With Snowie's ranges the 3-bettor in the SB actually has 52% equity on 752 and 56% on 522, and that 4% equity difference doesn't sound a lot, but apparently it leads to an entirely different c-betting strat, and thus an entirely different continuance frequency.
On boards like AQT, the SB's range equity jumps up to 66%, which is incredibly high. On most boards, the equities run much closer, but that still doesn't mean that the frequency of betting and calling should be the same on all of them.

I mean, we all know this. We expect to get more folds on K83r than T76tt, so we bet more air on boards where the fold equity is high. I don't see how MDF is even a consideration. You continue more often on boards that are good for your range, and fold more often on boards that are bad for you.

It doesn't necessarily make the pre-flop plays profitable, but it absolutely can in many cases especially if flop fold percentage is very high. Also if we're using a MDF(any2) method (which takes preflop into account) we can precisely determine if the play is as a whole is +EV or not.

But part of that 3BB is preflop steal value.

I agree that MDF is poorly applied when used on specific flops, but for flop continuation range in general I think it mostly holds in common poker spots. Saying something like "folding more than MDF(range) allows is fine" is IMO generally wrong, its folding too much.

That said new players are probably generally playing against low-stakes loose/passive opponents so folding more than MDF is probably correct as an exploiting maneuver. So its probably not a bad idea to just abandon MDF altogether since its easily misused and not the best exploit-play anyway.

Yes. This happens very frequently when one player has a range advantage.

It wasn't meant as a trick question. I am trying to construct a scenario where MDF is an accurate approximation of equilibrium prior to the river. It is something I believe I understand but don't have a solver to verify. MDF relies on two false assumptions, that the worst bluffs have no equity and that we should prevent villain from being able to profitably bet hands with no equity. On a drawless board, bluffs at least have very little equity. When deciding how to respond to a raise after choosing to bet, preventing the worst hands in villain's range from being able to profitably raise actually is a reasonable goal, whereas it often isn't when facing a bet.

Allowing villain to profitably bet ATC doesn't clearly mean we are not at equilibrium. There isn't a strategy which dominates ours here, however allowing villain to profitably raise ATC is a dominated strategy (possibly with some weird exceptions) The reason is that if villain can profitably raise ATC, he never has incentive to fold, which means we have no incentive to bluff and our bet/folds have made a mistake by betting. I believe MDF is a fairly close approximation of equilibrium when considering how to defend against a raise on a very static flop. Further I believe that betting and folding to a raise more frequently than MDF never occurs at equilibrium. Can you construct any real poker situation, or any toy game where we should bet and fold to a raise more frequently than MDF?

Oh I see what you mean.
It's probably unlikely that that scenario arises, although I can't rule it out entirely. I don't have any examples right now, but I'm probably getting a solver in the next couple of weeks, so I'll report back on this topic.
FWIW, I was looking at my own HUD pop-up stats the other day and was surprised to see how often I call when faced with a raise on the flop. People are always saying "You should over-fold to post-flop raises", but if you have a good betting range in the first place, you should have plenty of hands that can continue when they get raised.

could anyone please elaborate on this so I can better understand? I kind of get it but please confirm if you can.

Why is the amount of money invested in the pot relevant to what your MDF should be?

Would this be because say, you over-called a 2bet on the btn and see a flop 3 ways? So MDF should be relative to the amount invested by you since the other player should, in theory, "defend" his equity of the pot?

Someone please dumb this down for me.

very simple, when you are in the Big Blind you will get very good Odds to call.
btn minraises and Sb folds, now you Need to call 1bb for a pot of 3.5bb.
that means calling and winning the Pot 1 out 4 times is better than folding preflop. (4.5bb /4 = 1.125bb ). that means it is fine to have a weaker range than the Button Player. with a weaker range you simply cannot always defend according to MDF but you dont have to, because the only reason you called preflop is because you got to see the flop cheaper and you dont have to win it to 50%.

So it is based solely on your odds preflop? What about once you get to the river and SPR is low? It becomes more relevant then?

no it is based on the strength of your range. you dont fold a Hand that is +ev to Play. and you dont continue with a Hand that is -ev . but the great pot Odds lead to a "weaker" range ... sometimes a rivercard is very bad for YOUR range and then you cannot meet MDF and just have to overfold because most Hands in your range will be -ev river calls. but that is "fine" because Villain can not pick a Rivercard.

so under what circumstance is MDF relevant in the same way its taught?

when players ranges have pretty much the same amount of equity on a given board. No player has a range advantage. Now you should meet MDF to win "your" fair share of the pot.

the more combos a player has to value bet, the more bluffs he can add to his betting range. if villain has a huge range advantage he has much more hands he can bet for value, thus he can also bluff a lot more frequently. At this point it is really difficult for Villain to "overbluff" because he has so many Value combos in his range.

I would not want to play red baron because i would loose a lot of money. Trying to meet MDF on a board where Villain has a huge range Advantage is pretty much the same thing

cool great job at explaining this, thank you


so if villain bets $1 into $2 on the river our MDF is supposed to be 66%. In this case how much equity does our overall range need to have vs his before he bet in order to justify using MDF? And if we don't have the required equity how do we determine our "real" MDF? Or are we just going to overfold everything?

Each hand in your range needs the required equity needed to make your call profitable.

In the example your hand needs 25% equity (more due to rake considerations) to make a call.

So using MDF we would call the top 66% of hands that hold 25% equity vs his bet right? So what zuko is saying is that if his betting range is so strong that none of our bluff catchers have 25% equity then MDF is void and we just fold everything correct? Am I missing something? If I got that right then yea thats pretty basic stuff and I just leveled myself lol.

*edit*

Assuming the previous spot then MDF, being a GTO-strat, would make back all money lost vs a value-only range by seeing a free showdown with its otherwise bluff-catching hands when villain underbluffs correct?

So pot odds alone decide what your MDF should be, and your range equity in relation to those pot odds decide whether you should implement it no? If villain jams the river then surely you never have the same range equity as him (unless of course he's super unbalanced and over-bluffing like crazy).

If you had more than the required number of hands to call, you would only call 66%.

You are calling only to make villain's bluffs indifferent to checking or bluffing at the same time trying to avoid calling and paying off villain's value bets more than is necessary to accomplish that.

okay I think I got it, haven't studied this in awhile and when I did it was generally called 1-alpha so just kind of leveled myself here. Thanks for the explanation appreciate it.

sounds good to me

A big thank you to all that posted here. A big help to me and others. A fair discussion. I learned a lot.

MDF is flawed in some circumstances, primarily preflop. I will be working on that.

The results of millions of simulated hands show a dramatic increase in win rate. Not proof certain, but offers some confidence.

MDF can increase your win rate even if flawed.