As far as I understand, range and frequency go hand in hand; what really matters is which one we prioritise.  

GTO strategies often revolve around pot odds and minimum frequencies, which allow one player to capture ~100% of the pot when not met.  And strictly speaking, these frequencies don't really care about the hand value, at least not directly so.  

Say, you need to defend with 66% of your range in a certain spot.  If you call only 50%, I don't care what you have in that 50% range - I can just bet any 2 (or 4) cards and show immediate profit.

In order for you to prevent this, you should build a >66% calling range.  In practice, you will often fill in this range from top up, by calling with the best 66% hands and folding the rest, for example. 

However, what's more important is that you do defend 66% of the time, not what you defend with.  If  you plan on defending with {top pair, middle pair + gutter, etc.} without looking at the overall frequency, you can easily be under- or over-defending in this given spot, and it's not hard for the bettor to adjust to that.

Thus, knowing the frequency helps us a lot when building ranges.  It's not the ultimate guide, but still a quite useful one.  Granted, frequency- and range-based approaches often do overlap, but there's a major difference.  If we start from frequencies, we can always fill in the ranges and adjust accordingly.  But if we start from ranges, we can build a perfectly balanced range yet still be folding 70% on flop, allowing our opponent to bluff with any 4 cards profitably.  Frequency alone doesn't mess up ranges, but ranges alone can mess up frequencies.

- midori

I forgot to mention something, so here it goes.

Everyone would agree with me that the ultimate goal of playing a hand is to maximise its EV.  What I said below (or above? I don't know) holds true as long as our opponents don't have massive, exploitative leaks.  For example, if their overall strategy and range are well balanced, we're probably not gonna make much money by running a triple barrel bluff with our 2nd nut blocker.  

However, if they happen to have these leaks, which is not all too uncommon at low-mid stakes, it's entirely possible that we should take a very exploitative approach to fully take advantage of that, at the expense of changing our frequencies.  Common examples would be very tight river folds with 2nd or 3rd nuts when villain just has to have it.  Frequency wise, our fold is probably unjustifiable.  In practice though, we probably should call 0% in that spot; otherwise we just burn money.  

But in most spots, this is because our opponents have firstly violated those frequency rules, thereby not playing GTO anymore.  And if we limit our discussion to GTO or GTO-ish spots, I don't think these cases will be conflicting with what I have said before.

Yes, you are expressing a common viewpoint in the poker community.  I believe it's a misunderstanding though.  There isn't really any such thing in game theory as minimum defense frequency.  It's perfectly possible (and also likely) that the structure of some games and/or stack sizes create spots where it's profitable for a player to bet any {2, 3, 4, x} cards.  Just think about many late game satellite situations and you'll understand that to be true.  In cash games, frequencies are really dictated by ranges.  A range in one spot may give you license to bet 100% of the time, and another range in another spot may require you to fold 100% of the time.  I don't have the solution to PLO so I can't say whether or not these spots actually come up in the equilibrium, but there wouldn't be anything particularly odd if they did.  There aren't really any frequency rules.  It's all dictated by ranges and EV.

Your example of barreling with a blocker is a bit off imo.  The purpose of barreling with blockers is not to make them profitable in themselves.  The purpose is to force the opponent to call a wider range and thereby giving value to your value hands.  Bluffs generally do not need to be profitable.  (though they can't be -EV either, and this is where frequencies actually do play a part)

I think your argument that it doesn't matter what's in the range as long as the frequency is right -- that points out quite well one of the dangers of starting with balance and frequencies.  What's in the range is ALL that matters.  This can be hard to see intuitively for a game like PLO, but look at solutions to simpler games (short stack shove/fold games in NLHE for example) and you'll see that what's in the ranges is really the entire solution, and it depends on position, stack sizes and the equities between the involved ranges.

And of course, everything starts to break down in 3+ player situations in poker, where cooperative situations can show up quite frequently, and the premises of non-cooperative zero-sum games may no longer hold.  I do think game theory offers useful models for analyzing poker games, but it's important to start with the right parameters.  Otherwise you may end up with strategies that are quite a bit off.

Jonna,

Thanks for your reply, and you make some good points.  I'm not sure if I can explain my thoughts well, but I'll give it a shot.

There isn't really any such thing in game theory as minimum defense frequency.

I agree.  To be honest, I don't see any reason why there should be such a thing in GTO strategy.

Thing is, in most spots but the simplest ones, we don't know what the GTO strategy would look like.  We can make speculations about what it would not look like, though, and MDF can play a role in this.  Suppose we are facing a pot-sized bet on the flop.  We don't know what the exact GTO strategy might be, but if our strategy is to fold 80% of the time in this spot, that is likely to be non-optimal.  

