Should I call this river check-raise?

I totally believe him, and it looks like you over-thought this one, and somehow leveled yourself into folding the best hand. V's line is very consistent with worse 9x.

im talking about having 100 or 0 equity vs his range, theres no way this is balanced even a tiny bit, call is either going to be -55bb or +140bb or w/e it is with probably no in between here (regardless of your hole cards assuming you can beat a bluff). this is just not the guy / spot to use the solver for imo, you should be noticeably outperforming the solver in most nodes (especially the 0% ones) vs recs u play vs on a regular basis. i think hand reading is probably the most important skill in these spots as opposed to game theory, is why i harped a bit on how deciding KK makes sense for his line is probably a large error. its hard because i feel like most of the thread has been spent working backwards from "they dont bluff x/r the river -> fold everything"

i said this in the first thread you posted i responded to, most of live poker winrate comes down to these once off weird judgement spots vs opponents that have binary "strategies", probably infinitely more so if you play at stakes / games without strong regs.

i dont think v had a weaker 9x lol

The point in defining my range is to figure out the hands I defend with at MDF facing the check-raise on the river. That range has been filtered as you suggested after facing the bets on the flop and the turn, and the adjustment I'm making as far as live low stakes poker is concerned is to overfold to the river check raise, as it's significantly under-bluffed in my experience.

I don't think I'm betting gigantic with KK or 99 once I'm checked to on the river. Those hands are part of the polarized range that I would bet, which includes KTcc as the weakest value hand and many weak pairs and missed flush draws as bluffs. I'm betting the same size with that whole range - varying the bet size according to hand strength is not something that I do, as it gives away information to observant opponents. I don't think I have enough decent bluff candidates to start betting much larger than I did, without overbluffing with missed flush draws. I don't think I ever use a smaller size on this river than what I used, and it would get pretty complicated to balance ranges if I start splitting and use multiple bet sizes. It's certainly doable, but I preferred to keep it simple in this analysis.

I'd argue that I'm polarized when I choose to bet the river here and not check back. When I go for thin value (for example with KT) it's the weakest value hand in the range. I agree a larger size would be better to use, but my lack of bluffs prevents me from going much larger - unless I start turning some hands that I was intending to showdown into bluffs, such as the 7x pairs. But I don't have enough value bets for that to be necessary.

Yes, it's a tricky spot with this hand facing the river check-raise, because I'm relatively close to the bottom of the value part of my range. I think A9+ has a pretty straightforward call; for one thing because it beats a lot more 9x then my T9 does.

Yes villain definitely knows I will value bet thin/bluff this river when he checks to me, and I agree my hand is under-repped. I am betting AA and the best Kx when he checks to me, as well as the combos of 9x that didn't raise earlier in the hand. But QQ-TT is probably checking back and taking their showdown value.

He's completely polarized on the river until he checks, after which he's capped (with a small number of super nutted slow plays), but he then repolarizes when he check-raises. Naturally this is super hard to balance and raises a few questions like which hands are check-calling in this spot? Maybe some weak Kx of clubs? It's hard to think of many others. And what are the bluffs when he check-raises the river? I would guess 8x missed flushed draws, as they have the best blockers (8s), and perhaps 7x too - but it's difficult to say for sure.

Yes I agree that at least in theory a lot of his strongest hands should indeed check-raise flop, and it's unlikely that he fires flop and turn and then checks the river with a nutted value hand, seeing as my range is apparently capped and likely to check back at a large frequency.

"The most likely hands that donk flop, and then barrel turn, but then check to you on the river are going to be hands that aren't certain to be ahead if he bets and you call, and don't really want to bet and get raised, but are likely best if you check back, and can call a fairly chunky bet, and might also decide to raise if you bet small" - sure, agreed - but I think he might just check-call with many of the 9x hands, and those that he raises I am behind.

Honestly, I still don't believe him, and I'm 95% sure he had a straight or better. I'll see him later this week and offer to buy him dinner if he tells me what he had, with no BS. He's a good friend and I'm sure he'll be open to this.

That's only if you're assuming the BB's flatting pre with ATC.

All of his 9x he calls with are ahead of hero's. K9s, J9s, Q9s, A9s, A9o, K9o, and mabye even Q9o. 89 and 9T are blocked but possible smaller hands but they have less combos.

Yes I agree that solver output/MDF etc is nowhere near as relevant as population tendencies facing this check-raise on the river, and that is why I found the fold. I was sure that almost all 9x are meant to call when faced with the raise, but - at least as I saw it - I made an exploitative adjustment and overfolded. I think this adjustment is valid against the general player pool and against this villain specifically. I've got over 1000 hours against him and I don't remember ever seeing him check-raise the river as a bluff.

