Villian is a regular.

Was not sure what a 1/3 bet mean here, so was peel here on flop to see what happens on turn, but now is going a little bit tricky..
-Pot the turn and get it in here? If he has it, he has it..
-turn check behind and hope to get to showdown on the river...?
-what is our plan for the river?

So our hand here plays very poorly to a three bet. BB should be squeezing quite tightly here, raising just 6% of his range. So slightly more than half of that right away is AA. So what do we do if the flop comes 223? Are we going to check and call down, and hope that he is betting the half of his range that isn't aces? Or are we just going to check and fold, letting him win the pot with JT98 ds? Neither option is attractive. Of course we could spike a king, but even then there is no guarantee we get paid, and to maximize our chances of getting paid we probably have to slowplay it, so we take the additional risk of getting outdrawn. We are also not closing the action, so if BTN is a nit who flatted say bad aces then we are in an ugly spot once he repots, probably forfeiting our call.

Actually the situation is pretty close, because the rare times we do smash the flop with low SPR we are probably getting paid pretty good. If we were closing the action pre, after say raise, re-raise, cold call, then we would have a profitable call most likely. Stack sizes are quite relevant here. BTN is extremely short. What if he just puts it all in with a weaker rundown hand that is doing fine against a very tight range but is worried about playing three way? BB is deep so we do have better implied odds, but if we don't smash the flop or we flop say a flush draw now we have the added complication of being deeper, against a very strong range.

I think we should bet the turn. This is probably the strongest hand we ever have in this spot.

what was your perceived range of villain? is he capable of squeezing with A blocker against loose opponents? does (s)he only squeeze premium pair OOP?

That being said BTN was short stacked so we can probably discount any non AA/KK hands from BB's squeezing range.

small c-bet on rather dry board does not seem that weird (again with short stacked BTN). if BTN or CO check-shoves flop, BB knows what to do. turn check seems interesting but if you shove, BB's only folding hands that you already beat like QQ- and probably won't pay you off with bare top pair (if my preflop assumption is correct, BB wouldn't have that many A$B$B$B!AA hand anyway).

I think playing river would be more +Ev than shoving the turn but would need more info before breaking down to every river cards

Seems like we have to bet, as villain will have plenty of axxx hands that call and should almost never raise. I don't think hero can really rep 35xx but can have some semibluffs and a mix of made hands including 2p, sets and combos.

Sizing large is likely best, anywhere 3/4 psb and higher.

Is calling flop standard here? I’m folding more than calling. Actually I’m folding so much more 3 ways with action behind. I don’t know if I can ever call. I can raise or fold and probably fold.

If calling flop is standard in this spot I’d like to hear why.

So if we look at vision, we actually do want to peel preflop here vs two 100 bb stacks, even though we are not closing the action. Even KK54 suited to the 5 wants to call. Looking at a similar situation the flop looks like a peel as well. We also have backdoor nut spades, giving us more flexibility on turns, should have good implied odds on our gutty. We are getting a great price, the third player can't reopen the action if they do shove (and even if they were 100 bb deep this is not a spot where they can really ever raise). We will have decent equity against part of villain's range (the AKQT type hands that he squeezes) and will be crushing a small part of villain's range, QJT9 hands. Even against aces we need 25% and have 15%. Against AQJT we have 40% equity. Against 9876 we are 85%. So we are taking the worst of a third of the time, but getting the best of it 2/3rds of the time. Well that is not exactly correct because there is a portion of his non aces range that also crushes us but that is the general picture.

In retrospect tho I think the turn really needs to check back. A substantial part of villain's range is aces (36%), which we are obviously in bad shape against, and would ideally like to only have to call a small river bet against (since having seen this turn we can't fold). We can't get any value from the rundowns, nor do we need any protection. And while AAA is usually betting this turn, vision does want to check top set 18% of the time, usually when it has low hearts as well. Vision plays KK34 as a pure check, and usually checks KK unless it is a straight or has an ace.

Is the xback for 100bb stacks? I think at 150bb vs villain we should be more inclined to bet - fairly minor point though as i think the merits of xback are pretty clear and if i ever arrive in this spot i am mixing in practice.

for 100 bb stacks and a pot that is heads up the whole way. Also IIRC I did UTG vs SB, because there wasn't a squeeze option (it's only for hu hands), so I felt that more accurately represented villain's squeezing range.

Thank for reply guys.
As play: I checked back turn. I was not sure about villians range here. Is he calling me with Axxx here? I think, if I am going to bet here, he would fold all airs and all other stuffs most of the times..
I am not sure, if I am going to lose some value here with my 2nd set on this kind of draw heavy turn??
My consideration is: if he has a draw here he should going to bet it on the turn, right?
Actually the rivercard was a T of diamonds and he bet 1/2 pot..Thats was confusing me even more...I folded.

River fold seems fine. Villain should have a ton of ad and qd in range when he checks turn.

Price isnt terrible to bluffcatch but we don't really block anything that makes us more eager to call.

I missed the short stack part for preflop play. Anyways, calling flop makes sense now.

Turn check back for me is tight. I want to bet here 60% pot I think. We are deep and I think we have the best hand. His flop bet size is strange and I dont know how balanced it is for him to do this. If we check the turn, we HAVE to call the river, right?

River is really interesting I think, can we discuss it? Why are we worried about diamonds? Sure, they are in his range but once we only call the flop and check the turn, wouldnt villian bet almost every river? This is where I get confused... If we call flop thinking he can have AQTx hands, we hit our nut card on the turn but check? He might be betting 2 pair here now.

I would like to hear more about why trn is standard check and river is a fold on that line. If we bet turn and he calls, then he bets river, I can see an obvious fold.

1) set of kings is nothing more than bluff catcher against thinking opponent who is willing to let CO realize bit of equity by not relentlessly building pot so BB's turn check range could still be very strong ( AA heavy that is) and is capable of check-raising profitably
2) CO's range is capped on A high board runout as he cannot credibly represent set of aces so range wise, hero is not better polarized nor favorite against BB and there's little reason to bet.
3) Kd turn is not really as amazing as it seems because hero still only beats BB's bluffs
->ofc all these are assuming BB is balanced opponent not passive/equity driven bot

CO might be able to hero call on non-straight rivers by pot controlling turn but Td is like the worst card from deck

in retrospect, let's not call KK without at least one more supporting feature beside single suitedness like connectivity to king/A blocker on deep stacked 3bet MW pot as it generates too much negative implied odds

preflop is fine i guess but not sure about flop call with no A and only one bdfd and wheelgutter. wondered what monker says but only had 100bb sims for A32 and A54 with 50% and 100% sizes for a bb squeeze vs co and btn and results are not too clear here. with the shorty behind its very different again ofc. sometimes we need something a little stronger to continue like 2 bdfd and sometimes bdnfd is enough. see for yourself if its any kind of help here (filtered out made straights etc.)

I think half pot sizing changes the situation dramatically. And even then, with a full stack behind us (not a shorty who can not reopen the action), monker is still finding some peels specifically with BDNFD, which we have.

Thanks guys for this nice work with solver!!