Betting flop is good for the reasons you gave, but you have to fold to the check-raise. Just because your opponent could be bluffing doesn’t mean you should call. As you acknowledged, you have poor equity against his range and little hope of improving, which makes your hand a bad bluff-catcher.

MovieFX said
This is something I am struggling with (in fact I posted a question about this in another thread). Why does someone who flops a Full House in this range check-raise? Is it just a matter of targeting the top of Hero’s range and not caring about the rest? Hero may float the check-raise with over-pairs, some AKs and a few rare 7s or 8s (rare IMO due to position of open, if they are there they are probably part of a suited connector/1-2 gapper) so this seems awfully slim as a value line. In this exact hand, we hero folds to the check-raise or the 4 doesn’t hit, V wins the minimum. Granted a call by V can look strong here too, but at least it isn’t as polarizing. 

I agree that folding the check-raise is good because even if V doesn’t hit the board so hard he may still have overs or an over-pair. In fact, I think hands like 55, 66, 99, TT, A8, 9T and 56 are all possible and more likely to check-raise and they are all ahead or drawing with overs.

Yes, essentially. This is a bit like asking, “Why re-raise pocket Aces before the flop?” Of course your opponent will fold sometimes, but overall you generally do best by building a pot against the of his range. Keep in mind that folding is probably be correct even if you knew Villain would NOT check-raise a full house, as you are drawing almost as poorly against any trips, any 8, any overpair, etc. and even in the best-case scenario where V is in fact semi-bluffing you aren’t a favorite.

MovieFX said

Foucault said

MovieFX said
This is something I am struggling with (in fact I posted a question about this in another thread). Why does someone who flops a Full House in this range check-raise? 

…This is a bit like asking, “Why re-raise pocket Aces before the flop?” Of course your opponent will fold sometimes, but overall you generally do best by building a pot against the of his range. …

That is such a great way to throw it back. I really should be check-raising more of my own monsters to balance my steals anyway. I guess if the board is dry enough it may even look so much like a steal that people will come along light.

Yes. “Balancing steals” is not necessarily an end in itself, but the fact that you could be bluffing is what gives your opponents incentive to call with bluff-catchers when you have monster hands, just as the fact that you could have monsters is what gives your opponents incentive to fold to your bluffs.

MovieFX said

…actually, A7 looks like a perfect fit too…sigh…I think my call just became a crying one…. 

Just because you don’t have the nuts doesn’t make it a crying call. As you and others have pointed out, V can be shoving worse for value, which makes this a very profitable call. No one “finds a fold on the river”, and even looking for one is extremely results oriented thinking.