Can you please clarify what you mean with regard to hand reading and "binary strategies"?

Sure, a large amount of the EV in these games can be from spots like this, especially on the river where the betsizes are massive.

I agree that it's very unlikely villain had a weaker 9. My guess is that it's a straight or better, with a small fraction of bluffs.

yawn

binary strategy - pure strategy ie 1 or 0. in this case he either always has a bluff or always has value. there is no range for this, he just shows up here with this hand and does whatever he's going to do. is what i meant by you either having 0 equity or 100 vs this line, and you'll find out immediately if you go to showdown.

i think looking at fish's line with logic is more important than things like mdf blockers etc.

i told you why i think this is a spot that's going to be a bluff much more often than other river x/r spots. you also want to be really careful about the assumptions you're making when you don't have hard statistics (actual mda data) and are instead going off of feelings or memories as human brain is HORRIBLE with statistics. there's also clear data for certain segments of river x/rs that are overbluffed from what i've seen, and afaik donks on paired boards are also supposed to be weak / bluff so u kind of need to take everything with a grain of salt and look at his line and does it seem to line up for value. here, i don't really think it does. if you think he has a STR+, i don't see how u can think that a9 is a better call than t9.

we have to move on though lol

fun exercise would be to node lock oop to never xing the river w 9x+ and see how ip responds, esp if u give it v small bet option

Sure, what you're saying is generally true. However in this specific game it's a very fixed group of players, there is only one table at the casino, and everyone is very aware of how much everyone else has won/lost throughout the day. Villain in this hand is for sure a consistent winner and we're good friends. He does play at other casinos and I'm unsure of how he does there, but I doubt he's losing. Sure, some players do better in some games than they do in others, but in general most players are either winning in all games, or losing in all games, and there is not much grey area or in-between. Most games are more or less the same, assuming a large player pool.

Probability dictates many things as a non-zero possibility; that doesn't mean they're true. I'm 95% sure my read on villain's playing style and winrate is accurate.

Yes, good point - in BB vs BTN he's meant to defend as follows:

So in theory the only 9x he has that is worse than my hand (T9) is 95s, 94s, some 93s, and 98o. (Note that 97 and 96 are boats on the board in this hand, 9976K).

Okay thanks. In that case I don't think he has a binary strategy here. I'll give him some credit and say that this can be a bluff some of the time. But it's certainly a value-heavy check-raise.

Yes I agree logic and the consideration of population tendencies is more important than MDF and blockers etc in this case. I am certainly very careful in the assumptions I make playing poker, but in this case I think there is little doubt. I agree that feelings/memories are a bad way to guide one's play and I'd argue that what is more important is understanding the psychology of the player you're against and the reasoning behind the actions that they take. Sometimes these things can be emotional too, and in my opinion in the case of this hand and similar hands, when the general population river monsters many have a tendency to freeze and slow down if they were being aggressive and/or airballing on previous streets.

Can you give some examples of rivers that are overbluffed when check-raised?

I'm not sure about donks on paired boards meaning weakness/value, but it does make sense from the point of view of psychology that they are weak (many players don't want to fastplay their trips because they fear scaring off their customer, etc).

I do see where you're coming from with his line not necessarily lining up for value.

To be clear, I think this specific villain had a straight+. When I said A9 is a better call than T9, I meant on average and against the general player pool, as some may check-raise some 9x that beat T9 but are weaker than A9, so of course A9 is a more profitable call.

I'll take a look tomorrow at node locking OOP to never check the river with 9x+ (and give it a very small bet option, amongst others) and see how IP responds. I expect IP to get ultra aggressive facing checks from a clearly capped range, for one thing. What are you expecting the outcome to be?

