You really just need to think about villain's range and how your range interacts with that. Let me specify.

From the preflop -> flop -> turn -> river, you should consciously be narrowing villains range down as well as your own in your head to come up with a good idea of what bluffs villain may have, what value hands he has, and then the same for you. For example, it could be a river spot where villain could very easily be overbluffing with QJ on a KTXXX run out and you decide to hero down blocking some of his value range and none of his bluffs with the ideology that he could easily be overbluffing turn/rivers as a function of his range and sizing.

RANGES, THINK ABOUT THEM. Both yours and your opponent. If you think you're beat, you probably are. Think about how your opponent plays and what hands he can have. Exploitation starts there, and thus higher EV.

Beginner here. Sounds wrong to me. Let say there is no reads in a game, then the only things that matter is how you and your opponent defend the pot. The important point here being that your opponent is held by the same constraint as you: on any board, he must be able to defend the pot with his range.

I'm pretty sure that's wrong. Because that's the opposite: you must be able to defend the pot on any board using your range (and not the opposite, a.k.a you must not defend your range with the boards), or you would be exploitable. To exploit you, I just have to find the boards where you range is weak or strong.

Am I missing something? Is that wrong? Why?

There's no reason you have to defend every card. The probabilistic nature of the game means no matter how hard you try you may not be able to profitably defend every potential outcome, let alone be able to manage such a strategy as a human player.



You're missing the fact that actions on previous streets and revealed cards will limit your range drastically to the point it may be unrealistic for you to defend properly. It all evens out though like Arty said (i.e. your opponents have the same problem).

Yup.

This is really interesting and basically what thread is talking about (lol)

So what you are saying with not defending correctly being correct... has to do with us calling way too much/being -EV if we are trying to defend on every card like u mentioned? Or am i thinking about this incorrectly not too sure that's why i asked.

I open UTG, you call on the button.

Flop comes 322. I never have quads or a boat, because I don't open 33/22 UTG, but it doesn't really matter to me, because when the flop comes AAK, you never have quads or a boat, because you don't flat AA/KK/AK pre.

My range doesn't need to be able to defend perfectly in every situation. It just needs to be strong overall.

A more common situation would one between UTG and the BB, where the board comes out all low cards with several straights possible. What UTG loses on boards like 64378, it makes up on boards like AKTxx or AAJxx. I'm not gonna start playing 54s UTG just so I can flop the nuts on 632. That's just a bad board for me, but it's a rare one that barely needs thinking about.

Well put and yeah makes total sense, but i thought board coverage was a thing/i don't even understand what board coverage means i just hear people say it a lot.

Well that's part of it. The other part is just that revealed information + Probability can virtually eliminate your ability to defend.

Quick example.

You call a raise from the button in the BB and the flop comes:

2h 3s 9h

Button cbets and you call.

Turn is Ah so the board reads:

2h 3s 9h Ah

The button now has a pretty profitable continuation bet almost regardless of your holding.

Given you didn't 3 bet you likely didn't have the Ah any way but if villain is holding the Kh and to a lesser extent the Qh or Jh it just severely limits the number of combos you could have with a flush. Now image this scenario is an extremely obvious example an there are other boards and textures where the same thing can happen.

Yeah i get what you are saying.

Such as on certain turn and river run outs where say it's an A or K and say for example you know villain will never float w/overs, so now we have the range advantage right as well as he won't be able to defend properly because he never really gets to the turn or river with any Ax or Kx?

Yup another good example.

Edit: Though I will say I think players in general have become more aware of defending A high, so that K on the turn is probably a better barrel card.

Also board coverage is definitely a thing, but your opening ranges can only open so many "crappy" hands before you can no longer defend against 3b. I like to call this "range saturation". You may have 100 combos of obvious opens that can defend well vs 3bets, but you can only add so many hands in before you can no longer defend and villain starts profiting with ATC. Something like 54s and T8s may definitely be marginally profitable/break even opens even from the UTG position, but once you add so many of these hands in you are simply opening too wide

Thanks for the detailed explanation. Good point: there is position where you can defend 100% of boards, some where you can defend only 90%, some positions where you break even and some positions, like the position 18 in a 20 player game , where you can't defend properly a decent amount of boards and where you would be allin on any open.

How could we identify the spots where MDF makes sense and the spots where it doesn't?
I guess MDF applies when the ranges are symetrical, right?
From a mathematical perspective, does this mean when the EV of our range = more or less 50% vs Villain's range? or when the hand strengthes distribution is more or less the same in both range?

This means that Villain's bluffing combos should represent 30% of the betting part of his range, right?
So this means that he should bluff 30/70=0.42 weak combo for each value combo in his value betting range, right?

