ConceptsBetting
MDF and alpha
MDF is how much of your range has to continue against a bet; alpha is how often that bet must make you fold.
What it is
Alpha is the break-even fold rate of a bet that never wins when called: the bet risks its own size to win the pot, so it needs the opponent to fold bet / (pot + bet) of the time.
The minimum defence frequency (MDF) is the other side of the same number: 1 − alpha = pot / (pot + bet). If the defender folds more than that, any two cards can bet and profit, so a balanced defender continues at least MDF of their range — by calling or raising.
Why it matters
They put numbers on "am I folding too much?" and "how often does this bluff need to work?". A pot-sized bet must work half the time; a third-pot bet, a quarter.
They apply after the flop. Preflop the blinds are posted before anyone decides, ranges are far apart, and MDF misreads defence as a leak. Rail compares your defence with MDF on postflop streets only.
MDF is a guide against an unknown opponent, not a law. Against someone who rarely bluffs, defend less; against someone who bluffs too much, more.
The maths
Alpha equals the bet divided by the pot plus the bet, where the pot is before the bet.
The minimum defence frequency equals the pot divided by the pot plus the bet.
- pot
- the pot before the bet
| Bet | Alpha | MDF | Caller needs |
|---|---|---|---|
| 25% | 20% | 80% | 16.7% |
| 33% | 24.8% | 75.2% | 19.9% |
| 50% | 33.3% | 66.7% | 25% |
| 75% | 42.9% | 57.1% | 30% |
| 100% | 50% | 50% | 33.3% |
| 150% | 60% | 40% | 37.5% |
| 200% | 66.7% | 33.3% | 40% |
Worked example
A three-quarter-pot bet
The pot is 10 bb and your opponent bets 7.5 bb.
- Alpha: 7.5 / (10 + 7.5) ≈ 42.9%. A pure bluff needs you to fold that often.
- MDF: 10 / 17.5 ≈ 57.1%. Out of 100 combos you arrive with, continue with at least 57.
- For a single call, the price is 7.5 / (17.5 + 7.5) = 30% equity.
Three numbers, one bet: the bettor's alpha, the defender's MDF, and the caller's price. The table under the maths has them for the common sizes.
Try it
Move the bet size and watch alpha and MDF trade places: bigger bets need fewer folds per bet but ask the defender to give up more.
Common mistakes
- Using MDF preflop, where it mistakes normal folding for a leak.
- Defending to MDF on every street: 57% three times in a row is 19% of where you started — and that may be right, but only if the bets are balanced.
- Forgetting that raises count as defence.
- Defending to MDF against an opponent who never bluffs.
Related concepts
- Pot oddsThe share of the final pot a call costs — and so the equity a call needs to break even.
- Bluff-catchingCalling with a hand that beats only bluffs: the price says how often they need to be bluffing.
- Bet sizing and polarisationSmall, big or overbet: every size has a job, and the job depends on the board and on which hands you bet.