What MDF is
Minimum defense frequency (MDF) is the % you have to continue with against a bet so the
bettor can't show a profit by bluffing with any two cards. The
pot is 1 and the bet is B, as a fraction of the pot.
The formulas
Pot odds = B / (1 + 2B). The caller risks B to win the pot plus the bet.
Bluffs = pot odds. A betting range with this share of bluffs leaves the caller indifferent, and
Value bets = 1 − bluffs.
Bluff to value = bluffs / value bets = B / (1 + B)
Alpha = B / (1 + B), the fold frequency a pure bluff needs to break even.
MDF = 1 − alpha = 1 / (1 + B)
MDF by bet size
| Bet (% pot) | Pot odds | Alpha | MDF |
|---|---|---|---|
| 25% | 16.7% | 20.0% | 80.0% |
| 33% | 19.9% | 24.8% | 75.2% |
| 50% | 25.0% | 33.3% | 66.7% |
| 66% | 28.4% | 39.8% | 60.2% |
| 75% | 30.0% | 42.9% | 57.1% |
| 100% | 33.3% | 50.0% | 50.0% |
| 150% | 37.5% | 60.0% | 40.0% |
| 200% | 40.0% | 66.7% | 33.3% |
Example
The pot is 100 and your opponent bets 100. Pot odds are 100 / (100 + 100 + 100) = 33.3%, so a balanced range is a third bluffs and two thirds value. Alpha is 100 / (100 + 100) = 50%, so you have to defend 50% of your range.
Assumptions
Single bet, no raises, and the bettor is bluffing the correct range. Does not consider blockers. MDF is a baseline and not a rule.