Analyzing a River C/R Range
Posted by Sean Lefort
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At around the 15 min mark when you're looking at our turn defending range in pokerstove you accidentally clear the range and instead look at the 10.1% river range. I do this all the time in pokerstove, if you cancel out of the combo selecting screen a certain way it replaces your range w/ a 100% (random) range instead. Just an annoying quirk of the software. You then look at the same 10.1% range again a couple minutes later when looking at the river.
That said, this is by far my favorite type of training video. I love looking at theory in depth this way, and I think it helps my decision-making much more than a 4-6 tabling sweat session or HH review. Please keep this great content coming!
Last comment/question for now, I often hear you/other players focus greatly on preventing villians from profiting w/ ATC in a range of spots. While this certainly makes sense, aren't there also many spots where we have to sigh/concede that we simply cannot profitably defend at a high enough frequency? I worry that in trying to always defend at the right frequency we may actually set ourselves up for more -EV spots later in the hand or with our strategy overall. (IE we force ourselves to float too wide OOP on a K72 flop and have too many hands we can't continue with on turn/river.)
Your last point is a very good/valid one. It actually just came up as a topic in another thread, though unfortunately I can't recall where. There are certainly situations where range vs. range advantage (with respect to frequency of nut hands) is so great that the dominated range is shooting itself in the foot by striving to defend appropriately using GTO concepts. Extreme examples would be in 3bet hands with flops of 222 or T98xx. Essentially, the dominating range just has too many nut hands and this makes the dominated range's bluff-catchers futile in some respects. I like to play these spots on a more exploitative-based level.
That being said, I don't suspect these situations arise all that often. Once the boards get a little wetter/drier (ie. stray from the extremes of the spectrum) then they're falling quickly into the category of situations where we're justified in playing strategies that ensure our opponent's bluffs are not auto-profiting.
I understand how you get 28%,but I get confused with those 2 frequencies.
Same can be reviewed for flop cbetting. You said in an earlier video that hero's optimal bluffing frequency is 28.57% if hero cbets 2/3pot,but again,can't hero bluff more if his bluff cbet needs to work only 40%?
If hero bluffs more than 28% of the time, villain's bluff-catchers all become profitable calls. The 28% resembles that perfect frequency that makes our opponent's bluff-catchers INDIFFERENT to calling/folding. Ie. EV of call = 0 = EV of fold.
The 57.5% is the % of the time villain should correctly fold the river. If he folds more than that (and you are aware that he is going to do so), then yes by all means, exploitatively rip him apart by bluffing everything that can't win by showing down and completely scrap everything else. However, there's no reason to think he will fold > 57.5% in general unless you have a specific read.
I recommend watching my second video as it should hopefully do a better job of explaining this stuff than I can here with text.
It would however be interesting to understand what villains 'normalized' gto frequencies are at various streets / scenarios (flop / turn / river cb %, c/r, defending %, etc) in order to spot situations where villain plays a style where we should deviate from gto and play am exploitive strategy to maximize value. The simplest example is if villain only flop cb 20% as in that scenario we should presumably defend less than what a gto strategy would dictate. The same principle would apply to basically any situation you could think of.
If easy enough, maybe you could upload a cheat sheet with what you consider 'normalized' gto like frequencies in various situations, where the best counterstrategy would be a gto strategy. This would allow us to spot situations where we should deviate from a gto strategy and play an exploitive strategymuch more easily. Thanks
So getting to know opponent's frequencies is a good start for thinking about making some adjustments, but also getting a better idea for specific regions of their ranges is when you can really make some exploitative-based adjustments. (For example if someone is CBing 80%+, you may see that he's (1) CBing very thinly for value with protection-type hands, and/or that he's (2) still CHKing back some very strong hands. Seeing either of these things (in conjunction with his 80% flop-CB%) tells me that lots of flop CRing is going to be tough for his range to handle.
Essentially what I'm saying is that its not quite as easy as just dictating your strategy versus certain frequencies until you have a better idea of what those frequencies are filled with hands-wise. I certainly will be making some more explo-based videos in the future but I feel like GTO concepts are what most players struggle with and thus GTO vids stand to have the greater marginal watching benefits.
I m quite curious about how you are constructing the preflop ranges. I understand the idea about the threshold of not letting your opponent open and profit strictly based on you folding your bb however I struggle to understand how this is relevant. Lets say for arguments sake that it is not possible to prevent your opponent from "auto profiting" preflop by just clicking the raise button because of the structure of the game (not saying that the structure of nlhe is like this). You are then making the bottom of his range even more profitable by defending. Therefore what is relevant is the ability to maximize the profit of your range. By defending well over the threshold it shows how irrelevant it is just because by defending the 50% range that you state in this video you are maximizing the profit of your preflop range as a whole.
Also just wanted to add that I think the PPT odds oracle would make your analysis a lot easier. You can save ranges and chose layers of suits much more efficiently so you don t need to swear when you accidentally erase a range :D. Check it out imo.
Thanks again for all the work and stuff to think about.
"Lets say for arguments sake that it is not possible to prevent your opponent from "auto profiting" preflop by just clicking the raise button because of the structure of the game (not saying that the structure of nlhe is like this). You are then making the bottom of his range even more profitable by defending."
