I wanted to figure out what my FR UTG opening range would have to be so that it's unexploitable from 3bets, and found the results suprising. Basically, if I don't defend with 33% of my range from any position, I instantly lose money, assuming he went 3x.

This means that if one is gonna defend with this range:

AA-QQ,AK

They can only be unexploited if their opening range is:

JJ-22,AQ,AxJx-AxTx,KxQx-KxTx,QxJx-QxTx,JxTx,Tx9x

TT+ and AQ+ is 4.7% of hands, so let's say whenever I 3bet, each opponent has a 5% chance of 4betting me. So the chance that I'll have to fold my 3bet to a cold 4bet is (1-.95^n), where n=number of players left to act. So if I'm on the CO a, and 3bet someone, I have a 1-.95^3= 14% chance of getting cold 4betted. That's quite a lot. So I can add that to the EV function to figure out how often they need to fold for preflop to be instantly profitable.

So BE threshold is B/(B+P)+(1-.95^n)

Let's say I 3bet to 9bb, a small aggressive size, from the CO, against a MP opener:

BE=9/(9+.5+1+3)+(1-95^3)

BE=.666667+.142625

BE=.809292

So if MP defends with QQ+AK, that's 34 hands. I can't figure out how to calculate it out percentage wise(help please), but if I turn it ino a ratio, it's 4:1. Meaning a person can have 136 non-premium hands in there opening range that they can open without possibly being exploited by 3bets. This would come down to:

JJ-22,AQ-AJ,KQ,AxTx,KxJx-KxTx,QxJx-QxTx,JxTx, Tx9x exactly 136 combos.

Which is 12.8% of hands. So if somebody 3bets against a person with wider range than this, they instantly make money. Note though, that one has to open tighter than ^ to be unexploitable, there's a fairly big gap of frequencies where both the opener and the 3bettor are losing money.

So just how much bb is being made per extra combo over the threshold? Does anyone know how to calculate this?