Hey guys,

I'm constructing 3-bet defending ranges, and I think I'm on the right track.
Starting with my OR, from where I split the ranges in 4 groups: 4bet value; call vs 3bet; 4bet bluff; fold.

I'm using Minimum defense frequency as a tool to choose the amout of combo's to defend.

Now I'm using multiple sources on this topic, and the different sources seem to deviate from each other quitte a lot when it comes to MDF.

I have 2 questions that would help me a lot of (partly) answered.

1. MDF is based on the RFE that villain offers himself, e.g. cu 2,5x open vs sb 9x 3bet comes down to RFE 68%. Should we defend roughly 32% here, or as other sources say, add 10-15% since villains RFE adds the same percentage during the fact he can flop equity even with bluffs, make +EV cbets on preferable etc?

Long story short, in the example above (when we try to be balanced), do we roughly defend more towards 32%, towards 45%, or somwhere in the middle?

2. Do we make adjustments in the MDF in micro games during the high rake? And if so how do we adjust?


Hope the post is not too long, and that you guys can give me a direction from which I can continue building my own ranges .

Kind Regards,
Dagobert.

i would suggest grifting GTO ranges as opposed to trying your approach, which although useful intellectual exercise, will not garner nearly as good of an end result.

even once you've acquired GTO range- or have done your method, its going to be extremely fluid in practice. high rake incentivizes taking it down pre, but your opponents tendencies also come into play to where you may be vsing stations and disincentivized to raise anything other than pure value, and for an insanely imbalanced sizing at that (which would change all of the calculations you've done based upon a static sizing)

The real values that get outputted from solves for these things aren't particularly close to the MDF for a number of reasons, but there are important aspects to take into consideration:

1. stack depth

2. size of 3b as a fxn of (1.)

3. number of players that can interact with the 3b (basically how many can "share" the defense)

4. rake is quite a big one as a lot of evs can be very close to 0 without rake

5. Being IP/OOP (equity realization basically)

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First, I'm not entirely sure what the RFE stands for, but this type of exercise is more or less just going to give you a lower bound. In your example where SB is risking 8.5bb to win a pot of (9+2.5+1) = 12 then the mdf is 1-a where a is equal to 8.5/12.5 = 0.68 = 68%, so you can say that definitively the folding frequency of the BB and you combined will not exceed 68%. This sort of gives you an absolute lower bound. In this situation the BB 4bs around 5% (which I'm sort of hand waving, it might be okay for you to estimate this to be in the 4-6% range based on experience, but would be very difficult to do by pen and paper).

If we say this then the overall highest amount of folding we would do would be (BB fold freq)*(our folding freq) <= 0.68, if BB folding freq = ~0.95 and we solve for (our folding freq) = x, then

0.95*x=0.68, x = 0.68/0.95 = ~0.72 ~ 72%

so now we've done some mehhh math to get to the fact we'll defend at least 28% of hands. You can basically say after having done this that the equilibrium output would never have us fold more than 72%, which to be honest is not particularly useful.

1. If we ran a preflop solver for this we'd likely be defending 65-70% of hands and no where near that ~30% lower bound value (at 100bb eff). So to answer your question do we defend more towards 32%, 45% or in the middle? At 100bb eff it would be quite a bit more than the outputs you got.

2. Yes, rake has a pretty significant impact on preflop ranges when designing 3bet ranges and defending against them. At ~0 rake a lot of hands are very close to 0ev and when you add in rake a lot of them then turn into -ev hands. The short answer is you adjust by being tighter

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To give you some more basic concepts for the things listed above at the beginning (1-5)

1. as stack depth increases --> you typically defend more

2. as 3b size increases --> you defend less

3. if there are more people to interact with the 3b then you would defend less. An example would be you RFI UTG and then MP 3bets you, there is shared defense vs. the MP between you and the CO/BTN/SB and BB which results in you basically not having to defend as much ---> equilibrium has MP being quite tight also so utg would fold quite a bit more in the UTG vs MP node when compared to UTG vs BTN for example

4. as rake increases ranges tighten

5. if you take the same hands/sizings/stack depth, etc. and you only change ip/oop, you will find IP will defend quite a bit more and this has to deal with the fact that IP can always check behind and therefore typically realizes quite a bit more equity than OOP so more hands become profitable. (this is called equity realization)