You’re seeing the flop with an SPR of 1.5. Barring a bad turn card, the money should be going in no matter what. You said that you expected V to bet “any two cards” if Hero checks the flop. That means we gain 5BB when he doesn’t improve and lose 15BB when he does. There is no hand that will improve anywhere near 1/3 of the time on the turn, and especially given that we can avoid losing that 15BB on the worst turn cards (at the price of occasionally getting bluffed), checking the flop will be very profitable given your assumptions. Yes, there’s some randomness involved. This is poker, it’s a gambling game, you need to stop looking for sure things and start thinking in terms of EV.

Yes. If I didn’t expect much aggression from V, then I’m probably just make a small bet on the flop and call a check-shove if it came to that. It’s important to be clear that you are betting for value, with the intention of getting it in, though – not for “information” with the intention of folding later.

MovieFX said
I’m not sure I understand the flop check either. KQ and AQ are in our range PF so why not turn our under-pair in to a bluff and bet when we are expected to?

Because better hands won’t fold, which is a pretty important element of a profitable bluff. Check out my Bluffing series for more on choosing good candidates for bluffing.

Here is where you are challenging my thinking though…Lets say I C-bet and V calls. I think he likely has either a 7, Q, under-pair or flush draw. Now I’m on the turn with the betting lead and I probably get the chance to check through, but then I let the draws get a free card and ALL of these hands could bet the river, so that seems bad. If I bet the turn, a flush draw and maybe a weak Q (doubtful) may or may not fold and V may still bet all of these hands on the river. Perhaps some turn aggression may cause all hands to check hoping to c/r, so we get to check behind. Or perhaps it suppresses thin value bets from all but trips, making a river call more profitable? This is why betting to keep control seems attractive to me. It seems like V has to play more straightforward or cause a blocking-bet-effect as a form of pot control. I could be betting 40% pot on both streets rather than calling larger bets? If V ever comes over the top (more likely on the turn with trips), then I can fold. I feel like this ends up cheaper. Crazy-talk?

Yep, pretty much :-). Take a look at your equity vs that range that you assigned Villain for seeing this flop, and consider how rarely he has a hand better than TT. With an SPR of 1.5, your hand is much too strong to be thinking about bet-folding on the flop and you really shouldn’t be thinking in terms of how to avoid paying off. It may not feel like it, but you have a value hand here, and you should be thinking about how to put money in from ahead. Unless the turn dramatically changes things, you should be going to the felt with this hand, which means that you WANT your opponent in there betting weaker hands, because when he has better he is going to get paid anyway. Of course you’ll be beat rather often when the money goes in, but there’s nothing you can do about that. As you are kind of recognizing, any line that involves folding later likely involves too high a risk of folding the best hand. The pot is large relative to your stack, and you’re just going to have to stack off with some hands that aren’t as strong as you’d like. Accept that, and make the most of it.