I also want to do some analysis of what villain's donk/donk/check-raise line might look like.

i fairly sure this is always for value or always a bluff by the time he gets to the river raise node like this. its just not a standard line and its mostly weighing he never raises the river as a bluff vs he never checks the river with a better hand but i doubt this is a line he takes consistently enough to have any semblance of balance. but moving on.

so the river thing, the sim may not show it because if your hand has 100% equity vs his range solver may just decide to jam absolute hand stregnth be damned and force oop to deal with it, but the takeaway is going to be esp vs weaker players, they're going to have alot of imbalances in their lines that let you do things that dont seem obvious. a good ex here is pretend oop never xs with a 9+, you could conceivably bet something tiny with JJ or TT or whatever that you wont see show up in a solver (because its incredibly exploitable) and get all kinds of weird calls / raises from oop. this is generally a large part of what you want to be doing against fish, where your hands end up having alot more value than they do against normal players (both bc wider ranges everywhere and because they play transparently / dont protect themselves), and you can do all kinds of fun sizes and lines as a result. theres a reasonably famous pg and c on here where the author coined the term coffee bet where he would minbet for exceptionally thin value into fish (stuff like third pair when it was likely to be good but would seem ridiculous to bet on the surface) that i think ends up working really really well vs recs.

again is perhaps not the best hh example of this concept, but its basically betting for very thin value / to induce raises from very weak ranges. would think the kxcc hands you want to value bet fit better into this line (small bet not necessarily min) than 125 (also could conceivably size way down w good hands if you think he is just always xfing)

in terms of things that are overbluffed, specifically small bet (<35%) otr facing xr is overbluffed from what i remember, and i would imagine if IP caps themselves in some way you see more bluffs than you should as well. fairly basic, when ip's range appears weaker, people are more likely to bluff. i don't think river xr's are as underbluffed as people think from online mda at least, maybe live but i think the biggest thing live is rivers are just under checkraised in general so becomes very very difficult to get a sample and obviously there is a large cohort of people who only have value. but the ev live is being able to distinguish between who does and doesn't fit that demographic, noticing when someone is upset and has changed demographics, and figuring out how to push them over the line (bc as evidenced by this particular v description, when unstudied people try to add aggro to their game they way way overdo it because they don't understand what proper strategy looks like).

okok this is fr my last post here

It is 2026. Submersible has just added to page 45 of this thread and said it will be his last post.

In all seriousness this has been a great debate and lots and lots of food for thought on many levels

I imagine it's about 90% value and 10% bluffs - but that is of course just speculation.

It's certainly a good argument that he never checks the river with a better hand. I wouldn't say never, but I would say seldom. Absolutely it isn't a line he takes consistently enough to be balanced. I've never seen him take this line before, and I imagine of all the most common possible lines (within reason) from flop to river, this has to be a rare one.

Yes I imagine if you're forcing OOP to check everything weaker than a 9 on this river than IP is going to bluff at a very high frequency. That said, I'm sure the solver will manage to balance it and call appropriately vs this aggression. And as you indicated, it certainly opens the door for IP to go for extremely thin value too. Interesting idea with the coffee bet stuff. Does this actually translate well into live play though? I guess ultimately it means just that you can squeeze a little more value out of hands that would usually check back?

When I looked at the river in this hand, I only looked at using one size and balancing my range accordingly. If I was to start making "coffee bets" with Kx, 7x, 6x etc and introduce a second, smaller bet size on the river in order to do, I would presumably have to balance it with some bluff combos - and I know from looking at my range in earlier posts that there are only busted flush draws left over to use as bluffs (especially if I'm now value betting 7x and 6x, which were used as bluffs some of the time when I was only betting with one size). The issue I would have with this approach is that it then means I bet the river with two sizes - 66% pot and, let's say, 10% pot for the "coffee bet". If this was my strategy then over time observant villains would understand that large bet = big value/bluff and small bet = thin value/bluff, which is obviously problematic, right? So I would have to start taking some thick value out of the large bet range and add them to the small bet range in order to "protect" the latter, and as a result I don't get max value from some of my big hands. So what is the best way to balance here? Or should I just accept that yes, I'm imbalanced, but low stakes player pool is probably not going to notice/exploit me effectively, so it should be okay?

Yes that's interesting about small bets on the river facing a check raise with the latter being overbluffed. I imagine this often occurs when there has been a lot of passivity earlier in the hand, too.

Definitely the river check-raise is underbluffed live, but I agree it's difficult to get a decent sample on this. Most players just have it, but there are of course exceptions - and those have usually made themselves known in earlier hands or previous sessions. Against an unknown player I would play the percentages and assume that it's value the vast majority of the time. And yes definitely it's important to recognize when players are on tilt, drunk, experimenting etc.

LOL

Yes it's been a great discussion, I've enjoyed it as well.

OP raised to $15 on the BTN at 2/5, and SB folded. That's 3x open is a pretty small raise size in a raked game. Why wouldn't the BB defend with a pretty wide range, in this configuration? He could have a ton of 9x here, and I would say the best combos in your list would RAISE, not flat call.

