Originally Posted by Smileyphil
However what if we are 3 Bet OOP when we have a hand like QQ or JJ. Is this a profitable shove? What about AK? (Those are the main "trouble" hands)
Again, my math sucks, so huge grain of salt.
Villain's 3bet range and his perception of our 4bet shove range are critical.
If Villain's 3bet range is 3%, our pot equity against that range with JJ is 45%. If he folds everything to a 4bet shove except KK+, our equity against his calling range is 19%.
There are 24 combos of KK+, while the 3% range of hands is a total of 76 hands (99+, AKs), so he's folding 68% of the time.
I think the math is:
.68*20bb's (when he folds to the 4bet shove)
+ .32*(.19*100bb's) (when he calls and we win
) - .32*80bb's (when he calls and we lose
) = 13.6bb's + 6.08bb's - 25.6bb's = -5.92bb's
Contrast w a Villain who's 3bet range is 8% and who still only calls a 4bet shove with KK+. Now he's got 164 combos of hands and only calls with 24, so he folds 85% of the time. Using the same JJ scenario:
.85*20bb's + .15*(.19*100bb's) - .15*80bb's = 17bb's + 2.85bb's - 12bb's = 7.85bb's
Obviously it helps a lot to know his 3bet range, but also what calling range for the 4bet shove is - that is going to be influenced by his perception of Hero and his willingness to gamble (some guys are convinced that a 4bet shove has to be AK, so pairs are more likely to call; some guys never fold AK; etc.).