Quick answer: in general it'll be better to 4bet bluff a polarized range, but depending on their tendencies, we could flip it the other way.
vs a polarized 3bettor who folds his trash and ships his value:
I'm not going to go into combos, but in general you're looking for a breakdown of nuts:air of like 2:1 or worse for a 4bet to work here, based purely on the odds we're laying ourselves for a bluff preflop.
3bb-10bb-24bb sizing means we have to risk 21bb to win like 14bb. 21/(21+14) = .6 We need him to fold at least %60 of the time on avg for the play to show a profit, or in other words, his value (ie shippable) part of his range makes up more than %60 of his entire 3betting range, then we can't 4bet bluff profitably.
When villain starts 3bet/shoving parts of his air range, like A2s for example, then our bluff gets less profitable obviously, as his shippable:non-shippable ratio gets bigger, and our % for immediate folds grows.
vs a depolarized player:
This is where it gets sticky, but in general it's worse to 4bet bluff a player like this since he'll do something like 3bet/shove hands like AQ too often for us to show a profit. Again going back to the nuts:air thing, his ratio will be to high.
The other side of this argument, is if someone is 3betting a toppened %6 range, then they'll have stuff like ATs in their range, in which case they may have to fold to a 4bet as well.
Most people at the micros haven't figured out to 3bet a polarized range against regs (which in general is the correct thing to do), and as such do stuff like 3bet/call a 4bet with TT, then we have to deal with them postflop. You start to see more people 3bet polarized ranges at 50-200nl and do so completely unbalanced, so 4bet bluffing them starts to get more attractive.
vs a polarized 3bettor who folds his trash and ships his value:
I'm not going to go into combos, but in general you're looking for a breakdown of nuts:air of like 2:1 or worse for a 4bet to work here, based purely on the odds we're laying ourselves for a bluff preflop.
3bb-10bb-24bb sizing means we have to risk 21bb to win like 14bb. 21/(21+14) = .6 We need him to fold at least %60 of the time on avg for the play to show a profit, or in other words, his value (ie shippable) part of his range makes up more than %60 of his entire 3betting range, then we can't 4bet bluff profitably.
When villain starts 3bet/shoving parts of his air range, like A2s for example, then our bluff gets less profitable obviously, as his shippable:non-shippable ratio gets bigger, and our % for immediate folds grows.
vs a depolarized player:
This is where it gets sticky, but in general it's worse to 4bet bluff a player like this since he'll do something like 3bet/shove hands like AQ too often for us to show a profit. Again going back to the nuts:air thing, his ratio will be to high.
The other side of this argument, is if someone is 3betting a toppened %6 range, then they'll have stuff like ATs in their range, in which case they may have to fold to a 4bet as well.
Most people at the micros haven't figured out to 3bet a polarized range against regs (which in general is the correct thing to do), and as such do stuff like 3bet/call a 4bet with TT, then we have to deal with them postflop. You start to see more people 3bet polarized ranges at 50-200nl and do so completely unbalanced, so 4bet bluffing them starts to get more attractive.