Hello!

I have been toying with excel and 3betting math/ranges. To try get a handle on some GTO strategy and just a general feel of the math. Could somebody confirm what I have?

Note, I haven't adjusted the ranges, I just plugged the percentages into Equilab to get a rough estimate.

Villains Opening Range UTG : 15% (77+, A7s+, K9s+, QTs+, JTs, ATo+, KTo+, QJo)

Villain 4Bet Range : 2.56% (QQ+, AKs, AKo)

Villains Call Range: 2.11 (JJ-TT, AQs, AQo)

Given these opening ranges, Villain folds to 3b 68.87% of the time:

1 - ((4b range + call range) / opening range) = 68.87%

So they are only defending 31.13% of the range that they are opening, if they never bluff.

Now, given some standard opening sizes:

Villain Opens 3bb

We 3Bet IP to 9bb

Blinds are 1.5bb

For an immediate profit, villain must fold more than 66.67% of the time 9/(9+3+1.5).

Villain is actually folding 68.87% of the time, given a 2.2% margin of error.

Does this imply we make an immediate profit by 3betting him, with any two, assuming he never adjusts and is a complete robot?

So in short. Given these standard 3betting sizes, You must defend a minimum of 33% of your opening range to ensure villain cannot make an immedate profit by 3betting you? 

And given this baseline. How do we go about constructing a calling range, given villains approximate 3betting range?

Or have I completely gone wrong with my maths? (it happens often!!)