BB Defend Frequency: MDF Calculation by Position

Context: KEPU article: bb-defend-frequency-mdf-by-position (part 1/2)

1. Definition and Core Concepts

Minimum Defense Frequency (abbreviated as MDF) is an important concept in Texas Hold'em. It represents the minimum frequency with which we need to defend (call or raise) against an opponent's bet to prevent them from profitably bluffing with any two cards. Preflop, when the BB faces an open-raise from a different position, MDF still applies but needs to be adjusted based on pot odds and the opponent's range.

The formula for MDF is: MDF = Pot Size / (Pot Size + Bet Size). For example, when an opponent raises to 3BB and the pot already contains 1.5BB (small blind + big blind), the bet size is 3BB, and the pot size is considered as the pot before the opponent's bet (1.5BB) + the opponent's bet (3BB) = 4.5BB? No, more precisely, in MDF calculation, the pot refers to the pot before the opponent's bet, and the bet size is the additional chips the opponent puts in. Usually, in preflop processing, we simplify: BB faces an open-raise to XBB, the pot already has 1.5BB (including BB's own 1BB), the opponent raises to XBB, then the MDF we need to defend is X / (1.5 + X). But note, this formula assumes that after the opponent bets, we either call or fold, without considering a re-raise. In practice, MDF is more commonly used postflop; preflop, due to the varying strength of opponent ranges, MDF is only a reference.

However, in practice, the BB's defense frequency is usually higher than the theoretical MDF, because the BB has a positional disadvantage postflop and has already invested 1BB, needing to protect that investment. Additionally, opponents' opening ranges vary by position, so MDF also needs to be adjusted by position.

2. Principles and Positional Impact

Opening ranges vary greatly by position. UTG has the tightest opening range, about 10%-15% of hands; MP about 15%-20%; CO about 20%-30%; BU about 30%-50%; SB (small blind) also has a wide range since it's not a pure steal. Against tighter ranges, the BB needs to defend more conservatively because the opponent has more strong hands; against wider ranges, the BB can defend more broadly because the opponent has more bluffs.

Theoretically, MDF calculation is uniform. For example, facing a 3BB open, MDF = 3/(1.5+3) = 66.7%. But in actual defense, the BB does not mechanically defend 66.7% of hands because factors like postflop playability and range exclusion must be considered. Generally, the BB's default defense strategy is: against UTG open, defend about 40%-50% of hands; against MP about 50%-60%; against CO about 60%-70%; against BU about 70%-80%; against SB about 60%-70% (SB's range is wide but has a positional advantage).

3. Practical Examples

Assume a 6-max cash game, blinds 0.5/1, effective stack 100BB.

Example 1: UTG opens to 3BB. What hands can BB defend?

• Theoretical MDF: 3/(1.5+3)=66.7%, but UTG range is strong, actual defense about 45%.
• Typical defense range: 22+, A2s+, K9s+, Q9s+, J9s+, T8s+, 98s, 87s, 76s, AJo+, KQo, QJo (about 45% of hands).
• Note: Weak suited connectors like 54s are usually folded because it's hard to profit against UTG's strong range.

Example 2: BU opens to 3BB. BB defense?

• Theoretical MDF is still 66.7%, but BU range is wide, actual defense about 75%.
• Typical defense range: 22+, A2s+, K2s+, Q2s+, J2s+, T6s+, 96s+, 86s+, 75s+, 65s+, 54s, A2o+, K4o+, Q8o+, J8o+, T8o+, 98o, 87o (about 75% of hands).
• When the opponent raises larger (e.g., 3.5BB), MDF drops to 3.5/(1.5+3.5)=70%, so the defense range should be tightened accordingly.

4. Common Mistakes

1. Blindly applying MDF: Many players think that defending at MDF prevents exploitation, but MDF assumes the opponent's betting range is balanced and includes bluffs. Preflop, an opponent's opening range is usually not polarized, so the actual defense frequency should be lower than MDF. For example, facing an UTG open, MDF requires defending 66.7%, but postflop positional disadvantage makes calling -EV, so actual defense is only about 45%.

2. Ignoring stack depth: With deep stacks (>100BB), BB can play more speculative hands like small pairs and suited connectors due to good implied odds; with short stacks (<30BB), focus more on preflop all-in or fold, so defense range is tighter.

3. Not adjusting for different raise sizes: The larger the raise, the lower the MDF, and the tighter the defense range should be. For example, facing a CO 2.5BB raise, MDF=2.5/(1.5+2.5)=62.5%, while facing a 3.5BB raise, MDF=70%. In practice, larger raises require folding more marginal hands.

4. Ignoring 3bet strategy: MDF only discusses calling, but BB can defend by 3betting. 3betting can narrow the opponent's range and seize the initiative. Typically, against UTG, the 3bet range is about 4%-6% (e.g., TT+, AQ+); against BU, the 3bet range can expand to 8%-12% (including suited connectors, medium Ax, etc.).

5. Summary

When BB faces opens from different positions, defense frequency should not be mechanically equal to MDF. Instead, it must comprehensively consider position, opponent range, stack depth, and postflop skill. As a general guide:

• Against tight positions (UTG, MP): defend tighter, about 40%-50%, mostly pairs and high cards.
• Against loose positions (CO, BU): defend wider, about 65%-75%, can include suited connectors and small Ax.
• Against SB: defend moderately, about 60%-70%, note SB's steal frequency.
• Adjust based on raise size: larger raise, less defense.
• Combine with 3bet: use value hands and some bluff hands to 3bet, preventing over-exploitation.

Finally, the BB's defend frequency should be dynamically adjusted based on the opponent's actual tendencies: if the opponent steals blinds too often, loosen the defense and increase 3-bets; if the opponent rarely steals folds, tighten the defense. Regularly reviewing and recording the opponent's open-raise frequency is the best way to optimize the BB's defend range.