What Is the Chen Formula?
First published in The Mathematics of Poker (co-authored by Bill Chen and Jerrod Ankenman), the Chen Formula compresses complex pre-flop hand dynamics into a quick mental math calculation.
Instead of memorizing hundreds of starting hand charts, players can calculate a single score between -1 and 20+ by evaluating five key factors:
- Highest Card Value
- Pocket Pair Multipliers
- Suited Cards Bonus
- Card Closeness & Gaps (Connector Bonus)
- Small Connector Penalties
Step-by-Step: How to Calculate Your Chen Score
Follow these 5 simple steps to calculate the Chen score for any Texas Hold’em starting hand:
Step 1: Score Your Highest Card
Assign base points to your highest card:
- Ace: 10 points
- King: 8 points
- Queen: 7 points
- Jack: 6 points
- 10 through 2: Half of the card’s face value (e.g., $10 = 5$ pts, $8 = 4$ pts, $2 = 1$ pt)
Step 2: Pairs Multiply
If you hold a pocket pair:
- Multiply your high-card base score by 2 (e.g., Pocket Kings = $8 \times 2 = 16$ points).
- Minimum pair bonus: Any pair from 5s down to 2s receives a minimum score of 5 points.
Step 3: Suited Cards Bonus
- If your cards are of the same suit, add +2 points.
Step 4: Closeness & Gaps (Connector Check)
Subtract points based on the gap between your cards:
- No gap (Connected, e.g. 9-8, Q-J): Subtract 0 points.
- 1-card gap (e.g. 9-7, J-9): Subtract -1 point.
- 2-card gap (e.g. 9-6, K-J): Subtract -2 points.
- 3-card gap (e.g. 9-5, Q-8): Subtract -4 points.
- 4+ card gap (e.g. 9-4, A-2): Subtract -5 points.
Step 5: Small Connector Bonus / Penalty
- If your cards have a 0 or 1-card gap AND both cards are lower than a Queen:
- Add +1 bonus point (e.g., 7-6 suited, 8-7 suited get +1 point for straight playability).
- If your final score has a decimal fraction (e.g. 4.5), round up to the nearest whole integer.
Calculation Examples
Example 1: Pocket Aces (AA)
- High card Ace = 10 points.
- Pair multiplier: $10 \times 2 = 20$ points.
- No gap / suited adjustments needed.
- Final Chen Score: 20 (The highest score possible in Texas Hold’em).
Example 2: Ace-King Suited (AKs)
- High card Ace = 10 points.
- Suited bonus = +2 points.
- Gap: Connected (0 gap) = 0 penalty.
- Final Chen Score: 12
Example 3: 7-6 Suited (76s)
- High card 7 = 3.5 points.
- Suited bonus = +2 points ($3.5 + 2 = 5.5$).
- Connected (0 gap) = 0 penalty.
- Small connector bonus (both cards < Queen) = +1 point ($5.5 + 1 = 6.5$).
- Round up:
- Final Chen Score: 7
Example 4: Pocket Twos (22)
- High card 2 = 1 point.
- Pair rule: Minimum score for any pocket pair is 5 points.
- Final Chen Score: 5
How to Use Chen Scores at the Table
Bill Chen recommended the following baseline betting thresholds for standard full-ring games:
| Chen Score | Relative Strength | Recommended Action |
|---|---|---|
| 12+ | Elite Monsters (AA, KK, QQ, AKs) | Raise from any position; re-raise / 4-bet aggressively. |
| 10 – 11 | Strong Premium (JJ, TT, AKo, AQs) | Standard raise from early/middle position. |
| 8 – 9 | Playable Broadways & Pairs (99, 88, KQs, AJs, AQo) | Open from middle position; call raises from late position. |
| 7 | Speculative / Cutoff Hands (77, JTs, QJs, 87s) | Steal blinds from the Cutoff or Button unopened. |
| 5 – 6 | Marginal / Small Pairs (22–66, suited connectors) | Play for set-mining or implied odds on the Button or Big Blind. |
| < 5 | Weak Holdings | Fold in almost all full-ring situations. |
Summary
The Chen Formula provides a quantitative, mathematically grounded benchmark for pre-flop hand quality. As you explore our heads-up matchups, cross-reference each hand’s Chen score with its exact simulated equity to understand how card structure drives long-term profitability.
