I think those that play me frequently would also vouch that I take a fair number of “trappy” lines with strong hands, and especially here, with a low SPR, it is going to be easy to get all of the chips in even without a bet on the flop. Of course it is also a fairly wet board, where both ranges are likely to have a lot of equity, which acts to discourage slow playing strong hands to a degree.
But it’s not at all rare for me to pass on a continuation bet with a strong hand. I’m mostly playing my range on the flop, rather than my actual holding, especially against stronger players.
Still, I agree… any time you check you expect to open the door to at least a slightly higher frequency of bluffs, and that is exactly what makes this spot a bit more difficult, and hence why a small c-bet on the flop makes the decision a bit more cut and dry in the event that the response is an all in raise. But making decisions easier with a specific hand… I don’t really think that is the road to finding the best plays on each street; more broadly you want to think about how you want to play your entire range, and if for a given board you want to c-bet everything (usually a small c-bet then), or carve out a balanced checking range for a small segment of your hands, with a larger c-bet for the hands that take that line.
On the whole I think this board favored the 4! range. What does Kaei 3 bet from the big blind over a cutoff range? Of course we don’t know, but 4 handed and with some confidence that he can push a lower ranked player like me around, I think it is likely broader than the range in orange below:
The calling range then is likely also broader than the hands below in green:
Notice that he still has most of the strongest holdings (even a sliver of KTs), but that that does not make up the majority of his range. Note also that a range anything at all like this still has a ton of gut shot straight draws (which I’ve also got with KK too, of course), and that many of these make up reasonable bluffing candidates.
My 4! range? Well, it’s live poker, so who know what it really looks like, and I don’t have a chart for 4 handed (where there is less bunching effect, and so I should be able to 4! a bit wider), but:
I’ve got a sliver of KTs also, far more top set hands, but also far fewer middle and bottom set.
I guess where I’m going: I have a range advantage on this board, but I don’t think it is gigantic, and while I have more top set, I think he has more total sets on this board, and so nut advantage is even murkier, and so I’m leaning toward thinking that having a check back range is probably ok, and that rather than a small continuation bet with most or all of my hands, a larger CB with a smaller part of my range might make sense.
When it comes to calling here, if you think your opponent is likely to be very balanced, then calling a small percentage of the time with a bluff catcher like this makes sense. But humans tend to almost never be all that close to perfect balance, and if you think there will be too many wild bluffs, KK slips into a high frequency call quite quickly. Conversely, even a slight decrease in bluffs from the optimal frequency, and I think KK probably becomes a 100% fold.