A9s, K9s, even Q9s and J9s are going to be raised off often enough by the BB, facing a BTN open. A9o and K9o are probably raised at some frequency, especially if V and OP have some history together, and V thinks OP might be opening too wide. Q9o and J9o are certainly not impossible raises.

I'm not saying T9o should be folded on the BTN, but if V knows OP is capable of opening that wide, then he can flat call and show up post flop with a couple other 9x combos that OP beats (98s/95s). He could certainly get here and also take this line with K7s .

Sure, OP's hand blocks V's 9x, but instead of trying to figure out how nutted V might be, we should probably start by just taking his actions at face value. He donked out for 2/3 pot on 9c9h7c. It looks like he has a value hand that is vulnerable, and doesn't want to give hero a free card, or even a cheap card. It looks a lot like some weak 9x, or maybe even a strong 7x, much more than 97 or 77, or T8, unless it's Tc8c.

I understand that I appear to be very much in the minority opinion on this one, but the actions from pre-flop to river lend themselves as much to a weak 9x or K7s as to a super-nutted hand. V might have been going for the check-raise with a better hand, but OP's smallish bet size opened the door for V to raise with some worse ones.

What's the optimal RFI size in a $2/$5 game with 10% rake up to $10 + $2 for bonuses once the pot is over $20? The range below is how BB is meant to defend vs a 2.5bb open in a cash game with slightly lower rake than the one I was playing in:

It goes as wide as about 50% of 93s and 97o combos. I can only assume that (at least in theory) the BB in the game I was playing in is meant to defend a fair bit tighter than this, seeing as it's a larger RFI size, and there's a larger rake too. That said, I don't think that it's that unreasonable this specific villain will defend something like that wide, perhaps down to 95s. But he certainly doesn't 3bet as much as the equilibrium range suggests. I'd say there is a minimal chance that any combos of A9, K9, Q9, J9, T9 and 98 are getting 3bet.

K7 is an interesting bluff candidate on the river but I find it hard to believe he's donking the flop with this hand.

I agree there's definitely some merit to taking villain's actions at face value. But I just don't think he's check-raising worse 9x than T9 for value; I imagine he would check-call with those hands. I know you mentioned that he might decide to turn some of those into bluffs too, which is definitely viable - but again I don't think this villain thinks or plays that way, and I've never seen him turn trips into a bluff previously.

I also don't think my river size (66% pot) is that small, considering that he's ostensibly capped his range with the check on the river, and the front door flush missed. I honestly think I'm going to get check-raised less than 5% of the time, and that my trips should go for some value vs Kx and other holdings that can call this bet.

People can randomly do a lot of things, but...

GTO BB 3bets a lot less than any other position HU.

Vs. BTN open (for 2.5x, and no rake, but w/e) BB...
Pure calls: A9o/Q9o/T9o/A9s/K9s/Q9s/97s/96s/95s
Pure 3bets: T9s
High 3bets: 99/98s
50/50 3bets: K9o
Some 3bet: J9s/J9o

...so (if V defends close to GTO and has a 9) we beat a single combo. of 95s. Even assuming he doesn't 3bet 98s correctly only gives us one more combo.

If you include rake then BB vs. BTN robots go into 2.5x 3bet or fold mode, down to T9o/96s... which lol.

Where is this range taken from?

Super gross spot, without reads I probably fold

Smash live cash ranges, which is my goto, but the general concept (BB calls a lot HU) I've seen in lots of places including GTOw.

Eg. Kanu's Advanced Cash Game strategy BB Vs. BTN open...

Pure calls: A9o/K9o/Q9o/T9o/A9s/Q9s/96s/95s/94s/93s/92s
Pure 3bets: J9s/T9s
High 3bets: 99/98s
Some 3bet: K9s/J9s/97s

...which roughly swaps a few high 9o for lower suited variants ... so good news there, you get like 4 9x combos. we can beat.

Once again, I think you're spending too much effort trying to determine what V should do, rather than accepting the reality of what he probably is doing. If the usual open in the game is $15, okay, but if it's $20, as it is in many 2/5 games, then he's going to be calling wider. Even at $15, or $20, he could be calling wider than your charts.

You're also putting too much emphasis on bet size relative to the pot and your perception of his range, rather than looking at your bet size relative to the remaining stack depth. Your flat calls on flop and turn, followed by your river bet size do as much, if not more to cap your range than his check on the river.

Interesting, thanks. I use the cash game charts from Michael Acevdeo's Modern Poker Theory - but they are now five years old, so perhaps I should consider updating.