I have recently been studying the minimum defense frequency when facing aggression and I do think I have a grasp on the concept. However, it struck me that the MDF logic is fundamentally different that the thought process that we have learned traditionally when facing aggression, which is calling based on pot odds. How do these concepts relate to each other in theory? When do we use which approach in game? I elaborate my question below...
If we simplify and only look at end of action spots (e.g. facing a bet on the river), then the logic goes like this:
1. Calling based on Minimum Defense Frequency
This is the game-theory optimal percentage of our range that we should call in order to prevent Villain from making auto-profit against us by adding any more bluffs to his range. In essence, calling based on the MDF means that Villain won't have any auto-profit with his bet, can't just bet any-two cards, and as the caller we remain unexploitable by bluffs.
The MDF is calculated using
MDF = 1 - Bet/(Pot+Bet). E.g. for a half pot size bet, the MDF is 1 - 0.5/(1+0.5) = 0.67.
If we call 67% of the time and win against Villain's bluffs, then the EV for Villain to add any further bluffs to his range is 0.
2. Calling based on Pot Odds
The traditional approach to facing aggression on the river is based on a formula calculating the required equity that we need with our hand against Villain's range and then see whether our hand actually beats this portion of Villain's range:
Required Equity = Bet / (Pot + Bet + Our bet if we call). E.g. for a half pot size bet, we would need to win 0.5 / (1+0.5+0.5) = 0.25, so our hand needs to win 25% of the time.
3. My Question
So I have the feeling that these two concepts stand in sharp contrast to each other. Using the MDF, we look at the portion of our range that we need to call in order to remain unexploitable by bluffs. Based on pot odds, we actually call the portion of hands that makes the call a winning play. Isn't it possible that even when we call using the MDF, we are overall loosing money? E.g. it might be that we call 67% of our range vs. Villain but not all out of these hands have at least 25% equity vs. Villain's range. Wouldn't the MDF need to take way more factors into account, e.g. our and Villain's position, board texture, ranges etc.?