Please excuse me since the answer to this is probably standard. Long story, easy question:

BB: Villain(covers me):
I haven't played any hands against him. Late 40s/early 50s guy, looks of Middle Eastern or maybe Italian descent, wants to come off like a tough guy. Moderately tight pre-flop. Most hands I've watched him play have been in limped pots, where he's overbet the pot with top pair and kept pushing it unimproved on moderately scary boards. He's checked-called large river bets quickly with top pair. Wants you to know that you can't bluff him off a hand. I haven't sat at this table long enough to have a good handle on him.

UTG: Donator(~$250):
30s-40s European-looking guy. Sat down at my table recently.
Possibly the worst player I've ever seen in live 1/2: super-loose passive, calling down large bets with anything, sometimes hoping to catch a pair that wouldn't even be top pair. Is calling raises with about 75% of his hands and often chasing until the river. Players are taking turns at value betting him relentlessly. Recently I stacked him for his last $160.

UTG+1: Hero($360):
Switched to this table not long ago after running pretty bad on another one. Been card dead on this table, so image should be pretty tight. I've barely shown down any hands and have shown down no bluffs.

Was about to leave after stuck but decided to stick around a bit after Donator showed up. Donator has recently rebought after I stacked him.

Then there was this hand ...

Donator posts a $4 live straddle (for the first time).
Hero picks up KcKs and raises to $15
All fold to Villain in big blind, who raises to $27.
This is the first time I've seen him (or anyone at this table, for that matter) 3bet.

Donator calls. Donator could have literally anything that looks pretty.
Hero raises to $100.
Villain calls right away (which looked a bit defensive to me).
I hate these 3 or 4-bet pots live because they don't come up enough for me to have a clue of villain ranges. So I just assume the standard very tight range.
I figured his range was pretty narrow at AK, QQ, but I can't say for sure. Judging by how he would overplay other hands, I figured he'd just shove with KK+ here. I don't think he'd call with any ace other than AK.

Donator ... calls!

Pot is now $301 before rake and my stack is $260.

Flop:
Ac 9c 5s

Villain gestures "all-in". Great.
Donator folds (lol).
Pot is now $560, $260 to call.
Hero?

So we basically had a HU pot where someone's throwing in a bonus $100.
Flop sucks. Online I call instantly (is this wrong?).

I fold here. Played it well pre though.

Given this: "Switched to this table not long ago after running pretty bad on another one".

And this: "This is the first time I've seen him (or anyone at this table, for that matter) 3bet".

My inclination would be to play it a bit defensively and just call that first ever 3-bet, though I can't fault the big 4-bet with second nutz pre.

Since Hero has the black kings, he has a backdoor draw to the nutz, there are still (possibly) two cowboys available to trip up and beat aces, and enough doubt that the vills may not have aces. The odds may be a bit thin, but considering what's in there already, I can justify a puke call here. If the hand had been red kings, or Hero didn't have the K, then it's a fold. If the kings took a pratfall here, reload.

I like the 4bet with the donator in the hand but would probably size it smaller just to make sure he doesn't fold. Probably around $75. Easy fold on the flop as played.

You'd take the Kc into account when it adds only about 4% equity? I suppose, put optimistically, it doubles my chances of winning if I'm behind vs AK.

With limited info on V I think this is a fold. If V has an Ace I hate the way he played it though.

If we put villain on JJ+, AQs+, AK, we only have 48.64%.
If we put him on QQ+, AK we drop to 39.94%

We're getting 1 - 2.15 pot odds
We get 1 - 2.06 in the first case so that's a slightly +EV call
We get 1 - 2.5 in the second case so that's a slightly more -EV call
(Is this correct? Seems really weird to convert a % to a x - x ratio)

Think it's really close, in most situations I think the first range is more realistic, but if villain uses the second range only a small amount of the time, it's a -EV call.

Yeah, I was going to ask about the hand from his perspective - he didn't seem to have any strategy at all other than "I have a good starting hand that I hate to fold, but I've had a great session so far and I'd hate to lose a big pot. But I guess I have to call." This was based just on body language and timing. That's why I assumed either AK or QQ. He had been obviously been running well up until then (had at least double the max buy-in), though I didn't witness it.

Is he really donk shoving an underpair?

I'd put villain on AJ+ like 80% of the time and fold.
He might do this with something else trying to represent the A? Or even hoping to be best?

Sucks, fold.

Moderately tight pre-flop. Most hands I've watched him play have been in limped pots, where he's overbet the pot with top pair and kept pushing it unimproved on moderately scary boards. He's checked-called large river bets quickly with top pair.

In a 3 bet pot here, I'd think we have to assume this V has an Ace. What else is V 3 betting with, where V continues of an Ace high board fearlessly? Could be JJ+, but this really seems like A broadway. Proabably AQ+.

I just assume the standard very tight range.
I figured his range was pretty narrow at AK, QQ, but I can't say for sure. Judging by how he would overplay other hands, I figured he'd just shove with KK+ here. I don't think he'd call with any ace other than AK. -- pretty much dead on IMO.

