Weird line !
I guess the value hands that the line reps are QT, K9, KJ, KQ, all of which you block, and some funky overpairs to turn + sets (but discounted bc of weird line). I'd discount most AK bc of turn call. Board isn't super wet though but I suppose A2, A4, 46s, 67, QQ, AJ might show up here too, depending on villain's aggro frequency. Seems relatively close getting 2-1. Maybe look at villain's stats if available and adjust?

• Disclaimer: I play NL25z, but some regs probably overlap are at NL50 level...

fold the flop for 0 ev or raise the cbet for 0 ev, it is that easy, dont get into this shit spot

Facing the overbet I'm thinking we don't have a huge raising range on the turn and so for balance we're going to have plenty of higher equity draws to use.

On river I'm not sure you can value bet - he can have all the sets still as well as AA. Strong J and QQ I don't think make up enough combos to have a profitable bet but you do have decent showdown value. I'd probably c/f - I doubt he bets worse here very often.

In my sim we don't arrive at the turn with anything we can checkraise for value except 99 and J9 having pure checkraised 55 33 J5 and J3 on the flop. J9 looks to be checkraising only about 15% of the time so we really don't need many bluffs here. 87s nearly pure and 64s mixed seem to be enough bluffs to balance here. In sim KTo is a pure fold on turn

Your play is obv slightly ok to do once in a blue moon vs right opp and if done with any sort of real frequency you'll be losing a ton of $.
Now river, the only problem is that he doesn't really have any bluffs... He would x back all hands you beat. I would bet that at these stakes opp's would even x back KQ here.

I'm not huge fan of bluffraising overbet in this situation, and if you want some bluffs after this line then you should do it with OESD or something like A3. As played on river you have weird spot but it is probably fold. He probably shouldnt 3bet flop so on river he has all sets, QT, many twopairs and his bluff candidates are only T8 and 76s.

First instinct is that he will be very polarized on that spot and the T kinda blocks a good part of his folds. It's an overbet and we just called the flop so we are incentivized to call and not raise since our value raising range too often would be something like 99 and J9.
Now I went to check on a solver, didn't run a sim on this exact one but had one close enough with J42r. The solver appears to agree on value range (but also puts a ton of Khigh bluffs on villains range that I didn't see, so that makes the K blocker worse, but then again he bluffs with some Qhigh too so it probably evens out). Anyway, on that board with a 9 coming on the turn it prefers to bluff T8s that he ocasionally calls flop, some small % of QT and the combos of 53s that called flop. I guess this board is even worsebecause we have more OESD with 42s and 64s to put into raising range.

My more human way to look at it was comparing raising with QT and raising with KT. We have more equity with KT because he is polarized, sure, but we make the nuts more often with QT so it is doing better against his calling range and think that's the equity that matter here. We don't have enough value to bluff that often and since I'd rather do it with QT than KT, KT is out. Ofc T8s, 24s and 64s are better bluffs too but we won't have too many of them OTT since we're mostly raising the lower ones OTF and T8 goes in the bin a lot OTF as well.

First things first, nice flop float, too many people just roll over and fold this hand because it's super marginal but on J high boards with 2 low cards we really do want to fight back and some of that is done through calling. Good of you to recognise that on a rainbow board you're going to need to find some pretty marginal floats in order to properly call here.

On the turn I think that raising this might not be the worst thing in the world but there are a lot of other hands that I'd raise first as a bluff, you're going to have some 76 and 64 that didn't raise the flop, maybe some 87, T8 or Q8 with a bdfd, QT you could potentially be floating all of it so I just want to show you how easy it is to get wildly out of line here especially when you consider how rarely you've turned a strong value hand on this 9. You want to be looking to get more aggro on turns which complete some of your flop, floats particularly if you have an offsuit straight that your opponent only has the suited version of, so on this board on a 4 where we can have 76o, 54o, A2o, 62s, 43s, J4s while our opponent should be folding the majority if not all of these hands preflop we really want to be upping our aggression. Compare this to a 9 where they will have all the J9o and the only non-duplicated strong hands we can have is 93s (maybe 95s depending on villain).

