Hello everyone, juste wondering something about the GTO strat and the direct odds that our oponent gets when he bluff (cbet for example)

So let's take the case of our oponant cbeting the flop for pot, he's getting 1:1, therefore if we fold more than 50% our opponent makes profit
Then my question is : does this mean that we have to defend 50% of our range in theory ???

The thing that seems weird for me is that if we defend only 50% of our range in that scenario, our opponent obviously has a really profitable cbet, because he's already neutral for the times we fold, but he still keeps his equity when we call (and gets also some extra ev still when we raise unless he makes big mistakes cause worst case he fold all the time he doesn't loose more but he can still have a hand or EV+ mooves also when we raise)
Therefore the opponent's cbet is obviously profitable, and i guess by deduction we make a mistake by defending only 50%

But not sure about this though and it's pretty weird cause that would mean that basically we should defends like huge amoutn of time when opponent cbet 1/2 pot in theory land
So if someone could clarify a bit, in theory how much of our range do we have to defend against a cbet

First, I think this minimum defense frequency stuff is far from being proven to be GTO. It aims to keep your opponent from "automatically profiting" but ignores the fact that the GTO case could very well be that he automatically profits and you can't do anything about it.

Second, yes, this is basically it. If you want to prevent him from profiting with ATC in his range, then you need to defend 50% of the time or more. Sort of. This is also pretending that there is no future action in the hand, i.e. that he gives up once called and you win.

Yeah, both the OP and rustybrooks post is good.

Ok thanks for the answer
I kinda feel as well that this is a bit science fiction and in practice there are just way too many other parameters to take into account for us to just want to blindly defends the amout or more to not make vilain auto profit i guess ?

So then how should we implements this information of defense to not make vilain auto profit with bluffs in game ?

There have been lots of threads discussing the MDF. It's a decent approximation of good play, but it's not perfect. The basic (and intuitive) idea is that you should defend more often against smaller bets than larger ones, because of pot odds. In the long run you might find it's correct to fold a little less than 50% of the time when facing a bet on any street (assuming villain usually makes bets of between half pot and full pot), but on some boards where there is a range imbalance (one player has many more nutted combos than the other) you should defend more or less often than MDF would predict, and you should continue in the hand just based on the expectation of making money or not.
Sometimes the board is so ugly for your range that you should check-fold at an "exploitable" frequency, but if you have good ranges overall there will be just as many board textures where you have the range advantage, and can call/raise more often than the pot odds require.

Ok that's what i thought so it's still a good indicator i guess

If you're OOP, you need only defend enough of your range to make his weakest GTO cbet have an EV equal to checking. Every hand in IP's range can generally check behind for a significant EV, so proper defense just means making cbetting less attractive than checking behind for some of IP's range. Defense frequencies IP are generally higher because OOP's checking option isn't as robust, but its still the same concept.

Also this all is assuming that both players' ranges are well blended with bluffs and showdown hands. A huge skew in the equities can make the MDF stuff go out the window. If OOP checks and IP has a range that is 90% nutted hands, its perfectly reasonable (and optimal) for OOP to c/f 100% of his range. Also, generally the worst hands with no showdown value do not count toward OOP's minimum defense frequency once they check, because they aren't exploited at all by folding. If OOP checks river, and IP bets pot, generally OOP needs to defend with 50% of his range that beats a bluff. On the contrary, the no SD value hands count toward IP's minimum defense on the river because those hands will often bluff 100% when checked to, and thus OOP gains significantly from folding out IP's zero equity hands.

Thanks for the explanation
Depends a lot on if the ranges are already equilibrated and to similar strenghts (so i guess this stuff applys the most on BvB and HU for example ?)
And also depends on the position caus of the EV of checking IP
And the bottom of the range that has no equity against the range doesn't count in the MDF range OOP, not true for IP caus we take out the oportunity to make him bluff his zero equity hands, and therefore win as making IP fold those hands even if they have 0 equity, if i resume what i understood, ty !