What if we are in a spot were we can't find so many bluffing combos in Villain's range?
In such case, even if he bets 75% of the pot, this now means that we can't consider such a high bluffing frequency and we should now call a tighter range only based on EV calculation (taking into account our equity vs his supposed VB range + the few remaining bluffs), right?

(For example, here is a spot where I can't see many bluffing combos : http://forumserver.twoplustwo.com/56.../#post51054985
so even if Villain bets $146 into a $148 pot, I don't think he's got 97/295 = 33% bluffs
So that this example fits the current thread, please consider that there's no river card to come and if we call we see the showdown).

sry, I meant "equity", and not "EV", so my question was :

From a mathematical perspective, does this mean when the equity of our range = more or less 50% vs Villain's range? or when the hand strengthes distribution is more or less the same in both range?

Not necessarily.

So many posts here about posts why mdf doesnt work or does work etc, but no one is really going deeper, why, what it actually is looking to model etc, when it can direcyl used, when it needs to be modified etc.


You should go back to indifference principle and then from there go to mdf, what mdf means, how to combine mdf and indifference principle when mdf doesnt directly apply. It's actually not too complicated to get rough models with streeth math even on earlier streets on some simpler textures.

ty for the reply,

which models? is there an example somewhere?
I know Piosolver and GTORB, but I'd be interested in finding a simple model.

by streetmath i mean pen and paper, alternatively excel

hmm I don't get it : how can you modelize simply the hand you should call with given Villain and Hero's ranges, the board and the odds?
This sounds very complex to me!!!

In that spot, Snowie's range is close to the frequencies predicted by the MDF model. It has 6 combos of AQs/AJs and 4 combos of 54s (which it jams 92% of the time, which translates to 3.7 combos), so it's balanced fairly close to the 2:1 value:bluff ratio.
Snowie is weird though. It calls with AQs/AJs and shoves 54s, but when it calls it only has a 0.02% of a pot-sized bet for the river.

ty ArtyMcFly, regarding this HH and Snowie, I have replied to you in the thread (http://forumserver.twoplustwo.com/sh...67&postcount=3) in order not to derail this one.

But if we consider that there's no river to come in this spot, calling here is just to prevent being exploited by some crazy maniac who would turn Ax, 7x, 2x or mid-pair into a bluff.

Would you consider Villain has 33% of bluffs in his range after this Turn play?
If not, how would you quantify his bluffing combos in order to evaluate your EV for calling?

I generally use Snowie for getting a general idea of what theoretically strong/balanced/pseudo-GTO poker looks like. I don't count combos or work out what the MDF is. I don't do much math. In the real world, I'm more of a feel player.
I'm kind of half-joking. In your hand, I wouldn't be barreling the turn, but if I did and villain check-raises, I just ask myself "Does he ever bluff here or raise with worse?"
If he's unbalanced and almost always has me beat, I fold. Usually in spots like that where I barrel with a non-nut hand in a big pot, it's because I've already decided villain is loose/crazy enough for me to play for stacks. I hate bet-folding.

Few questions again... :?

-How do we find the EV of our range, do we just add up the EV of all the hands in our range so confused here...
-In what spots would you say MDF can be directly used then? I provided an example OTR, but i'm sure there are certain run outs where it applies similarly on but now im confused as to when it applies and doesn't apply could u give an example possibly

I would say calculate the EV of all the hands in your range vs Villain's range, and then calculate the average.


I am still wondering too...
Would love to read more answers to my previous question :

Example: I open raise 3 big blinds in the cutoff, folds to the big blind, he 3 bets all in for 20 big blinds, should we make his 0% bluff indifferent by applying strict mdf? No because he has two cards and those cards have equity. Thus making a 0% equity bluff indifferent is a mistake. Instead, put him on a range and estimate your equity vs that range. If you have enough equity to profitably call then call. If not then fold.

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I raise 3 big blinds in the cutoff, only the big blind calls.

Flop AAKr

Checks through

Turn 5o

Checks through

River 6o

Big blind bets 1/2 pot. Should I apply strict mdf to make an 0% equity bluff indifferent? Not sure but I think yes because there are or should be hands in the big blinds range that have 0% equity vs my range. Thus making a 0% equity bluff indifferent on the river becomes a priority.

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I raise 3 big blinds in the cutoff, only the big blind calls.

Flop AAKr

Checks through.

Turn 5o

Checks through.

River 6o

Checks to me, I bet 1/2 pot. Should the big blind apply strict mdf to make a 0% equity bluff indifferent? I think no because even my worst hands may have a shred of showdown equity vs my opponents range. Thus if the big blind wanted to make my bluffs indifferent to betting or checking the river he should fold more than strict mdf would suggest.