MDF and alpha: how much to defend against a bet and how often a bluff needs folds

What MDF is

MDF answers one specific question: what percentage of my range must call or raise so my opponent cannot bluff with any hand and win?

MDF = P / (P + A), where P is the pot before the bet and A is the bet.

Example: river, the pot is 30 bb and your opponent bets 20 bb. MDF = 30 / (30 + 20) = 60%. If you fold more than 40% of the hands you reached the river with, any bluff from your opponent makes money, even with the worst possible hand.

MDF is measured over your whole range at that point in the hand, not over the hand you hold. It does not tell you whether to call with K♥J♦; it tells you how many of your hands must continue, and you pick which ones: the best.

What alpha is: the folds a bluff needs

Alpha is the same math from the bettor's side. A pure bluff wins the pot when your opponent folds and loses the bet when they call:

EV = F × P − (1 − F) × A. The bluff's EV is 0 when F = A / (P + A). That number is alpha.

With 20 bb into a 30 bb pot, alpha = 20 / 50 = 40%. If your opponent folds more than 40%, your bluff wins; if they fold less, it loses.

With a 2× pot bet (60 bb into a 30 bb pot), alpha = 60 / 90 = 66.7%: an overbet bluff needs a huge number of folds, which is why it only makes sense when your opponent's range is weak or capped.

How MDF, alpha and pot odds relate

Three different numbers come from the same pot and bet:

• Alpha = A / (P + A). How often your opponent must fold for your pure bluff to be worth 0.
• MDF = P / (P + A) = 1 − alpha. How much of your range must continue so their bluff cannot win with any hand.
• Equity to call = A / (P + 2A). What pot odds require for a call with a bluff-catcher to be worth 0.

The third has a practical consequence: if your opponent bets the river with a polarized range (very strong hands and bluffs), the share of bluffs that makes your bluff-catchers indifferent is precisely A / (P + 2A). Against a pot-sized bet, one third of the betting range is bluffs: 1 bluff for every 2 value hands. That is the basis of the value-to-bluff ratio.

MDF and alpha by bet size

How to read it:

• Small bets force you to defend a lot. Against 1/3 pot you must continue with 75% of your range, but each call needs only 20% equity.
• Big bets let you fold more, but each bluff needs more folds and each call needs more equity.
• The bluff share of a polarized range follows the last column: 1 bluff for every 4 value hands against 1/3 pot, 1 for every 2 against pot, 2 for every 3 against 2× pot.

A worked example with combos

You defend the BB against the BTN in a single-raised pot and reach the river with 40 combos: 12 strong hands (two pair or better), 18 top pairs and 10 missed draws.

• The BTN bets 1/3 pot. MDF 75%: you must continue with 30 combos. You call or raise with the 12 strong hands and the 18 top pairs, and fold the 10 missed draws.
• The BTN bets 2/3 pot. MDF 60%: 24 combos. You continue with the 12 strong hands and the 12 best top pairs; you fold the 6 weakest top pairs and the 10 draws.
• The BTN bets pot. MDF 50%: 20 combos. You continue with the 12 strong hands and the 8 best top pairs (by kicker and blockers), and fold the 10 weakest top pairs.

That is how MDF is used: not to decide whether one hand calls, but to rank your range from best to worst and see where the cut falls.

When NOT to apply MDF blindly

MDF assumes your opponent can bluff with any hand and that your range is able to defend. Often neither is true:

• Opponents who under-bluff. If, against a 30 bb pot-sized bet, your opponent has only 10% bluffs, calling with a bluff-catcher is worth 0.10 × 60 − 0.90 × 30 = −21 bb. Defending MDF against them gives chips away: over-folding is the right exploit. And against someone who over-bluffs, you call more.
• Preflop. There is dead money in the blinds, players left to act and very different ranges by position; preflop defense comes from the charts, not from MDF.
• Multiway pots. MDF is shared among several defenders; no single player has to cover it alone.
• Capped range or no nut advantage. If your range is capped and your opponent has the nut advantage, defending 50% against an overbet forces you to call with hands that almost never win.
• Street by street. Defending 60% on flop, turn and river leaves 0.6 × 0.6 × 0.6 = 21.6% of your starting range. MDF applies to the range that reaches each street, not to your preflop range.

How to practice it

Memorize the table for the five sizes and, in every river spot, rank your range before deciding which hand calls. In POKER AULA the Calculator gives you MDF, alpha and required equity for any pot and bet, and the Training mode puts you against bets of different sizes and explains why to continue or fold against each player type. MDF and alpha are taught in the Upper Intermediate level and applied to full ranges in Professional. You can try it free for 48 hours.