Let's say I 2bet to 2.5bb with a 16% range from MP and someone 3bets me to 11bb from the BB with a 6% range. I decide to continue against the 3bet with a 4% range.

Therefore I continue to the 3bet 25% of the time. According to MDF, I need to continue 28.5% of the time or greater to stop my opponent auto-profiting.

Now my opponent notices that I am folding 75% of the time and he knows that the math dictates that I can only afford to be folding 71.5% of the time or less. He knows that he is auto-profiting in this spot, so he decides to loosen up significantly to exploit me, and so he now 3bets me with a 50% range, and I am completely oblivious to this, meaning it appears that he will now be owning the hell out of me going forward.

Now going by the mantra 'if your opponents loosen up, you should tighten up, and if your opponents tighten up, you should loosen up', then as my opponent is loosening up his 3bet range, I should remain tight and only continue with 4% of hands still in this spot, but then if I am remaining tight, my opponent could argue he is playing correctly by loosening up. So therefore this seems like an awful mantra to me as in this situation it does not seem helpful or conclusive at all.

Now back to this situation. If I were to continue only with the top 4% of hands, (say 99+, AKo, AKs), then my opponents bluffs are auto profiting approximately 0.5bb per hand.

However this is just a pre-flop amount, and there is still post-flop play where I will call the 3bet with some of this tight range, including AA and KK sometimes. Now because my range is tight, I have probably a 70/30 equity edge over my opponent, so will this not allow me to more than win back that 0.5bb per hand post flop on later streets? His 50% range will not make strong enough hands often enough, and there will be some severe reverse implied odds for many of his hands, where he loses most of the big post-flop pots to me. He may end up spewing off post-flop with his air-heavy range and lose significant EV.

Does this latter idea render the notion of his hands auto-profiting pre-flop rather moot? If it does, then you could argue that I am obliviously exploiting my opponent even though he assumed that he was the one exploiting me, because he was only looking at the pre-flop part of the equation and he is not looking at the full picture, is that correct? In his desperation to regularly force an apparently profitable pre-flop opportunity for himself, he ends up overlooking that he could be -EV overall from doing this, and is in essence exploiting himself, is that right?

That mantra is worthless. Vs someone who is 3betting you with 50% of hands you should be calling his 3b and 4betting him relentlessly. You would basically never fold a single hand from your opening range.

The postflop thing doesn't matter, he is already autoprofiting preflop. Even if he was to check fold flop with every single holding, he would already be making money off of you. Postflop can't make you lose more EV than the money you risk preflop, as long as you aren't playing like a reet. Worst case scenario you could check-fold anything worse than trips and you would already have a barely +EV strategy once the flop hits.

Have you heard of that mantra though? What is it in relation too?

As for the locked in pre-flop profit, I can potentially see that if you just check/fold loads and only continue with two pair or better on the flop with your 'pre-flop air' hands, then the locked in profit maybe does stay with those hands, but surely you can potentially lose more if you try some kind of betting strategy with those 'air' hands whereby you try to win the pot a lot even on those occasions when you don't have much of a hand? I mean you seem to conclude that it is possible for you to lose the EV back, so if so, we can't really draw too many conclusions about a spot that has 'locked in pre-flop profit' as you need to judge the hand as a whole still?

For example, if you just check/fold all of your air without two pair or a strong draw, then aren't you allowing me to have a guaranteed flop profit as you will not meet MDF when you check to me and I will be betting? Perhaps I bet with 100% of my range which will include a wiffed AKo/AKs a lot, and I would then view this spot in my mind as 'printing money with my bluffs'.

So you may have a pre-flop profit of 0.5bb/hand, but in a 22.5bb pot on the flop, if you check/fold a particular 'air' combo and I bet 50% pot with all of my range, must you not continue to this bet at least 33% of the time to stop me insta-profiting back?

So in a 22.5bb pot, if you check/fold 80% of the time say, then my bet earns me an auto-profit on the flop of 15.75bb per hand, which is far bigger than the 0.5bb per hand that you already have locked up.

