While I was doing some work (okay, monkeying around) with GTO+, looking at cbetting frequencies, I came across a couple similar results to the above. In this solution, effective stack size is 27.5 bb and the pot is 7.5bb (an approximation of 30bb mtt play with antes). Note that BTN here does have 50% of KK+.

GTO+ suggests we should mostly bet TT-KK, and about 50% of AA and Ax--which makes a lot of sense to me. However, instead of betting our lower PPS, GTO+ suggests that we should check/raise more than 50% of them as well as some stronger Ax and only x/c AA, some weaker Ax, and even some weaker offsuit broadways. This goes against basically everything I intuitively think about this spot--i.e. that we want to protect our equity, that we should raise hands that are at the top of our range, and that we should mainly x/c the middle of our range.

Could anyone help shed light on this spot? Obviously, it's pretty contrived and is the closest I could get to basically not having any flop at all. But I think it's pretty illustrative of us playing versus BTN's mostly capped range.

FWIW, I haven't quite figured out the best way to choose sizings in GTO+. I think that the solution might really be suggesting that we check/jam the flop with these pairs. But this still begs the question of why risking a free card is better than betting out.

I don't work with solvers but typically nash equilibriums solutions come with a strategy for all players. Have you looked at yhe other players strategy to try and make sense of the results?

For example what is the other player betting when we check?

What are they calling when we c/r?

In the range I have, BTN has 50% KK+ and 100% 3s-8s. MP has 55+. The rest are some scattered Ax hands, which BTN likes to bet small at a very high frequency when checked to. This in itself is already a little confusing to me.

It's as if BTN is betting to deny equity of any hand below A-high and then MP is x/j to deny the equity of the hands BTN wants to deny equity with. When MP x/j however, BTN is calling with all pocket pairs and 15c of Ax, give or take.

I'm starting to think that the result is extremely dependent on bet sizing... so maybe I should figure out which sizings produce the highest EV and then take another look.

Apparently the line that is vastly superior is betting our lowest pairs, betting about 50% of our middling pairs, and mostly checking KK+. And then... almost min x/r with our 66-TT and betting 8bb into 24bb OTT with a stack of 19bb. Color me a little confused.

What a rabbit hole this is.

I feel like this line makes a lot more sense. We're going to be stacking with our pps here anyway, but the best ones really aren't worried about turns so it's totally unnecessary to go for bets or x/rs. And the smallest ones benefit most from the added protection bets (folding out a hand like 98s or T8s is great for 55, but 99 doesn't really care), so betting them at the highest frequency seems the most natural. Turn play seems a little weird, but you probably force a ton of double defends from A hi when you take that line.

Right, I am totally down with checking our KK+ and maybe even some QQ. But I'd definitely be worried about the flop going x,x--with 55-TT there are just so many difficult turn cards, aren't there? Maybe our range is simply protected by our other broadway checks. I don't know, poker has been giving me headaches, increasingly, lately.

I don't think it going x/x would be too much of a disaster with a hand like TT. There are a handful of bad turns, but the vast majority of them are alright, and even on the "bad" ones we'll still be ahead a super high frequency and willing to call down. I would be very inclined to bet all my 55-77 here personally, though.

All that said, keep in mind that even Tx or Jx turn usually isn't as bad as it appears. We're only super concerned with A and K as they have all the offsuit combos. And turns between 3 and 8 or so are basically dead cards that connect with very little, even if we have a hand like 55.

I think you are maybe over focused on our specific hand when we have low pocket pairs rather than thinking about our range.

If we bet low pocket pairs, lets say 55, the continuing range is going to realize his equity, and then we will have a problem where we both

Bet flop and check turn with a capped range
or
villain flats and gets to realize his equity, AND gets an opportunity for us to go bet/check and then bluff.

By checking, sure we risk giving a free card, but we are giving a free card to a weak range that didn't stab. Villain has a similar dilema where he needs to be betting alot of his own pocket pairs to deny our equity. So when villain checks back, we have a range advantage and can delay cbet.