I'd say it's a pretty standard fold. I can't think of much you're beating.

Start with (ignoring ties) win % : lose % and reduce.
Your first example is 51.36 : 48.64 , slightly better than 1:1
Second one is 60:39 , say 60:40, so 3:2

Those are pretty generous PF ranges for villain imo. I think he folds AQs and most JJ to the 4bet, and repops KK+.

I don't understand the rest of the post. He's not gonna shove his entire PF range 100% of the time (though I probably would if I were him and found myself with in his shoes -- I have under 1 PSB left in my stack).

With 260 behind, I probably fold. If you had 200 behind, I would probably call.

As an aside, how do we rate villain's play here?
Also, I'm curious as to how you guys think would we should play AK as Villain in this hand PF? How about KK? QQ? AA? JJ?
Assume that we have the same info on Donator, and that the new Villain (me in this hand) has a UTG+1 PF open-raise range of 99+,AJs+,KQs,AQo+ and a rare SC.

What would be the reasoning here?
260:560 vs 200:500

Yep, I sure would. The math is not the be-all and end-all for Poker. In the first place, the math is necessarily fuzzy. It's the nature of the game: players don't muck their cards face up, so you don't know the composition of the pack. If a call here is -EV, it only costs you a small fraction of a bet. The call could also be slightly +EV, and you gain a small fraction of a bet.

There are metagame considerations here: win or lose, if you show them you can call with kings while an ace is out, you gain the reputation for being somewhat sticky. This can pay dividends in future hands when they give your bets respect and let you pick up the small pots uncontested. It adds up and compensates for whatever -EV you're taking right now. A call is basically flipping, but you have to show them you can gamble with them.

I would fold to the allin considering he didn't 5 bet allin preflop makes me think he has AK aq regardless the ace hit the flop and definitely a fold here you played it really well preflop It just Sucks the Ace flopped but I'd lay it down and play another hand.

Just a pod odds calculation. You probably only win the pot about 25% of the time that you call (when he has QQ/JJ and trying to rep an Ace, knowing you have kings, or when he has an ace and you hit your king(s). AK is a huge part of his range when he has an ace, so you are drawing to one out a large percentage of the time).

200/760 still gives you the right odds to call with 25% equity, 260/820 you dont quite have the odds but it is close.

EDIT: I just realized it would be 200/700, so not quite as good odds as I first thought.

Does Villain really usually jam with JJ/QQ here with a donator and a tight pf 4bettor still to act? That's just hideously awful. I'd give his range every combo of AK and a couple of QQ (and probably some AA also tbh; flatting the 4b with the donator still to act pf would be reasonable). If his pf range is only premiums, our equity in this pot is extremely sensitive to the likelihood that he'll jam QQ here, due to there just being so few combos in his range. If he's doing it 1/3 of the time, it's a clear fold, if he's doing it 2/3 of the time, it's a clear call. We need to rely on reads and info here to make that judgment.

KK - tough, wouldn't want to put more than $60 in pre if we think we might have to fold. In this case we're 4 betting, so yep, I'm with it. Now that I look closer at it, V raised what appears to be the absolute minimum. I'd click it back to say $42. Folding if V jams. Maybe too nitty but a 5 bet here is only AA to me, where I play.

QQ - 3 bet because of the straddle, and call the small 4 bet.

JJ - 3 bet because of the straddle, maybe calling the small 4 bet, but not for set mining purposes. Only calling if V's range is possibly behind JJ. If there's doubt, fold.

Doubtful. But, for me there is no "usually" in these situations. They don't come up often so all I can do is make assumptions based on the play so far - but the pots so far were not played under the same circumstances. I miss online poker

I don't even know how much pots like these matter: on the one hand they're rare, but on the other, mistakes are very expensive either way.

Whatever he has it's probably not a good play.

All those hands highly depend on donator's tendencies against a 3bet. If he cold calls 3bets wide then 3bet all of them. If he calls single raises wide but cold calls 3bets tight then flat all of them.

There's overwhelming evidence that "tight" is not in Donator's vocabulary regardless of circumstances. He's been playing lottery, and now he just rebought and is straddling, so he *really* wants to gamble. He's not gonna get bullied off that $4 straddle, dammit, this is his chance to hit big.

Villain's 3bet is something I don't see myself doing regardless of my holding: he 3bet the minimum. Straddle was $4, I raised $12 to $15, he raised $12 to $27. If I wanted to suck someone in giving a good-looking price, I'd 3 bet more since Donator is extremely likely to call it, giving me a great price with most holdings and the luxury of position.

As far as my 4bet goes, it's almost against my religion to slow down with this hand when I see that at least one of my opponents looks like he wants to give action (unless 3bettor is super-nit, not enough evidence for that here). It would have been pukey if I got 5bet (I would seriously consider folding KK: from a fairly typical opponent (like V), the 5bet is AA close to 100%). Turned out pukey in a different way instead.

V's 3bet looked like some sort of "see where I'm at" thing. Not sure of the thinking behind it, if any.