So recently I've been reading about having a balanced flop checking range as the PFR. Obviously this is important because if we only check back middle pair/bottom pair/complete air then we will be very susceptible to bluffs later on.

My question is basically, 1. How do we decide which hands we want to check back for protection?, and 2. How does this change based on board texture?

I'll use this article on Upswing Poker as an example. On a flop of Ts9h4c, Ryan advises checking back JT (and all worse Tx) to protect our checking range when IP. OOP, he advocates shifting QT and KT from bets to checks to strengthen our checking range even more, as we have the potential to face 3 bets when we check rather than 2.

However, what would we do if the flop was Ts9s4c? With the flush draw on board, would we want to bet more of our Tx, as it's more likely Villain is drawing on us and we can get value? What top pairs would we check back with in this situation?

Basically I'm trying to figure out how to decide which top pairs should be bets on certain board textures, and which ones should be checked back to maintain a balanced checking range.

Thanks!

Not easy question. So many flops so many ranges
Besides opponents might be more or less happy raising flops it is a big issue.
Definitely as you said be more careful oop. The additional draw looks like you should bet more often but you can also bet with the same frequency and higher size.
The more vulnerable is your hand the more it is bet otf. E.g. hands with one card in FD suit are safer, better candidates for check.

Note that check range is only a part of your flop range. You could as well start with valuebet range, add bluffs according to betsize. Then everythig remains is check range. Now only have a look how often you x/f to stab, when it is too often add several checks, adjust bluff range cos you reduced value range, do again untill satisfied.

Good luck, it is time consuming but improves game very much.

It's funny how some things seem so obviouse once they are pointed out to you, but this is exactly what I needed and didn't realize it. Thank you.

(Note:Not OP)

I don't think the difference between a rainbow flop and a two-tone flop should alter your overall c-betting frequency much, and most of the made hands that check back on the former should also check back on the latter.

e.g. Suppose you check back QTcc on Ts9h4c. You have top pair, medium kicker and a backdoor flush draw.
If the flop had been Ts9s4c (a two-tone), you still have top pair, medium kicker and a backdoor flush draw.
While it might feel like your hand is vulnerable to flush draws on the two-tone board, you should remember that on the T94r, three quarters of villain's suited hands had a backdoor flush draw. On Ts9s4c, not only do half of his suited hands have no FD or BDFD, but with two spades on the flop, it's harder for him to have many combos of FDs. In effect, it kind of evens out. On a rainbow flop, villain has lots of BDFDs with medium-low equity, and on a two-tone flop he has a handful of FDs with high equity and a lot of air hands with no backdoors. Your hand therefore has a similar EV as a check back in both spots. The presence of a flush draw doesn't massively increase or decrease the relative strength of a one pair hand. It has a bigger effect on unpaired hands that you might semi-bluff with. (A frontdoor flush draw obviously has more equity than a combo with a BDFD, or a combo with no backdoors/blockers).

EDIT: On the latter point, if you have A5ss, then you hate seeing T94r with no spades, because your hand completely missed, so you check. If there's one spade, then you can consider betting with your BDNFD. If there are two spades, then you love your hand and will almost certainly bet it. All combos of QTs (apart from when the 9 and 4 are the correct suit, producing top pair + FD), just kind of say "meh" on all three boards and check back whether they have a blocker/backdoor or not.

This was really helpful advice. Definitely gonna work on this some more. Thanks!

Although Villain's range may have similar equity on T94r and Ts9s4c, he's probably going to call a bet with more FDFDs than BDFDs. So on the second board, he is definitely going to at least call a bet with XsXs. In contrast, that same hand may get folded on T94r where it only has a BDFD. Since Villain's calling range has more hands on Ts9s4c, aren't we incentivized to bet more of our TP since we can get called more?

I agree with your logic that you have to have a higher bet percentage on suited boards overall. The more connected the board, the higher betting percentage. You would almost certainly want to bet a T98 board,and might even be more likely to bet T97r.

The other factor is V's style. Against a calling station you obv want to bet more for value; against an aggro you want to c/c and c/r more.

Position, board connectedness, and opp's style seem to me to be the 3 factors to consider. I don't know if that leaves much else.

Card removal should allow you to check back some combos of top pair on fd boards and add in an equal number of combos of top pair to bet.

In the end you would be betting about the same amount, i think.

What if check-raises his frontdoor flush draws? Do you want to play for stacks (by calling down) with a marginal top pair on a board that is likely to be very "scary" by the river?
Most of the hands you bet with on either board should have robust equity and should be able to continue when they get check-raised. Top pair medium kicker doesn't want to play for stacks whether the flop is a rainbow or a two-tone, so I think it works best as a check in both situations. A hand like A5s with the nut flush draw does have robust equity (it can continue vs check-raises and barrels), but something like QThh on Ts9s4c does not.

Exploitatively - e.g. against someone that is passive OOP with draws - you can just bet all your top pairs for value, but in theory - against tough opponents - you don't want to start bloating the pot with marginal made hands.

I think it's "not an easy question", as Shamway said, because when you're working out whether betting or checking is best with mid-strength hands, there are many competing forces at work.

When you have QThh on Ts9h4c (rainbow), your hand literally has more equity vs villain's range, because he doesn't have any frontdoor flush draws. Since your hand is stronger on the rainbow (and has a higher EV), that might indicate it can go into your value-betting range on the T94r. The stronger the hand, the more likely you should be to bet it for value, after all. However, since your hand is less vulnerable on the rainbow, it could also mean that a lot of your EV comes from checking back to allow villain to pick up (and bluff with) a turned draw.

On the Ts9s4c (two-tone), your hand literally has less equity, because villain has some frontdoor flush draws. Maybe this means you should be more prone to check it back (for pot-control) because it can't go in your value range (it's not strong enough). The opposing force is that your hand is more vulnerable on this texture, so you can argue in favour of betting to deny free equity.

My belief is that these forces pulling you one way or the other more or less cancel each other out. If a hand is not an "obvious" value-bet or an "obvious" bet for protection, it's usually a check, or at least requires a mixed strategy, in which both options are viable. The sizing of the bet also makes a difference. I would assume that a pot-sized bet with QT on either board is a mistake (QT doesn't belong in a polarized range imo), but I don't see any reason why a small bet couldn't be optimal.

Good point. This is really important, perhaps the most important factor to consider. I was just watching a video on this topic and another thing to consider is opponent's tendency toward making betting/checking mistakes on later streets. Example, you decide to check and V checks back. The turn comes an over card and you check again, is V likely to bluff or check the over card? Same with flush draw that gets there- V likely to bluff or check back?

Agree. Small bet on both boards mixed in with some checks in the exact same spot seems pretty good.