Poker Formulas — Complete Reference

Terms · updated 2026-03-08

1. Pot Odds

Purpose: Required equity for a break-even call.

Formula:
Pot Odds = Risk / (Risk + Reward)

• Risk — call size
• Reward — current pot

Example:
Pot = 5.4 bb, Bet = 2.7 bb
Pot Odds = 2.7 / (2.7 + 5.4) = 0.333 = 33.3%

2. Break-even Frequency (Alpha)

Purpose: How often a bet must succeed to be zero EV.

Formula:
Alpha = Risk / (Risk + Reward)

Example:
Bet 1 pot = 100 bb
Alpha = 100 / (100 + 100) = 50%

3. Minimum Defense Frequency (MDF)

Purpose: Minimum defense frequency vs a bet to prevent opponent from profitable auto-bluffing.

Formula:
MDF = Pot / (Pot + Bet)

Example:
Pot = 100 bb, Bet = 50 bb
MDF = 100 / (100 + 50) = 0.666 = 66.6%

4. Expected Value (EV)

Purpose: Average profit/loss over time.

Formula:
EV = (Win × Win%) − (Loss × Loss%)

Example:
Bet 50 bb into pot 100 bb, Win% = 40%:
EV = (100 × 0.4) − (50 × 0.6) = 40 − 30 = +10 bb

5. Combinatorics

Purpose: Counting possible hand combinations.

Formula:
Combinations = C(n, k)

• Suited hands (AKs) → 4 combos
• Offsuit hands (AKo) → 12 combos
• Pocket pairs (TT) → 6 combos

6. Bluff / Value Ratios

Purpose: Set optimal bluff frequencies.

Formula:
Max Bluff Frequency = MDF − Hand Equity

Quick Reference Table — Alpha & MDF