his turn play is certainly consistent with a draw that just got there, so I agree with your assessment that J9xx makes up the majority of his range, and I would expect him to frequently reraise you on flop if he had a middle set.

so, since we know what his range is, the question is do you have the equity to draw regardless.

You have top set and an OESD.

this means you have 9 outs to fill up on the river, plus 4 aces and 4 9's for the nut straight, which equals to 17 outs. if you don't expect any bluffs or weaker sets in his range, I don't think you have the odds to continue. If you were deeper then you could make the case though.

If, on the other hand you think he has a bluffing range and plays his sets like this, I could see a case being made for getting it on the turn, but i'm a beginner so take my assessment with a fistful of salt.

pro poker tools is probably the best way to get an answer

Yeah looking back at this hand, you're right my turn play is the most questionable move here. I guess my river bet is ok if i have him as strong. I think can put him on J9xx 88xx even. And seeing as he gets checked to OTT there's the small possibility of bluffs. I do have a blocker in the J :)

Villian is 68/0/1.1

I ran this through PPT, I hope I did it correctly.

With a FD

I guess the question is, what equity do we need to call the turn? How do we calculate that? Sorry if it's a noob question but I've never really gone into too much detail with equities.

River

I like how you played the hand, except I would not pot the river.

That is, I might pot the river if I had a game plan of also making big river bluffs on scare cards. I'd need reads for that against this specific player. Generally, I would not bluff much against a super-loose-passive player (if I knew only the stats), and I would bet smaller and exploit his presumed unwillingness to fold.

There's a betsize somewhere in math-land that maximizes the EV for your river betting range. You should try to guesstimate that in-game.

If he was loose-aggressive, I would sometimes check-raise (including the occasional blocker bluff).

Turn

Tricky spot, but I like the check. You will have the best hand often. But if you bet and get pot-raised by BTN, you're in a bad spot. A passive player will show up with the nuts almost always. And if you bet and BTN calls, you can't shove the rest in on blank rivers (important factor). With ~16 outs, you'll be forced to check rivers much more often than bet. So you can't really avoid the problem of revealing to BTN that you don't have the turned nuts. Because you're deep and OOP.

With ~16 outs (discounting spades) you're getting the pot-odds to call a shove, but you're still not happy about having to put in 160 bb against the nuts. You'd like to protect your hand when ahead, but deep-stacked you also have to think about protecting your stack.

Now, they can certainly call with worse if you bet. And they can fold some hands that you're happy to fold out. But I still like the turn check-call with these stacks. $4PLO players are loose and bad, but if you think they'll have so much garbage that you never have to fear the nuts when the board changes, you are underestimating them. You can comfortably call a bet, and you won't be bluffed much on the river if you don't improve.

And lastly, when you check-call in spots like this, have a plan for whether or not you'll bluff some board-changing rivers. For example, you might decide to bet five of the spades as a bluff. If you have a bluffing range, you should generally bet bigger than if you're never bluffing.