I think it's very tough to know BB's coldcalling range is here, because I have absolutely no info on him. I would say most players at these limits would do this with pocket pairs, suited connectors and some big aces, maybe throw KQ in there as well. Of course some people may be much tighter, and some could be even looser.
I'm going to assume he 4bets QQ+,AK though. So let's say he has a cold calling range of something like this.
JJ-22,AQs-ATs,KQs,QJs,JTs,T9s,98s,87s,76s,AQo-AJo,KQo (114 hands)
That's fairly loose imo. So assuming he fold all his pocket pairs below TT (except 55 of course) and continues with second pair or better and draws, he continues with something like this:
JJ-TT,55,AQs-ATs+,KQs,QJs,JTs,T9s,98s,8d7d,7d6d,AQo-AJo,KQo (67 hands)
That means we have ~41% fold equity.
If he calls much tighter though, our fold equity plummets. If he coldcalls something like AJ/AQ/88-JJ (41 hands), then the only thing he's folding is 88 and 99, so we obviously have very little fold equity there (17%).
Even if he has a loose calling range though and folds relatively often (41% isn't too often imo), there's just so many bad turn cards. And A, K, Q or diamond is bad for us. Even a 9 isn't that great because one of the nines completes the flush draw, and a nine also completes KQ and 87dd. A 7 might be bad as well because it completes 98.
And of course, we are already behind against a number of hands as well (AJ/AT/JJ/TT/55/QJ/JT/T9). That's 31 hands that have us crushed already. And against the hands that we are ahead of, we're only a marginal favorite.
So I guess when you look at it that way, and have very little fold equity and not enough pot equity to make up for it, I guess it's just a check/fold.
If I'm approaching this the wrong way just tell me ♦
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