Is MDF unexploitable?

You ask your question as if you expect your answer to be the right one even though you notice it leads to a paradox.

Maybe your answer is not the right one.

If you never bluff you make the same money as if you always bluff and anything in between vs MDF, that's the point of it, to make you INDIFFERENT

I would add math but honestly it's just a matter of definitions, if MDF is what makes bluffs indifferent then not bluffing can't make more money than bluffing.

(All of this is assuming bluffs have 0% equity which is unrelated to your question but i wanna avoid nitpicks)

This is true even for bluffs with >0% equity as a check, no?

You just have to use the full formula for mdf, rather than the simplified form.

when the aggressor stops bluffing (because the defender makes him indifferent between betting and checking and therefore it doesnt matter) his overall betting frequency drops also

therefore the defender wins the pot more often uncontested

and this makes up for the case when the defender calls the value heavy bet of the aggressor

MDF is useful and is applicable in some, but not all, nash equilibrium spots in poker. Specifically, in polarized situations you'll often find the defender defends at a frequency that is approximate to MDF. You'll also find that typically the player IP will defend close to that frequency in aggregate for most spots. By "in aggregate" I mean for all possible turns/rivers. The nash equilibrium is going to cause some specific actions to be indifferent between one or more actions such as bet/check or call/fold. A simple toy game is the following shown below. Keep in mind when I explain this I'm specifically stating which parts are indifferent. If you change the ranges/sizings/etc. the frequencies will change, but the overall idea of indifference will be maintained if you re-solve for the nash equilibrium.

For the polarized situation, consider a simple toy game:

Board is: 2 2 2 2 3 ---> High card wins here, this is basically hold'em runout example of AKQ toy game.

OOP range: bluff catchers (TT/99/88)

IP range: polarized nuts/air (55, AA)

Stack depth: 100

Pot size: 100

The solution to the above toy game is OOP always checks to IP polarized range. IP will then bet all combos of AA as an all-in (6 combos), and bet half of his 55 (3 out of 6 combos) as an all-in. This frequency of bluffing makes OOP indifferent to bluff catching. OOP pot odds are 100/(100+100+100) = (1/3). IP bluff frequency is 3/(6+3) = (1/3). Because this indifference, the OOP simply defends at a frequency that makes IP indifferent to betting or checking 55 (0 EV bluff or check in this example). This frequency is equal to the risk/reward for bluffing with 55 in this instance or 100/(100+100) = (1/2) which is the MDF value. So, if you solve this in solver OOP will call 50% of TT/99/88. In this example any calling frequency of 9/18 of the possible calling combos will result in the same outcome/equilibrium since no blockers are relevant in this toy game.

Try to MDF this 😃

MDF doesn’t take into account that in some contexts you should be over defending and in other contexts you should be under defending.

If you purely defended MDF in every spot then by default you will be at least a bit exploitable. I tried to do this back in 2013/2014 and it is not recommended ��

MDF isn’t Nash. It’s just a calculation that makes bluffs indifferent.

You can find nodes constantly that aren’t going to jive with MDF.