I have often seen people in the past reference the fact that when you defend some of your range when facing a 3bet for example, that you need to over-defend when you have a calling range, (as opposed to strictly a 4bet or fold response), because your opponent can realise EV with his bluffs.

However, isn't this balanced out by the fact that sometimes your opponent is not 3bet bluffing and your calling range gets to out-flop his value range when you call? On these occasions the weaker part of your range gets to realise EV against his value hands right?

Therefore you don't necessarily need to defend more often due to the logic of your opponent flopping well with his 3bet bluffs?

I'm assuming you're referencing MDF, it is a just a simplified model but at its core it is saying but by "over-defend" you mean defend more often than it requires for your opponent to break even if he 3-bets and open mucks his hand every time postflop, then that is logical right since he obviously is expected to do better than that postflop strategy

I am in some ways referencing MDF, but not fully.

I am more questioning the principle that by calling a 3bet, your opponent gets to 'free roll' flops when they were 3betting you with A2s for example so you need to overcall with more hands to 'account for this', but then isn't this balanced by the fact that we ourselves also get to 'free roll' flops as the flop can help our hand just as much as it can help our opponent, and sometimes we have 88 and spike an 8 on the flop when our opponent was actually 3betting for value with AA or KK, so we may not really need to over-defend in practice to compensate for this, as who is to say which flops help which player?

It's probably a bit of a silly question as I don't really agree with MDF anyway, but if I were to agree with it, I am questioning the 'over-defend' part of the MDF theory and so I am wondering whether some MDF connoiseurs have an answer for this particular element of it, or whether the 'over-defend' part just came about in their mind because it felt right.

Ur mixing a bunch of things together.
If your opponent can profitably 3bet 72o against you because you defend MDF but he sometimes flops trips and beats you, it doesn't matter how well you're outflopping his value range, since this time he has 72o.
The EV of his AA isn't connected to the EV of his 72o in any way. They are completely independent events.

Surely these are not independent events because you are making a decision with what hands to call when you only have an approximation about his range, where he can indeed have AA and also some semi-bluffs.

You are playing your range against his range in the long run aren't you, and sometimes his semi-bluff 3bets will flop well and overtake the top part of your calling range, and sometimes the bottom part of your calling range will flop well and turn into value and his value 3bets turn into bluff catchers against you now. Why is the former situation taken into account but not the latter situation?

You're still mixing 2 different frames of reference. Making villain indifferent, in this case with defense frequencies, looks at the EV of VILLAINS holdings.
You're mixing that with what the EV of our holdings is.

Range vs range is just an abstraction, and imo a very misleading one specially for new players. In reality, every hand is played Hand vs Range, and the only connection between 2 hands in your range is how those affect villains strategy.
if villain can 3bet 72o against you and he takes the exploit, you're ****ed no matter how well you're doing vs AA.

Well your 72o example just opens up another can of worms, as for example if someone's 3bet range was 2% of hands, (AA, KK and 72o), then we should fold our specific hand of QQ to this 3bet if the 3bet is normal sized correct? But then wouldn't this allow the villain to print money with his bluffs vs our 3rd best starting hand in NLHE?

We need to consider avoiding giving money to our opponent's value just as much as stopping their bluff combos from 'owning us' right?

You just need to play each hand in the highest EV line in a vaccum, and as a secondary goal to keep your overall stats reasonable enough so that people don't abuse them. If QQ has enough EV to continue vs a range of AA,KK,72o, which it does, then you continue. Don't make this Defence frequency thing the core of your decision making.

How about QQ vs a range of AA,KK,72s? Surely then you need to fold right? But in doing so, you allow 72s to be a profitable bluff vs you.

Well you're talking about an exploit. You're adjusting to your opponents strategy and while you lose more against exactly his 72s, you make more (aka, lose less) against his AA/KK as well as other hands he would like to 3b like AKs.

If you so desire, you could just choose not to deviate from your GTO strategy and your opponent's bad play will cause you to beat him anyway. But your exploit as described above makes you beat him even harder.

Yes, and that's why you need to separate the 2 approaches since they're very often contradictory. Playing "balanced" requires you to keep 72 a -EV 3bet for villain, but playing exploitatively against this particular range requires you to fold most hands in your range and therefor make 72 a +EV 3bet.

The second approach makes you the most money, with the caveat that it needs an extremely strong read. The first approach will lead you to make some -EV decisions against this particular player, like continuing hands like KQs and what not, with the advantage of him not being able to shift his own strategy into 3betting any 2 cards profitably.

In real life, you should keep in mind both approaches and lean on the second one harder and harder as you gather stronger reads on your pool/opponent.

Does this not mean that a lot of solver work is not that applicable to real life games then, as really we should always be trying to work out what our specific opponent is doing and exploit him and not try to be balanced unless we feel he is balanced?

Yes, to some extent

Kinda, but solver work is in no way useless, as it'll show you how ranges and frequencies of them interact... It is of course useless if you blindly try to copy any strategy which is as complex as a solver output, which first of all is pretty much impossible unless you're rain man and second of all, as we can, with high accuracy, look at player pool tendencies first and our opponents tendencies second (given good sample sizes etc) we can deviate all the way to the bank. Playing a GTO strat vs non GTO players is never the highest EV (as you're leaving exploitative money on the table)

Understanding how and why a solver max exploits against itself with certain holdings could potentially give you more tools in your arsenal to be able to decide where to over fold, over bluff etc. Often you'll see that solver bluffs when there is some card removal effects (blockers) or chooses to check OOP with a strong hand, studying these outputs and rationalizing the whys of the solver will make you better at exploiting and increasing your potential EV.

Copying a "vs population" strat from some coach has the same pitfalls as copying some simplified GTO strat, you're not doing the work yourself and it will bite you in the ass as you'll move up.

Ya its the same with literally any game in existence. Imagine you're playing tennis and you know the guy has an unusually weak backhand, you may want to hit towards it at a higher frequency, but knowing how to play tennis properly in the first place is way more important than knowing that exploit.