Why can't my bet on the flop be viewed in the same way as some kind of 'delayed' pre-flop 4bet in this circumstance? For example if it was pre-flop and I min-4bet your 50% range to 22.5bb, wouldn't folding to that min-4bet 80% of the time make me print money pre-flop against you? If so, what difference does it make if I flat the 3bet and then put the extra 11.25 bb in on the flop to 'complete' my 4bet there? Haven't you still got to defend vs this amount of money going into the pot, and what street you do it on doesn't matter, (allbeit the differing street will change which combos count as 'value' and 'air' to you)?

I don't want to sound rude but you should sit down and try to understand a concept by yourself before trying to get to your own conclussions that contradict what has been calculated hundreds of times by better players.

If preflop I make an autoprofit raise, by definition, there's nothing you can do to gain that EV it back. I could play like a complete baboon and give it back to you by folding strong hands and calling air or some **** like that, but that has nothing to do with anything we're talking about.

Once you're postflop, even if you get to autoprofit, that autoprofit uses the frame of reference of the flop, in which half of the money has been contributed by you in the past. So in reality, if you "autoprofit" by 1 chip with your bluffs, you've already contributed say, 8 chips, which makes your overall loss throughout the hand with that holding be 7 chips.

Calling a 3b is not a "delayed 4bet" in any meaningful sense, because it doesn't deny the majority of the equity of villains bluffs. Calling is not bad though, and in this scenario, you should RFI tighter than usual and either call or 4b with every single holding in your starting range.

Also forget about that mantra lol

If there is nothing that can be done on later streets to give the EV back, then why is it that people obsess over river MDF so much? Or if they continuation bet the flop and face a raise, they try to continue with enough hands to meet MDF on the flop raise part of the equation alone, (part of the reason why cbetting 100% is so bad is because you can't meet MDF on a raise very easily).

How come I have never heard someone say ''don't worry lads, I know that I am overfoldng on the river here and my opponent is 'in theory' printing money against me with his bluffs, but this spot has come about after I have already taken a guaranteed pre-flop profit spot so I am good as I know that I am already +EV in the hand overall''.

If pre-flop player A 2bets and faces a 3bet from player B, we say that they need to meet MDF here, but then the occasions when A 4bets, then B needs to also meet a new MDF here. If B 5bets then A also needs to meet MDF in this spot too. Doesn't this also apply to all later spots on all later streets where MDF always needs to be met? From what you are saying it seems that if one of A or B messes up at some point and doesn't meet MDF, then all later MDF calculations are useless as the other player has already 'claimed EV' from that earlier spot and all later spots are irrelevant?

Another good example would be the initial example in this thread where I defend only 25%, then my opponent makes 0.5bb per hand. The breakeven defence would be 28.5%, but lets say I over-defend by continuing with 5% of my range, so instead of 99+,AKo,AKs, I instead use 88+,AKo,AKs,AQs,AJs. Now I am defending 31.25% of my range and substituting this value into the MDF equation means that my opponent goes from printing +0.5bb per hand to losing -0.375bb per hand. Does that mean that the 'air' portion of his range is locked in as -EV now because it is losing 0.375bb per hand, no matter what my opponent then does later in the hand? I mean if a positive number of EV gets locked in, then this should also apply to a negative number too right?

Alright bro, you found the loophole. Whenever you get exploited you're actually exploiting your opponent hard.

On a serious note, grab a pen and paper and calculate this before asking on a forum specially if your goal is to get a pat on the back for finding this new groundbreaking theory

I am genuinely asking as I am not sure on this myself, but if it is so obvious that you are correct, why are you not able to show it easily? It makes me question whether you fully understand these spots, and I don't mean that in a rude way as I do think you are a clever person that understands poker very well. However your knowledge can't be perfect and perhaps this is one area where you aren't fully sure either?

Just grab a pen and paper and calculate the EV of the 2 players, and assume player 2 check folds flop always, even when he hits a straight flush. See who is winning.

I have a good simple example to show my point more.

In my database where EP or MP open raises and I am in the BB with 44, 33 or 22 and I call the raise. If the open size that I face is 2.5bb then I need to win the pot 28.5% of the time or more to be profitable. If the open size that I face is 3.5bb then I need to win 33% of the time to break even. As I will have faced a mix of open sizes between 2.5bb and 3.5bb lets say that on average I need to win 30% of the time to profit according to MDF.