In this sense, MDF is nothing more than a shortcut that allows us to do some quick sanity check.  Of course, just because we defend more than the MDF doesn't necessarily mean our strategy is GTO, and it is entirely possible that the real GTO strategy in that spot actually requires us to defend less than the MDF.  However, that is something that we can know only after solving the game for this spot.  And since nobody has really done it yet (especially for PLO), we instead rely on MDF, assuming that it will allow us to get the big picture right.  

A range in one spot may give you license to bet 100% of the time, and another range in another spot may require you to fold 100% of the time. 

That's true.  There are spots where 3bettors can get away with betting 100% of their range on the flop, forcing the caller to fold 100% of the time.  There are spots where villain's range has so many flushes on the river that we have to fold our top set 100% of the time.  This is mostly a function of how the board texture interacts with both players' ranges.  On average though, assuming that the ranges on earlier street(s) aren't too far off, this shouldn't happen very often.  Do we know the full solution in these spots?  Most likely, we don't.  But intuitively speaking, when two similar ranges (note: on average) clash with each other, neither of them should be able to auto-profit too often.

And if I understand correctly, this can be a weakness of frequency-based approach if one is not being careful.  That said, it is important to change that frequency based on the things you mentioned - position, stack sizes, etc. - instead of sticking to "70% MDF" for every spot.

There aren't really any frequency rules.  It's all dictated by ranges and EV.

Once again, I don't disagree.  If we were to know what GTO strategy looks like, we can forget about frequencies, and just talk about ranges and EV.  In other words, in exactly solvable/solved spots, frequency rules go out of the window.  You mentioned preflop push/fold games as a counterexample.  These are (almost) exactly solved spots, and we know the solutions inside out.  Thus, we don't need to care about frequencies.  Unfortunately, this is not the case in most spots, and we are gonna assume that we (or villain) shouldn't be able to auto-profit upon building ranges/strategies, until it is proven otherwise.

That said, yes, it's all dictated by ranges and EV, but I'm afraid that might be an oversimplification for most postflop scenarios, whose GTO strategy should be fairly complex.  Frequency-based approach, in a sense, serves as an approximation to these complex strategies/solutions.  Granted, it only gives us a framework to work with, and doesn't tell us the exact details yet.  So it's only an approximation that, who knows, might get thrown out of the window once we figure out the true GTO strategy.  However, to my knowledge, it hasn't happened yet.

Well, that's a balanced view certainly.  Most models have some value, and no models (including GTO) provides all the answers.  The main benefit of any model is when we can learn something useful about what's being modeled, the game of PLO in this case.

In my opinion, the minimum defense model offers questionable value (over good player's intuition for example) at best, and can lead to completely nonsensical strategies in the worst case.  And then mixing it up with something supposedly GTO-ish and exploitative-ish... well, I think it becomes unclear.  Unclear what's really being asked, and unclear how the answer should be used in any reasonable way.

The main issue with poor models is that they lead to poor reasoning and poor conclusions.  MDF does have a place in many river situations, but applied to earlier street play it can easily lead in the wrong direction.  As a starting point for further analysis I suppose it does have some merit, and I think that's how Janda uses it.  Many people seem to miss that though, and think that MDF is the end result, which it clearly is not.

I suppose what I'm really saying is that applied GTO is in the domain of math and computer science now and onward.  Doing GTO-ish things with poor models and shooting a bit from the hip is probably not going to give excellent results, especially given the relative ease at which we can solve relatively complex spots already.  (this is clearly easier for holdem, but doable for plo also)

Jonna,

I guess we are on the same page, more or less.  Fwiw, I have never argued that the MDF is a universal solution or the ultimate remedy; to me, it rather seems like the best of all poor options.  I say poor options, not because the theory developed by other people so far seem futile, but because the GTO modeling with PLO is still at its onset, even with the advent of computing power and stuff.  

Like I said, it's possible that in a few years we will be just laughing at all these MDF arguments that we are using now.  How likely, I don't know, but that's certainly a possibility.  However, until thus proven, I think it's probably better to stick with it rather than not using it at all.  That's the status quo of PLO theories I guess, and without the intense use of computing power (which we have been lacking so far, although this is slowly improving), it's actually not so easy to build a GTO-ish strategy by looking at ranges and EV only, without referring to the frequency!  More likely, we just have to go back and forth between these two in a bit of self-consistent manner (set a target frequency, fill in the ranges, adjust the frequency, adjust the ranges, rinse and repeat).

Sorry for the rambling, and I'd love to have more discussion about it if you (or anyone else) is interested! 