This isn't necessarily true. If villain 2xing 72o is profitable regardless of what we do, it's still possible that us defending 100% is still optimal (and thus we're making his 72o less profitable by defending wider).
You're right in that defending far greater than the (1-alpha)% threshold implies that the threshold isn't all that relevant to begin with (preflop) and that's mostly a reflection of all the implied value on future streets. We don't have to worry about this when analyzing the river, only a little on turn analyses, a little more on flop analyses, and then pre-flop it becomes a strong effect with 3 full streets left to play. So essentially when we're defending 50%+ vs. 3x, we're making sure 72o doesn't profit pf (by defending > 37.5%) and *also* getting as close as possible (or surpassing) the threshold of making 72o unprofitable to open OVERALL because he will make some X% of the pot when we see flops (to make up for what he "loses" pre-flop).
The problem with adding even more hands (say 50% -> 100%) is that 72o now starts actually doing much better post-flop (35% instead of 30% equity) and you're adding a group of hands that are hurt a lot by (1) being OOP and (2) not having initiative.
So the best we can do is take all these factors into account for determining our pf defense frequencies. It's pretty obvious at this point from watching the best NLHU players in the world that vs. 100% MR, optimal is definitely > 75%+.. and vs. 90%+ 3x, definitely > 50%+. Getting more refined than that with theoretical analysis is pretty tough.
Hi Sean,
First of all I really enjoy your videos. They are my favorite videos on the site.
I love these theory concept videos. I think they are much more valuable in general than live play.
I also do A LOT of work myself trying to design my calling/raising ranges on each street and make sure
that they are balanced. And although I play solely PLO the principles are exactly the same of course.
I find it really interesting and challenging trying to "solve" this game of balancing my own ranges.
I have a couple of questions regarding your video:
How do you factor in the simple fact that villain has the initiative? As we know he is stealing more
than his SD equity just by being the aggressor since we will not be able to realize our equity evertime.
Do you factor this in when you design your x/c range oop? And how would you factor that into the equation?
It seams like a factor (just like rake at lowstakes) that we need to factor in when designing optimal
defense frequencies or how is yiur take on that?
Also, there is the matter of range strength. I know at HUNL ranges are very wide but at a 6max games for instance
there are certain flops that just favor a tight utg raiser a lot! In these cases it is really hard to
continue often enough not to make a cbet immediately profitable.
How should we think about these situations do you think?
Personally, I like to categorize a range into sub ranges like (very strong, strong, good, medium, weak, air)
and try to figure out how often different preflop ranges are distributed among these categories on
different flops. Then when I know his distribution of (very strong, strong, good, medium, weak, air) then
I know how to proceed with my medium-type hands for instance. But it is a lot of work in PLO! :)
Anyway, thanks for your thoughts in advance!
As for the initiative concept, it's certainly an important one. In one of my previous videos I introduced a variable "R" that represented the % of our equity that we'll get to realize, and both position and initiative were strong factors in contributing to how R might deviate from 100%. Of course, being OOP or not having the initiative are generally going to decrease R.
A big reason why we strive to achieve (and surpass) these (1-a)% defense thresholds is because it's helping to nullify our opponent's advantage of having the initiative. "As we know he is stealing more
than his SD equity just by being the aggressor" ... The reason this is true is because we're sometimes folding to his bluffs. But by striving to make most of his bluffs not profitable (or indifferent to chking), we're doing the best we can to combat his initiative.
In the case of constructing flatting ranges, initiative influences our hand choices by having us prefer hands that will find ways to get to showdown a higher % of the time (and thus help with making his bluffs not profitable on future streets). So we're looking to flat hands that are often going to be able to proceed against future bets on a wide array of board run-outs. By doing a good job of this, we minimize the impact that our opponent's initiative will have on the R% of our equity that we realize with our range.
As for your comment about range strength in HUNL vs. 6m, it's a very good point. Note my reply to Zizek (first comment after the video) regarding different flop textures and how extreme wet/dry boards can affect how we want to defend depending on range vs. range situations. The important part is to always be aware of the situation (whether it be HUNL, 6m, UTG vs. BTN, BB vs. BTN Steal, etcetc..) and make our general strategy adjustments accordingly.
I'm a math noob so these theory based videos and your clear explanations are really helping out for me! Thanks!
It is possible you released a PLO based theory video with math?
Also regarding what you replied to zizek about dominating range vs. dominated range. I have a question:
Suppose we have a situations where our MDF is 50% ie. pot 100 he pots 100 and is all in. For simplicity sakes lets say everytime we get to this situation there is two types of boards. And on one board we are folding 100% while the other we are calling 100%. This avgs our MDF to 50%.
So in real game play there are some boards which we just dont' have enough hands to defend with but on other boards we have a lot more. for example like 4bet pots in PLO where we have almost nothing on Axx flops but have a lot on 79Q. Is it ok mathematically to analyze your MDF with regards to all boards combined? or do we need to do this with each specific board?
Thanks!