However my actual results show me winning only 16% of the time, but my overall losses in these spots over 400+ samples is -0.05bb per hand, so I am making a +0.95bb improvement over folding. I am probably check/folding the flop at a ridiculously exploitable frequency and only calling a cbet when I have a set or a rare open ender, (approximately 14% of the time I will have that kind of hand which is incidentally very close to 16%). My IP opponent may try to take advantage of this and cbet 100% of his range against me and he will win the pot on the flop 86% of the time. However the occasions that I don't fold and we get to the turn, our turn ranges are very different as his range will be wide and full of air, and my range will be condensed to very strong sets, the occasional straight and at worst a pair + OESD). However even though his range is wide and my range is 'narrow', combowise we will be equivalent so if he has say 250 combos of hands in his opening and cbet range, I will have 250 combos of sets/straights/pair+OESD to balance it out, and EV wise I have the potential to crush my opponent on the turn if he doesn't give up a lot of his air immediately, which very few villains will do. The EV that I would have lost on the flop street, will likely be won back and then some on the turn and river, and this is born out by my results over a decent sample size.

So this goes to show that you can win less often percentage wise than the pre-flop math dictates that you can, so long as you win bigger pots when you do win, which will usually be the case as most players over cbet the flop to try and 'take the pot down'. This just gives you additional EV that the pre-flop math does not account for.

I agree that the 3bettor is up money if he check/folds at 100% frequency as he is already settling for his guaranteed +EV spot that he secured earlier in the hand when his opponent did not meet MDF.

However in practice, later post-flop spots will emerge that don't guarantee the 3bettor that he gets to keep his locked in EV, as he will likely put more money in post-flop OOP as an equity dog. This is because the locked in EV is only small and the 3bettor will have plenty of hands that he will 'want' to do better than the 0.5bb per hand. It is when he tries to do this that he may end up hemorrhaging EV back to the tighter IP player right?

A human brain with a range with equity can outperform check-folding 100% on flop, trust me...

How about with MDF and trying to prevent our opponent 3betting with 'any two cards', AKA a 100% range, how do we adjust it for a 50% range?

Presumably we can afford to defend less than MDF correct? Because our opponent is already letting us off the hook somewhat by not 3betting 100%?

MDF doesn't maximize your EV, it's a threshold for unexploitability under very specifc circumstances (not this one), how much you "should" defend for unexploitability doesn't change depending on how much you're actually getting 3bet.

You should defend the hands that have enough equity/implieds/blockers/playability to make more money than folding, which vs a 50% range should be your entire RFI range, as you should be opening somewhat tighter since your raise-folds aren't +EV opens

Thank you, this makes a lot of sense.

I guess it is impossible to exploit someone without being open to exploitation yourself is it? The winner in poker is the one who is really exploiting the other player in a given spot and the other player not realising it and failing to activate their available counter-exploitation.

All of this can be calculted. From HJ I expect us to be tightening up to around a 15% range and continuing every single hand to the 3bet.

If villains are playing reasonable and not 3betting 50%, then our strategy from HJ will be to open around the low 20s% and continuing around 45%-50% of the time vs an IP 3bettor and a standard sizing. This range will mostly contain suited broadways, pocket pairs, some suited connectors and some wheel suited aces

Why do people advocate defending IP more when often the OOP 3bettor will size up their 3bet to a 4x-5x sizing? Doesn't this worse price mean that we should flat less or perhaps a similar amount as flatting OOP?

If the larger OOP 3bet sizing doesn't make us defend less, then why does the OOP player do that as he is just bloating the pot more OOP and giving himself a worse price on his 3bet 'steal'.

We should defend more against an OOP 3bettor all else being equal, but bigger sizings from OOP will cause us to defend less of course.

Yes, so doesn't the effect balance out in practice? I find myself probably defending more OOP than IP in todays games, mainly due to price reasons.

Interestingly I find that 4bet bluffing when I am OOP seems more profitable than 4bet bluffing IP, even though in theory you get a better 4bet bluffing price when IP due to your opponent's large 3bet size. I think this is because often people will flat the 4bet when they are IP, so that allows me to realise equity on my 4bet bluff from OOP, whereas they are more willing to 5bet jam from the blinds over my 4bet IP. Also people probably 3bet more when IP than OOP, (not including LP vs blinds spots).