MDF and BF

MDF

If the pot is \(1\) and your opponent’s bet is \(b\):

• you fold: \(1 \times (1 - p(\text{you-call}))\)
• you call: \(-b \times p(\text{you-call})\)

Adding both cases:

\[ 1 \times (1 - p(\text{you-call})) + p(\text{you-call}) \times -b = 0 \]

Simplifying:

\[ 1 = (1 + b) \times p(\text{you-call}) \]

Solving for \(p(\text{you-call})\):

\[ p(\text{you-call}) = \frac{1}{1 + b} \]

Bluffing Frequency

• 0.75 pot
  • flop 67%
  • turn 50%
  • river 33%

How to bet

1. Size

• If you have nuts advantage, bet bigger.
• If you do not have nuts advantage, bet smaller.
• Nuts advantage: when you have more combinations of super strong hands (two-pair or better) than his opponent

2. Find Value Cards

The inequality \( \text{Equity} > 1 - \frac{1}{2(1+b)} \) suggests a threshold where a player’s equity (their share of the pot if the hand goes to showdown) should exceed a certain value in order for them to make a profitable move, such as calling or betting.

To understand this better, we can break it down:

• Setting Up the Inequality: The right side, \(1 - \frac{1}{2(1+b)}\), provides a boundary value. This boundary depends on the size of the bet \(b\) relative to the pot (normalized to 1).

• Interpretation of the Threshold: If a player’s equity in the hand is greater than \(1 - \frac{1}{2(1+b)}\), then their hand is likely profitable enough to proceed with aggressive action, such as betting or calling.

• Breakdown of the Expression:

  • For larger bets \(b\), \( \frac{1}{2(1+b)} \) becomes smaller, and therefore \(1 - \frac{1}{2(1+b)}\) approaches 1. This implies that when the bet is large, the player needs a higher equity to continue.
  • For smaller bets \(b\), \( \frac{1}{2(1+b)} \) is larger, meaning that \(1 - \frac{1}{2(1+b)}\) is lower. In this case, a player can proceed with lower equity since the risk is relatively lower.

3. Value bet

• If I check, the remaining streets < biggest that I can get, I 100% bet

4. What to bluff

• Backdoor Draw
• Frontdoor Draw

exploitation

Call

• If opponent bluff too much, call, otherwise not (BF to check)
• Only call one street.

Bluff

• If your opponent is calling too much, do not bluff, otherwise, bluff (MDF to check)