🛡️ What Is MDF?
The Minimum Defense Frequency (MDF) is the minimum fraction of your range you must defend — by calling or raising — to prevent an opponent from profitably bluffing you with any two cards.
If you fold more than \(1 - \text{MDF}\), your opponent can pick up the pot with a pure bluff at zero risk. The MDF formula is derived directly from making bluffs exactly break even:
$$\text{MDF} = \frac{\text{Pot}}{\text{Pot} + \text{Bet}}$$Basic Example
The pot is $100 and your opponent bets $50.
$$\text{MDF} = \frac{100}{100 + 50} = \frac{100}{150} = 66.7\%$$You must defend at least 66.7% of your range. If you fold more than 33.3% of the time, your opponent profits by bluffing with any hand — even 7-2 offsuit.
📐 Derivation from First Principles
To derive MDF, we set the bluffer's EV equal to zero and solve for the fold frequency.
Let \(P\) = pot size, \(B\) = bet size, \(f\) = fold frequency of the defender.
The bluffer's EV when betting with a pure bluff (zero showdown equity):
$$\text{EV(bluff)} = f \times P - (1 - f) \times B$$The first term: villain folds with probability \(f\), and the bluffer wins the pot \(P\).
The second term: villain calls with probability \((1-f)\), and the bluffer loses the bet \(B\).
Setting EV = 0 (making the bluff exactly break even):
$$f \times P = (1 - f) \times B$$ $$fP = B - fB$$ $$f(P + B) = B$$ $$f = \frac{B}{P + B}$$This is the maximum fold frequency. The minimum defense frequency is therefore:
$$\text{MDF} = 1 - f = 1 - \frac{B}{P+B} = \frac{P}{P+B}$$📊 MDF Table for Common Bet Sizes
The table below shows MDF values for the most common bet sizes as a fraction of the pot:
| Bet Size (% pot) | Bet (vs $100 pot) | MDF | Max Fold Frequency |
|---|---|---|---|
| 25% | $25 | 80.0% | 20.0% |
| 33% | $33 | 75.2% | 24.8% |
| 50% | $50 | 66.7% | 33.3% |
| 67% | $67 | 59.9% | 40.1% |
| 75% | $75 | 57.1% | 42.9% |
| 100% | $100 | 50.0% | 50.0% |
| 150% | $150 | 40.0% | 60.0% |
Notice that a pot-sized bet requires you to defend exactly 50% of your range — one of the cleanest numbers in poker math. Against a 33% pot bet, you only need to fold about 25% of the time — most of your range should be calling.
🔢 Applying MDF to Real Hands
Example A: Defending the BB vs. SB Steal
The SB raises to 3BB. The pot is 4.5BB (3BB + 1.5BB blinds). You must call 2BB from the BB.
Treat this as: pot = 2.5BB (already in pot before SB raise), SB's raise is the "bet" of 2BB you must call to win 4.5BB.
$$\text{MDF} = \frac{2.5}{2.5 + 2} = \frac{2.5}{4.5} = 55.6\%$$You should defend roughly 55–60% of your BB range against a standard 3BB open from the SB. Folding more than 44% gives the SB a profitable steal with any two cards.
Example B: Facing a River Bet
River pot is $180. Villain bets $120 (67% pot).
$$\text{MDF} = \frac{180}{180 + 120} = \frac{180}{300} = 60\%$$You must call with at least 60% of your river range. If your range contains 20 possible hand combinations, you must call with at least 12 of them. Identify your 12 strongest hands (best bluff-catchers and value hands) and call with those.
Example C: Multi-Street Considerations
MDF applies to each street independently, but the compounding effect matters. If villain bets three streets and you must defend 67% on each:
$$\text{Cumulative defense} = 0.67 \times 0.67 \times 0.67 \approx 30\%$$After three streets of 50%-pot bets, only about 30% of your original range has called down. This means villain's river range is heavily weighted toward value — the players who reach the river with you have strong hands. Recognize this when constructing river calling ranges.
⚖️ MDF vs. GTO
MDF is a lower bound — a minimum requirement, not an exact GTO prescription. Actual GTO solutions may defend more or less than MDF in specific spots for several reasons:
- Board texture: On wet boards where ranges are polarized, GTO may call more than MDF with the bottom of its range to prevent over-folding. On dry boards it may call exactly MDF.
- Range advantage: The player with a range advantage can sometimes fold more than MDF without being exploited, because the range advantage compensates.
- Raises: MDF counts raises as defense. Raising is often more efficient than calling for the bottom of a defending range.
- Nut advantage: The defender's nut advantage on the river affects optimal strategy — having more nut hands allows calling less with middling hands.
💡 Practical Usage
Using MDF quickly at the table:
- Identify the bet size as a fraction of the pot. A $75 bet into $100 is 75% pot.
- Recall MDF from the table: 75% pot → MDF = 57%.
- Count your range combinations (approximately). If you have 30 combos in your range, you need to defend at least 17.
- Sort your range by strength and call with the top 57%, fold the bottom 43%.
- Include some raises in your defense if you have strong hands that benefit from building the pot.