Hi,

The concept of Minimum Defense Frequency is mainly used when defending your blinds. In some spots it's a non-sense using it, but in other ones it's a fine approximation of GTO plays.


But does it make sense to use MDF postflop for example if I am BTN and called the UTG open preflop, and face a CB?

In this spot, let's say my preflop cold calling range is 10% of all the combos, i.e. 132 combos.
so if UTG Cbets half pot, alpha = 33%
so MDF should be 1-alpha = 67% of 132 combos = 88 combos
so I list the best profitable combos I have in my range including made hands and draws, and I defend ONLY these combos.
This implies that the 89th combo is folded even if it's a profitable call on the Flop.

Would this make sense?

Or given that we are IP and the spot is much easier than playing 3 streets OOP when defending BB vs CO, we could just call any profitable hand on each street and reevaluate later?

The 88 combos means that u have to defend at least 88, you can't possibly defend exactly 88 combos, but defend more is ok.

issue #1 with "at least" : if you can't find 88 profitable combos, you can't defend 88 combos, because you must not incorpoate losing plays in your GTO arsenal just for the purpose of balancing.

issue #2 with "at least" : if 100 combos might be defended profitably and therefore you elect to defend all of them instead of 88, then this means that MDF is useless in this spot, EV would be the only element to take into account. GTO tools seem to indicate that EV is not the only factor. Otherwise, they would call 100% of the time with combo XX, fold 100% of the time with combo YY and raise 100% of the time with combo ZZ.

IMO, in many spots only taking into account the EV of the various options available with the combo you hold instead of your range is absolutely not GTO and may lead to a very exploitable global strategy.

But I am not sure about the example given in 1st post.

It would not make sense to fold a hand that can profitably call. By the same token, it wouldn't make sense to call with an unprofitable (-EV) hand, even if it meant your range was folding "exploitably".
Maximising EV is the be all and end all. The aim of the game is to make money, not to prevent exploitation.

If EV was the only god in such a spot, how do you explain that Piosolver calls X% of the time with one combo and fold Y% of the time with the same combo in the same spot?

The EV of calling with this combos is the same when they call and when they fold.

But if you always call, then Villain can adjust and exploit you and calling becomes -EV.

So I do think we should balance our calls and folds in some spots (not even mentioning the raise option here), even though the call is slightly +EV in a vacuum.

(also, there are later streets to come so even if a call is +EV on the flop, this might be -EV if you take into account the later streets -> concept of Realization).

you must try to maximize the EV of your range, not the EV of the combo you hold.

Is the EV zero, by any chance?
If it's not, I can only assume the 'solution' is some distance from equilibrium and needs to be recomputed.
If you folded a combo that had a positive expectation, wouldn't that necessarily reduce the EV of your entire strategy? The sum total EV of your range is made from the EV of all the combos added up and averaged out, isn't it?

No, I am talking about spots where EV of calling >0.

Quick example with Piosolver :

BB def (56% calling range) vs SB steal (40% OPR)
Flop comes 9h7d3c
SB cbets 66% of the pot

With Kd5d, Piosolver says :
-raise 11% of the time -> EV of +0.6
-call 51% ott -> EV of +2.4
-fold 38% ott -> EV of 0

Imo, the explaination is just that if BB calls 100% ott with Kd5d, he becomes exploitable, and SB can adjust his CB range and then calling 100% ott with Kd5d would become -EV.

I think you forget that SB is a thinking player who can adjust later.
We are trying to get an unexploitable range for every action. So folding a combo that might be a slightly +EV call is a short term loss, but a long term gain because you con't be exploited later.

One interesting information with this same example :

is that I just noticed that Piosolver incorporates -EV actions in his plays. Like for example :

With Ks5s, Piosolver says :
-raise 2.5% of the time -> EV of -5.8
-call 1% ott -> EV of -7.8

I think this is probably because calculations stopped because it reached the desired accuracy.
I guess if the calculations continued until reaching the perfect equilibrium, these -EV plays would disappear.

No it doesn't make sense because you have position and a strong range. Board texture plays a big role, if the flop is something like Q98 then you'd be folding very seldom on the flop. If it's AA2 then you'd probably be folding more than MDF.

Think of your range and think of the board, the more connected it is with your range the more you're allowed to continue, even with very weak hands. On the opposite end the more disconnected the board is from your range, the more you have fold, even relatively strong hands.

MDF is for river mostly for river not pre or flop spots.If you defend MDF pre that is terrible strategy.I think on most board textures you should defend at least MDF but sometimes you range is so weak that your best strategy to fold too much,and some times its really strong that youll defend much more then MDF.

Every hand should be played in most +EV way possible and as result of that you get balanced ranges.

If you're able to defend more than MDF on a spesific board, chances are 1) Your preflop range is too tight, an extreme example would be that UTG opens and you only call with AA, and nothing else. Here you defend flop 100% of the time. 2) The flop is just too good for your range, so much that you have effectively won the hand by being dealt this flop. This should be a very rare occurrence.

MDF is only a concept that helps us better understand the game, as far as I know it is not used when a soft solves a spot.
There is an interesting thing not much known about MDF: MDF oop is always smaller than ip. The reason - MDF is computed by EV eqaution. The aim of MDF is to defend so wide that V's cb bluff is not +EV immediately.
EV(bluff) = FE *pot - (1-FE)*bet = 0. But V ip can check and realize some equity for free thus the equation should be FE *pot - (1-FE)*bet = E*pot(unknown depends on V 's hand).
In other words when V is in position V's bluffs need more folds than it looks at first sight and we can defend less than MDF oop.
Interesting how easy math supports the intuitive rule Defend less oop. It also shows that IP the correct def should be closer to MDF than oop.