Theory: Calling 3b with small/mid pocket pairs

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Theory: Calling 3b with small/mid pocket pairs

I made a very mathematicaly "rough" comparison between calling our small-mid pocket pairs vs folding them when facing a 3b HU, any more precise analysis, database reports or spotting the mistakes I made are more than welcome:

Things that I see as problematic in my calculations:

1.)I didn't account for the equity loss when we find ourselves in set over set situation holding the worst of it. If anyone knows how to do this please let us know

Let's say we raise to 3bb preflop and get 3b to 10bb preflop by a tight player who is 3b only AQs+,AK/TT+, and it folds back to us when we have 22-99 . When calling we will therefore be either heavily dominated of "flipping" but often having to fold because every card that is T+ is a scare card for us.

But looking at this from another perspective, we flop a set cca 12% of the time. Lets assume we fold everytime when we don't flop a set.

Considering how our villains range, he will fire a cbet almost always. Lets assume he always cbets half the pot. Pot is 21.5bb villain cbets 10.75bb...
Often the Villain will fire a second barrel too, lets make an estimate of 50% of the time.

So after we call on the flop, pot is 43bb on the turn and lets assume his "standard" turn cbet is at least 21.55bb. Lets assume he cbets turn 50% of the time.That is another 10.77bb added to our "value of setmining preflop". We multiply all that by 1.2( 12% of the time we flop a set) to get a final number of: 37.82bb

So a rough estimate of a "minimal value" of waiting to flop a set and letting villain fire two barrels is : 10bb( Villains preflop 3b) +10.75bb( Villains cbet) + 10.77bb( 50% of the time our Villain makes a turn cbet) x1.2(probability of flopping a set) =37.82

I think considering Villains range this is pretty conservative estimation of value we can expect to get when flopping a set vs him.

So from 10 times we called a preflop 3b of 10bb we lost -62.17bb( 100-37.82) so far.

If we compare that with folding 10/10 times and loosing -30bb that means we NEED TO MAKE 32.17BB UNIMPROVED TO MAKE CALLING THE 3B = FOLDING TO 3B

My assumptions:

I think we shouldn't have much problems getting at least those 32.17bb more when in position, not sure about OOP. Even if we breakeven vs folding vs 3b I think it does huge benefit for us as our range becomes much harder to play against, but more likely we can get more than 32.17bb at least IN POSITION which means we lose less than 3bb as we would if we folded.

Thoughts? If someone has some database of decent sample of calling 3b with small/mid PP that would be amazing!

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