Definition of minimum defense frequency
Minimum defense frequency (abbreviated as MDF) is the percentage of time a given player must not fold in response to an aggressive action from their opponent (either a bet, or a raise) to prevent their opponent from taking that aggressive action with any two cards.
Calculating minimum defense frequency
Let us look at an example:
In a 9 handed $1/3 live cash game, a player in middle position opens for $12. We call on the button. The blinds fold. Thus, there is $28 in the pot, going into the flop. The flop is checked by both players, the turn is checked by both players. On the river the middle position player decides to bet $14 (i.e. a half a pot sized bet). What is our minimum defense frequency?
The way to think about this in 2 steps:
- How often does the villain need us to fold, for his bet to break even?
The villain is risking $14 to win the $28 already in the pot. This means he is putting in $14/$42 = 33.33% of the new total pot size after his bet. So he needs us to fold 33.33% (or 1/3) of the time, in order to break even.
- Given this how often do we need to defend to stop him breaking even?
He needs us to fold 33.33% (1/3) of the time, in order to break even. So if we defend more than 66.67% (2/3) of the time, he does not break even.
Formula for minimum defense frequency
MDF = 100% – (Villain’s break even %)
MDF = 1 – (Villain’s break even fraction)
Don’t confuse pot odds & MDF
In the above example, when villain bets $14 into $28 on the river, we are getting 3:1 pot odds, i.e. we are being asked to call $14 to win a new pot size of $42. This means we only need to win 25% of the time when we call. This means we should be looking to call with all hands that have at least 25% equity, versus the range that we put villain on.
If we don’t have enough hands that have at least 25% equity versus villain, such that we can call 33.33% of the time, villain can bet with any 2 cards and make a profit.
- When facing a 1/3 pot sized bet, your MDF is 75%
- When facing a 1/2 pot sized bet, your MDF is 67%
- When facing a 2/3 pot sized bet, your MDF is 60%
- When facing a 3/4 pot sized bet, your MDF is 57%
- When facing a 1/1 pot sized bet, your MDF is 50%
- When facing a 2/1 pot sized bet, your MDF is 33%