I also think it's reasonable to consider to x/c your hand again, yes now it is getting fairly dicey and you can lose to some potential bluffs, from KQ and Ax gutters but you've got an overcard to the board and a gutshot to the nuts on full rainbow along with reasonable showdown vs a river give up because you beat all the open enders so just want to throw this option out there, not something to be doing vs overly tight players but against players that might find the more rogue bluffs like a random Q or K high with a bad kicker to throw in there along side their other strong equity driven stuff this is something to consider. I ran a quick sim to check how viable this is and pio was floating KQ again here but not KT so it is pretty close. Also this is kind of a fun and slightly weird exploit to run on people because pio is bluffing stuff like A6 with the future blockers to straights but it also partially bluffs hands like A6 to deny this play because it reduces the EV of floating a hand like this because you lose too often at showdown. In GTO world pio will often x to realise equity with open enders as IP but I think you'll see that in practice very much the opposite happens and people are very resistant to bluffing without at least a few outs they can confidently value bet on the river if they hit and they don't understand that they can bluff 2 streets and x back to win occasionally with weird merged bluffs. This probably doesn't gain a ton of EV but I find it interesting so thought I'd share.

Once you get to the river I think it's kind of interesting, honestly can't be too mad at call or fold, IP has a fair few natural bluffs but they also have a bunch of value hands, we block some but still not thrilled about it, theory call but I think you can argue for letting this go against a lot of players especially if you see them x back to just lose with stuff like T8 ever in this spot.

Just going back to the turn briefly it may sound really weird to float flop to just fold turn when we turn equity but that's because a lot of the EV we capture by floating particularly at low stakes is going to be from picking up the pot vs missed turn CB. If you want to continue floating people very light then the key to making it work is not to fight back incredibly hard vs their double barrel every time you turn equity; instead you should be looking to get very aggressive on rivers vs x back in fact you can most likely overbet any jack for value on most run outs and this is where your floats will pick up tons of EV at 50nl as people fold their entire range to you.

I also wonder if this is a GTO vs Exploit sort of situation. This line is really interesting to me, and isn't so much in my arsenal at the moment. I'm curious, was there a specific or pool level exploit involved here? I know you've previously mentioned players tend to overfold to flop c/rs - thanks again for that tip, it's been huge!. Is the c/c flop; c/r turn line on dry-ish boards an example of that here?
If so, it would imply villain/pool is generally overfolding turn, leaving mostly strong made hands and draws in his range. Was the idea to shove most bricks targeting the draws when you don't improve on river, or just give up since you've filtered range so much already?

Makes sense, nice exploit.
Thanks for sharing the hand and your thought process, it's great to get an understanding of these tricky hands!

Pre and flop look fine enough to me. Flop is a bit dicey but as others have mentioned we do need to make a lot of marginal defends on these very dry boards. One of the advantages of floating with two broadways is that people tend to overbluff turn cards which improve you a lot since they're perceived to be "scare cards" which are better for the pre-flop aggressor's range. I will say I would prefer it if we had KsTc or KsTh to make this play, just because blocking two BDFDs makes it a little less likely we'll face a turn barrel (and a little more likely we can realise equity/bluff rivers if turn goes check/check), but floating this combo isn't terrible, just a little marginal.

Turn, I think we should just fold. The important thing to recognise is that villain's overbet if very polarising and, as such, our c/r vs such a range should be even more polarised. Because of this, we should have very few bluffs here and all the bluffs we do have should have good equity. Even if we do this with every OESD we get to the turn with (and there are many), it will be overkill. Doing it with gutshots as well is just way overdoing it. Someone said above that a solver recommends continuing with KQ 100% vs this turn overbet, but I think we can fold that hand too and exploitatively continue with TPGK+/OESDs only based on the assumption that turn overbets at 50NL are not balanced and are more likely value heavy.

River is close. I definitely don't think we should bet as you suggest in your OP as we won't have 50% equity against any reasonable calling range. We block KJ/K5s/K3s/QT. Having said that we also block T8, which is the only natural bluff he can have apart from 64s and 78 (I know villain ended up showing 89 OTR, but that's very weird and I'm trying not to be results-orientated). KQ should probably be a call as it has all the same blocker effects as KT but doesn't block any of villain's bluffing range. With KT- flip a coin I guess?

Ran this spot through Snowie, and it thinks:
1. Flop call is very marginally -ev
2. Raising the giant bet on the turn or calling it is significally -ev
3. River is a 0 ev indifferent spot where it wants to fold 93% and call 7%.

The flop float could be justifiable and probably 0 to +ev if opponent cbet too much. Turn raise is really poor, as Snowie thinks calling is better than raising, even though both are very -ev. Your opponent has to be playing so terribly sub optimal for this line to be close to becoming 0 ev let alone +ev, and even then you end up an 0 ev river spot, which is awful.