Calculating Minimum Defending Ranges wrt to Equity.
Posted by Declan McKenna
Posted by
Declan McKenna
posted in
Mid Stakes
Calculating Minimum Defending Ranges wrt to Equity.
Pot = $1
Villain's c-bet = $1
Hand 1
Our ranges equity: 50%
Minimum Defending Frequency: 50%
Hand 2
Our ranges equity: 100%
Minimum Defending Frequency: 100%
Hand 3
Our ranges equity: 0%
Minimum Defending Frequency: 0%
Hand 4?
Our ranges equity: 25%
Minimum Defending Frequency: ?%
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20%
The terminology is not correct!! The "minimum defense frequency" ist not depending on your equity but on Villain´s betsize. It´s in ALL given scenarios 50% - because that´s the fold equity Villain needs for pure bluffs.
I'm aware of the conventional way to calculate minimum defence frequencies and that in doing so we would get 50% for all four hands. What I'm asking is whether it's possible to adjust these frequencies based on our ranges equity? Hand 2 and hand 3 illustrate two very simple examples where we can do this. Hand 4 would require some maths.
check out sean lefort's early video for explanation on the math behind MDF
OK, now I understand your question - but it makes no sense from a mathematical point of view. It´s completely irrelevant what equity your "range" has against Villain´s range. Let me give you an example. You have ten (10) combos in your range with following equities:
3x 100%
5x 30%
2x 25%
The overall equity of your range vs. Villain´s range is 50% (go ahead and check it :D). According to your idea you had to defend 50% of your range now (as a minimum!!!). But do you recognize that your range has only three combos you can profitably call with? So you´re starting to make unprofitable calls - to do what?!
If your overall range has poor equity vs. Villain´s range, it regularly doesn´t happen by chance - it´s a result of poor range construction.
No matter what, let your idea go - it´s not the right track to go. :)
Equity does matter. Your HU against a nit who folds his BB 80% of the time and only 3bets {QQ+}. Ignoring equity our minimum defending range to villain's 3bet would be around 35% of our opening range (which is going to be super wide). We'd be burning money to defend this much in thegiven scenario. When either our own or villain's range is stronger than the other, conventional minimum defending frequencies are inadequate. Equity is an imperfect way to measure the strength of our range but it's better than ignoring who's range is ahead all together.
In your example I'd definitely be floating some of the 30% and 25% hands. We would often float backdoors and gutshots with far less equity than this.
I was not talking about floating and stuff ... and OBVIOUSLY does equity matter, but not range vs. range, but hand vs. range.
I'm not arguing that equity is a perfect measure of who's range is the stronger, it's an estimation at best and get's worse the wider the ranges get. But an estimation with which we can tweak our defending ranges is far better than relying on minimum defending frequencies alone regardless of whether we crush or are crushed by our opponents range.
I'd argue there are many cases in which our range fairs badly against villains without poor range construction. My example above where we are playing exploitative against a poor opponent is one as are many postflop scenarios where we may face turn cards that unavoidably hit one of our ranges far better than the others.
I think you are some confused.
In this case our MDF would be ~30%.
A = 10bb / 3bb + 1.5bb + 10bb = 0.68
MDF = 1-a = 0.32 = 32%
When we check/call a hand like QsJs on a 2d5cTs board it's because we actually have around 45% equity vs a high cbetting range. Could be the case for BBvBTN/CO. We should defend more or less than 1-a based on the weakness/strenght of villains range.
If our equity range is strong, villain should not cbetting quite much, and if he is, we are winning more money manteaning our MDF frecquencies, and not taking poor equity combos and call with those ones too.
Your hand actually matters, you can't start making EV- calls, just because you think your range is strong, and pray to villain that he stop cbetting.
Make EV- floats looks more like an explotative approach to some villains leaks. But nothing to do with GTO and MDF.
My mistake I meant to say 35%, I've got exploitable fold to 3bet%s stuck in my head. I've corrected it.
I went with 7bb/(2 + 1.5 + 7) = 0.66.
Assuming we open 100% of hands vs a huge nit HU we'd be defending a minimum 35% range against the nits {QQ+} 3betting range, making the minimum defence frequency an awful strategy in this scenario because it ignores villains superior equity.
That´s because we would playing an explotative strategy ( open 100% buttons), so Minimum Defense Frecquency does not apply to this. And you have not to defend MDF on spots where villain it´s not trying to exploiting you. He is opening the door to make "explotative folds".
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