Why is QKo always a check on flop here, per solver?

the answer is going to depend on your exact config, but i don't think it's a mistake to just range cbet here (someone please correct me if i'm wrong)

Sent from my iPhone using Tapatalk

In the beginning KQo is a nice showdown hand imo. If the A is on the board we dont block any A combo of villain. So In theorie checking it down to the river is a good play (bluf catcher etc). It also gives us a chance to freely hit a K or a Q witch is still a good hand vs BB range. You can also range bet ofcourse to simplify your strategy.

For what its worth, i solved this in my own solver and it bets KQo like 10% of the time, which means its not a mistake to bet. And even if you range bet, you only lose about 3% of your range EV (3.08 vs 2.98) vs max exploit on this specific board, which i guess is not the biggest deal. However, if you range bet this board, which is definitely not the best for you, you probably cbet too much overall and that is definitely exploitable, even by micros players.

Other than that, your reasoning is not perfect - it seems that you want to bluff with KQ, which has about 45% equity. If you dont range bet this flop, then you should bet somewhat polar, and KQ is not bad enough to bluff. No better hand folds in theory (i dont have a single pair folding, not even Q2 or 32, even if you arent range betting).

its either villain has an ace or he dont. and you dont want to bet into an ace unless you have one yourself.
the risk of betting into an ace outweigh the benefit of folding out pairs.

betting just narrow villains range to so.ething strong and kq cant stand up to that even if it pairs on later streets.

ideally you want to keep villains range wide and give yourself a chanxe to pair up or even win with king high.

you shouldnt bluff with kq because its still a strong hand. its best to pick something else like JX and lower.

also if KK doesnt want to bet here then why would kq?

I think the solver bets because it wants to have the nuts on a J+T runout among other considerations which I certainly don't know. Those boards are not so good for in position because BB calls a lot of Ax preflop but folds or 3bets bad broadway hands.
If you check some hands here instead of range betting, then you have to check some pairs also, including some A's

I found it really difficult to determine the correct play in these spots when learning (still learning btw)

My logic: The main factor here is that we have too much showdown value, we’re holding a middling hand, and there could be a slight polarization error in betting. You could argue that we might bet for slight denial, but in my opinion, that shouldn’t change much.

Another factor: Yes, we have a range advantage here, and have some strong aces etc, but we aren’t crushing ace-high boards. He likely has more hands like A2o, 22, A8o, sometimes 82s etc. Therefore we cant default to just betting everything. I like to check and maybe do a delayed cbet to fold out small pocket pairs when we have more info? Thats why it is important to also have a protected check back range with weak Ax, so that we can do that.

Because solver is playing vs a 'perfectly' defending BB who doesn’t overfold. That’s why it shifts toward more checking.

Solver will want to protect its checking range on this board and bet turn when equity improves. Also, betting flop doesn't really achieve much for solver - better hands will call, worse hands will fold (theoretically).

That said, at 25NL - cbetting an Ace high board is exploitatively fine as I think population just folds a lot, so I think cbetting here personally is fine.