I prefer to think that the MDF doesn't depend on hand ranges, its the same regardless. What does depend on ranges is whether or not you want your strategy to adhere to MDF. Do you really need to try and play GTO or is it better to just try and exploit your opponent for as much as you can even if it means playing an exploitable strategy yourself?

and what about the flop and turn?
if I want to use the MDF on flop or turn : should I defend (1-A)% of my whole range or (1-A)% of my combos that can beat a bluff?

I guess it's (1-A)% of my whole range (won't fold nut flush draw because it doesn't beat a bluff), but I'd like to read thoughts on this.

No you will only consider continuing with hands that have enough showdown equity + ex-showdown equity (i.e. implied odds and/or fold equity) otherwise it's very likely you'll be continuing much too often with hands that are too weak.

but what if I want not to be exploited?

Let's say I am in BB facing a 100% BTN minraise steal, and BTN 100% CB half pot.
Of course I would fold all the combos if I think any other action is EV- (yes, I would fold 54s on JT9 flop for example).

But for all the grey spots, I want to defend 1-A on flop : should I defend (1-A)% of my whole range or (1-A)% of my combos that can beat a bluff?

You are misusing the word exploited. Continuing with less than the MDF doesn't mean you are getting exploited. It means that all hands in villain's range can bet with a positive expected value. That's it.

Now, in some situations it is almost trivial that if villain can profitably bet with his whole range, then you are being exploited. Say you're playing HU on the button. If villain can profitably reraise your opens with 100% of his hands than that's no bueno.

But let's take another example: 6max, 100BB eff stacks, UTG raises, you flat on the button and flop is 422. He bets 100% of his range. Trying to defend MDF in this spot is suicide. Villain is quite entitled to a profitable bluff with all his air here. Trying to defend enough here won't stop you from getting exploited. It will just lead to getting exploited even worse.

The logic of the situation is something like this: On the one hand you want to defend enough so that villain doesn't get to bluff profitably with his whole range. On the other hand your weakest calling hand still has to get 0EV on its call, against a well-constructed betting range. If villain's starting range is so strong that you can't do both, then you have to call less then the "minimum defense frequency".

I don't think that's a helpful description. MDF isn't connected to pot odds, it's connected to making pure bluffs 0EV, ignoring further streets. The two is closely connected, but there's a big difference when we are reacting to a raise, rather than a bet.

Ex.1: Villain bets 1 into a pot of 2. Pot odds is 3:1. Villain is risking 1 to win 2, so we need to call 67% to make him indifferent to doing it with all his hands. MDF is 67%.

Ex.2: Pot is 1, we bet 1 and get minraised. Pot odds is still 3:1. However now villain is risking 2 to win 2. We only need to defend 50% to make him indifferent. So MDF is 50%.

So we have two hands when we have the same pot odds, but the minimum defense frequency is different. That's because MDF is connected to how much villain is risking in relation to the size of the pot, not the odds we are getting.

Calling 1-A is a strategic response to a villain that only has a range of nuts or bluffs when betting.

The reason we call with that frequency of bluff ctachers is to keep villain from bluffing more frequently while also causing villain's bluff bets to be 0 EV.

So I'm not really sure how it's applicable to your hypothetical situation.

In your situation you would adopt an exploitive strategy of always continuing with all of your bluff catchers as well as probably a great deal of other hands that have both equity, implied odds, and fold equity.

You don't really have only defend by calling either.

The nuts/air vs bluff catcher game also breaks down a little bit over multiple streets and as well as with additional betting strategies because all hands have equity, range advantages can shift as more of the board is revealed, etc.


If you used 1-A for your whole range and a hand that was a -EV defense still fell into your 1-A calculation, would you still defend it?

Since 1-A grows as the bet size relative to the pot shrinks, what do you think the likelihood is that if you defend 1-A of your whole range that 1-A is going to contain -EV hands?

That's exactly the kind of thing we want to avoid, isn't it?
This is what GTO and MDF aim at fighting against, no?

I agree with this, Villain's range needs to be loose. This is why I chose my example : 100%OPR+100%CB
If Villain's range is too nut heavy, no need to think about MDF or GTO.
The interesting question here is where's the threshold?
When do we consider to be facing a loose range range that allow us to think in terms of GTO & MDF?