I have a vague idea of what you're asking but if you can be a little more precise I can hopefully provide a better answer. As for PLO videos.. we don't have any plans for me releasing any PLO videos this year. Sorry!
MDF is just minimum defense frequency.
My question is basically say we play 100 hands of PLO 4bet pots. And there is only 2 flops 222 and J78. And villain pots into us and is all in. We need to defend 50% here to not let him be auto profitable. So with our entire range, we pretty much never continue on 222 and on J78 we continue with a frequency higher than 50%. Perhaps this avgs out our defense frequency close to 50% which doesn't allow him to be immediately profitable in this situation. So i'm asking if its ok to look at the situation with regards to avg our MDF on all board types or would we have to have a MDF in each specific board.
Also, what about the idea of doing videos explaining specific chapters of Mathematics of Poker? That would be great
That's an interesting way to look at it and I think ultimately yes, it's a more precise way of analyzing the situation by also taking into account the fact that some of the more pronounced board textures that favor us or villain may be so pronounced that one of us no longer desires to achieve the MDF.
I think where it's most valuable as a concept is in constructing ranges for future streets. Ie. we want to flat call a certain range on the flop that will be able to defend the MDF on X% of turn cards where we set-up our range appropriately such that X approaches 100%. Of course, the finite nature of the cards and our range means its not possible to always get X up to 100% but it's a good factor to be thinking about when constructing flop ranges against good thinking players.
In practice, I think its best to treat each situation as one where you desire to achieve MDFs or one where (far more rare) the combination of board texture + ranges means that you're so dominating/dominated that you have the freedom to heavily over/under defend and you're best off optimizing your range by playing hands in a more "in a vacuum" sense.
How does the minimum defence % on the flop change when ppl don't cbet 100%?
Let's say somebody cbets pot, forcing us to defend < 50%, but only cbets 30% of the time. What would be the mathematical implication of this versus a guy who cbets pot, but does it 70% of the time?
This has to change our defend frequency, I'm just not sure how to exactly solve this.
The MDF concept targets villain's bluffs. So it's goal is to make sure his bluffs are not auto-profiting in isolation.
The frequency of a CB% may have some indication of it's complexion, but as you know, not all 30% CB%s are created equal. Some may be: (a) a linear top 30% of hands, or (b) a polarized range of {top 18%, bottom 12%}
Of course in situation (a), we care very little about MDF because our opponent's range is knowingly overweighted to value and we adjust accordingly. In situation (b), villain now has 40% of his range that consists of hands that have little equity but will auto-profit if we don't make sure we reach MDF.
Obviously its difficult to solve things directly but the important thing is to appreciate how our opponent's tendencies with respect to CB range complexion should affect our desire to ensure we're at MDF and/or exploitatively going in one direction or the other as an adjustment.
Edit: I just want to reiterate that I dont really think you are wrong with most of your theory except in associating mdf with gto. Mdf can be a very useful stat when used correctly (which I believe you do for the most part in these videos). I just believe its very limiting to what gto is to even call it gto and dangerous if one believes it is how one should think about gto.
A few questions:
a) As fot the MDF concept, would I be correct to understand that we are trying to prevent him from auto profiting with his bluff? Like, if we are folding way too often, he can basically bet 100% of his range and still be profitable, right? In that sense, is MDF concept only relevant when we are playing GTO strategy?
b) That said, if his flop c-bet % is low and is thought to have a lot more value hands than bluff, is it okay not to get caught up with the MDF concept because he's not bluffing that often anyway? In other words, since he is not playing the GTO strategy, we might as well deviate from it (=defending > MDF %), no?
c) Does the MDF concept take account for future street plays? For example, if MDF suggests that I defend a certain hand on the flop, does it guarantee that the EV of defending it will be better than that of folding, given that I play the hand "optimally" on turn and river?
d) I have noticed that you haven't included AThh and KThh in the flop c/r range. Is this just for the sake of combo counting, or you would prefer c/c'ing these hands as default?
Thanks in advance!
Hey and
thanks for all your videos
A few
questions (comments), I hope they are not coming too late after you posted this
video for you to answer:
-
Your
pre-flop range. Is that a theoretical range you built for the sick of this
video or the kind of range you will use as default against an unknown? The
problem if we 3-bet for value all the combos of 99+, KQ and AJ+ is that our
calling range will be pretty weak on Broadway boards. If this same board was
rainbow we would have hard time to bluff catch enough with a decent range. For balancing, would
it not be better to rather call with some combos from this 3bet value range?
-
On
the flop, you defend with all your 7s but not 88. Is it an oversight?
-
On
the river don’t you think our sets (with 77) are hands strong enough to be in
our CR value range?
If our villain constructs his river betting range as {made flushes, bluffs} (maybe he or she freezes with sets or worse at the sight of the river flush card) how would that change our ability to check-raise the river. would we opt for some other alternative line instead?
We protect our calling range by sometimes flatting some strong made hands, how do we adjust to villains that pot control often?
Great video
Hi Sean,
Vnice vid,
Did you choose to fold K8hh K6hh K2hh Q2hh J6hh on the turn and 65hh on the flop or did you put them in your flop/turn XR range as non good Showdown Value range who can improve to the nuts?!
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