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Originally Posted by poker-hero
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 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?
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I agree with this, Villain's range needs to be loose. This is why I chose my example : 100%OPR+100%CB
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.
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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?
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.
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When do we consider to be facing a loose range range that allow us to think in terms of GTO & MDF?
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.
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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)
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.