In order to achieve this, you want to defend (1-A)*your whole range, right?
(excluding the -EV calls, or moving these combos to our raising range if this is a EV+ move)

sounds like a very good remark, ty.

so basically, (1-A) MDF is only effective at the river, right?
2 things make me uncertain about this :
1. MDF is very often involved when it comes to defending preflop vs a steal (this is the essence of MDF right?)
2. there is a huge number of training vids using MDF on flop and turn (these 2 ones are focused on this concept : http://www.runitonce.com/poker-train...ing-optimal-3/ and http://www.runitonce.com/poker-train...view-workshop/ : full of bs imo, feel free to give your thoughts)


no, I mentioned this in my 2nd post.


no -EV moves should be done to reach the 1-A %

I don't know? Is it? Seems like a big assumption. I phrased my answer the way I did because I didn't want to make any assumptions that are untrue in some situations.

This thread contains two examples where the assumption fails. One where checking with air is not 0EV, therefore trying to make bluffs 0EV gives up more against value hands than necessary.

The other is when villain has so many value hands in his pre-bet range that he can't "properly" balance with bluffs. Here, again defending too much gives up more against valuebets than necessary.

There's at least one more situation where the assumption "we shouldn't give our opponent +EV bluffs with his whole range" fails. That is spots with strong card removal effects. It turns out that even if you defend with 50% of your range you will be defending 55% against some of your opponent's hands and 45% against some others. So what's the solution? Defend at least 50% against any bluff combo? Or against some "threshold" bluff hand?


In this case MDF fails to be optimal because the threshold bluffing hand has a non-zero EV when checking. Maybe. There's some complications because getting called while bluffing is not 0EV either.

It's not nutted hands per se, but any valuebets. If villain has 80 value hands and only 20 air then we can't defend "MDF" against a half-pot bet. It could be a thin value-bet, or the stone cold nuts, if villain is value heavy, because his range doesn't contain enough bluffs, then we should not defend with pure bluffcatchers at all. We will still call with hands that beat some of his valuebets of course.



GTO is a more general concept and thinking in terms of minimum defense frequencies should not be thought of as GTO at all. There are situations where they give similar results but how common these are is an open question.

Here is how I personally think about this:

MDF is the exact GTO solution to the simple bluffing toy game (look it up if you're not sure what it is). In situations where the assumptions of the toy game hold approximately, the GTO call frequency will be close to the MDF. The important assumptions of the bluffing game are:

• checking with non-value hands is 0EV
• there's enough non-value hands that we can't bluff with all of them
• no card removal

Basically, think of MDF as a first order approximation to GTO play in some particular spots.

I don't know what A means here so I can't answer, but there's a hint in my previous post. MDF is the frequency c such that the EV of a bluff is 0 (assuming 0EV when called). So for a pot size of 1 and bet of B

-B*c + 1*(1-c) = 0, and solve for c.

In quite a lot of spots, MDF isn't even a close approximation of the GTO solution for the river.
It's just a general guideline that works perfectly for toy games, but not particularly well for 'unlimited' holdem.

+1 to Arty,

Many spots have us calling significantly more than 1-a or significantly less. There are spots where we should fold our entire range.

As ambientsilence has stated MDF only provides an exact solution in the toy games where certain restrictions have been put into place on the game.

There is an excellent thread on this topic somewhere in this subforum (sorry on my phone so no links) where bobf performs simulations and shows that mdf is a pretty great approximation for continuing even on earlier streets, provided our range and our opponents range are very similar. If there is an imbalance one way or another then using mdf can be quite far off the mark.

I can't remember but I believe his sims were even restricted in that betting options were limited.




So I guess my question would be doesn't using your entire range form some logical inconsistencies then? Like how can you both drop -EV hands and defend 1-A if they intersect?

this one I guess : http://forumserver.twoplustwo.com/15...l#post49893095

I don't get his equation, but the thread is interesting indeed.

thanks

A = Hero's folding minimum frequency for Villain starting to autoprofit with his bluffs.

I think calculating 1-A and solving your equation is the same, but I am not sure because it's late here and my brain is slowly dying atm...

shouldn't you be more concerned about this villain in particular and less concerned about having a theroetically unexploitable strategy?