- midori

Computing power is actually not likely to help much with solving big bet poker games.  The exponential nature of the games mean that exhaustive calculations would take from now until the end of the universe basically.  If we improved computing power by a factor 1000 or even a million, the calculations would still take to the end of the universe.  And storing the solution would probably require more gigabytes than the number of atoms in the universe.  Clearly impractical.  And how would someone memorize and play that strategy?  New kinds of computers could change this, or someone could prove P=NP, but with our current technology paradigms it's somewhat unlikely that we'll see large poker games solved in our lifetimes.  Or at least before we solve the year 2038 problem, and maybe not before the return of Halley's Comet :)

What's more promising is what's going on in discrete optimization and in machine learning.  I'd expect most exciting things regarding poker software in the nearest future to spring from those areas.

Hard to take this much further in a video thread, but perhaps at some point there will be a poker theory forum on RIO  :)

TMJ,

Thanks for your kind words!  

Like I admitted in my earlier posts, I think frequency-based approach is a useful guideline in the absence of better alternatives, but I would be careful about applying it blindly to every spot.  Range imbalance becomes one consideration, villain's exploitable play another, etc.  Simply put, I (and maybe other players, too) use it in spots where I don't see any other good options for a quick and dirty range building.  

This vid by JNandez (let's not forget that this is actually a vid discussion thread, guys) deals with flop c-betting decisions.  I think it is a very practical example, because flop c-bet decision is the one we face the most often (besides preflop decisions), and pretty much every postflop decision stems from this one.  Now, this might sound counter-intuitive because, ideally, we need to take turn/river plays into consideration when debating on a flop c-bet, and that's fairly complex.  However, precisely because of that, constructing a robust, GTO-like (in its true sense) flop c-betting range is never easy, and probably close to impossible.  

Say, we are HU against BB on a K86dd flop ~100bb deep and he checks to us.  How often should we be c-betting here, and with what hands?  There are like 50 considerations here, if not more.  What does his preflop range look like?  How does he perceive my range?  Which range is he gonna put his hands into on this flop - x/f, x/c, x/r?  If he calls, what will be the turn card?   The list goes on forever, and all of a sudden we realise we timed out and checked back.  Boo.

It's true that these considerations are mostly about ranges and EV, as Jonna correctly pointed out.  No doubt about it.  Sad thing is, we simply can't "solve" for all these spots, yet we have hundreds of c-bet decisions to make every day, thousands every week, and so on.  And we can't really afford to not work on these ranges at all, either (I hate double negation, sorry about that).  This is, in my humble opinion, exactly where frequency-based approach can kick in and serve as a shortcut.  

Basically it tells us the following:

Guys, don't bother with those 50 variables.  Why not forget em and shoot for some frequency and fill in the ranges accordingly.  What frequency?  I don't know, how about 70%?  Or 50%?  It depends, you know.

I mean, these numbers (70% or 50%, w/e) are questionable at best, because they are almost entirely based on the pot odds alone.  If the ranges we build based on these numbers happen to coincide with the true GTO ranges, it would be miraculous.  I'll give you that.  But hey, it's probably better than not having a frequency threshold at all.  It keeps us from making some ridiculous frequency-based mistakes in certain spots.

A typical example of such a mistake would be players who check-folds everything worse than Ax on A72r against a BTN's c-bet, even though he seems to be opening and c-betting close to 80% of the time.  If they gave a tiny bit of thoughts to the frequencies involved here, they would realise that BTN has a TON of air in this spot that can't call a x/r (save for some floats), and could start check-raise bluffing profitably.  Sure, they could have reached the same conclusion if they analysed the ranges in detail, but just looking at the frequency would do it too, taking far less time and poker brain of theirs.

That said, I wouldn't be surprised at all if the GTO c-betting frequency is way different from the MDF-based one.  Given how simple the frequency-based approaches are, it would be a fluke indeed if they were the same or very similar.  Thus, it is possible that we might be losing some $$ by taking the frequency-based (i.e. suboptimal) approach.  

However, there are some flip sides of this story.  Firstly, we likely won't know what the true GTO frequencies are without actually solving it, and thus we won't know if and how we could do better on the fly.  Secondly, having already established a solid frequency-based gameplan, we can always adjust to different opponents with different frequencies; namely, we get the big pictures right first, and then fine-tune it whenever necessary.  Thirdly, we can make up for it by making superior decisions on later streets, with or without a frequency-based approach.

Once again, frequency- or MDF-based approach is nothing more than a shortcut to this complex game.  Making our gameplan around it and building ranges is very different from having a true GTO gameplan, which nobody knows yet.  But because we can't know better yet, it doesn't hurt to adopt this approach.  If used with caution, it will gives us more pros than cons.  You know, something is better than nothing.

Whoa, that was a wall of text from me again, sorry for the rambling.  I can only hope I made my points clear by now.  I could have extended this to turn and river spots as well, but I limited myself to flop spots because well, that's what this vid was all about. :)

- midori