pocket pairs when they get them. So someone might be folding 60  70% of their hands, but play all pocket pairs. This increases their chance of hitting a set on the flop significantly (because they won't be seeing the flop if they fold preflop with junk). Now, multiply this by the number of villains you're facing. Then consider what players will do when they don't hit a set with a small or medium: they might bet small, checkcall, or just checkfold. It is only when they have something big that they are willing to risk it all. And when this happens, you have the conditions sufficiently narrowed down to calculate the conditional probability, which is probably going to be relatively high. It is also possible that they have something else, such as a straight or a flush.
And now consider the fact that you see much more hands online than in reallife. Obviously when someone shoves with a set is an event you are going to remember much better than when everyone folded preflop and the button steals the blinds, or when no one has much of anything and the flop/turn/river goes checkcheck, checkcheck, and checkcheck, ending with you or the villain winning just a few
chips. Nothing interesting, so easy to forget. Or perhaps you cbet and the villain, who didn't hit their set, folds to your cbet. It's easy to forget about all those times.