This article explores the concepts of MDF and alpha: the thresholds for calling and bluffing.
The simplified betting model
MDF and alpha come from simplified betting models. They are useful because they turn a messy betting decision into a clean threshold problem.
The basic setup is:
- one player makes a bet
- the opponent must choose how often to continue
- the player who made the bet must also choose how often to bluff
What MDF means
MDF stands for minimum defense frequency. It is the minimum frequency with which a defender must continue against a bet to prevent bluffs from automatically becoming profitable.
What alpha means
Alpha is the minimum frequency that your opponent must fold to make a bluff profitable. Note that by definition, alpha and MDF are complementary:
MDF + alpha = 1
Calculating MDF and alpha
It is easiest to start by computing alpha, which is risk / (risk + reward).
For example, if you bluff 50 into a pot of 100, you either lose 50 chips (if your opponent calls) or win 100 chips (if your opponent folds). Therefore, you are risking 50 to win 100, and your alpha is 0.333. Your opponent must fold at least 33.3% of the time for your bluff to break even.
MDF is computed as 1 - alpha. In this example, MDF is 0.667, meaning your opponent must continue at least 66.7% of the time to prevent your bluff from being profitable.
| Bet Size | MDF | Alpha |
|---|---|---|
| B33 | 75% | 25% |
| B50 | 66.6% | 33.3% |
| B100 | 50% | 50% |
| B200 | 33.3% | 66.6% |
| B1000 | 9.1% | 90.9% |
Limitations of MDF and alpha
These concepts provide useful insight into simplified betting situations, but they are not universally applicable. For example, on earlier streets when bluffs have equity, implied odds, and future streets to consider, MDF and alpha do not provide a complete picture of the situation.
If our opponent does not have enough bluffs in their range, it is more profitable to overfold compared to MDF. Just like with blockers, MDF and alpha are tools to help us make better decisions, but they are not a substitute for common sense.
Common MDF and alpha mistakes
Beginners often:
- treat MDF as a law
- call because "I have to call this hand"
- bluff without considering how often the opponent folds to various bet sizes
Key takeaways
MDF and alpha are simplified thresholds for bluffing and defending against bluffs. They are useful, but they are not universal rules.