A bridge hand holds 10 high-card points on average, and 10 is also the most likely count: you get exactly 10 HCP on about 9.4% of deals. About 34.8% of hands hold 12 or more, enough to open by points alone, and only about 0.42% hold 22 or more, roughly one deal in 236.
The numbers below are exact: they count every possible 13-card hand on the scale ace 4, king 3, queen 2, jack 1.
Chance of Every Point Count
| HCP | Exactly | At least |
|---|---|---|
| 0 | 0.36% | 100% |
| 2 | 1.36% | 98.85% |
| 4 | 3.85% | 95.03% |
| 6 | 6.55% | 86.00% |
| 7 | 8.03% | 79.44% |
| 8 | 8.89% | 71.42% |
| 9 | 9.36% | 62.52% |
| 10 | 9.41% | 53.17% |
| 11 | 8.94% | 43.76% |
| 12 | 8.03% | 34.82% |
| 13 | 6.91% | 26.79% |
| 14 | 5.69% | 19.88% |
| 15 | 4.42% | 14.18% |
| 16 | 3.31% | 9.76% |
| 17 | 2.36% | 6.45% |
| 18 | 1.61% | 4.09% |
| 20 | 0.64% | 1.45% |
| 22 | 0.21% | 0.42% |
| 25 | 0.026% | 0.046% |
Seven to thirteen points cover about 60% of all hands. The extremes are very rare: a hand with no high cards at all comes about once in 275 deals, and the perfect 37 (four aces, four kings, four queens and one jack) about once in 159 billion.
Exactly and At Least
The two columns answer different questions. Exactly is the chance of one count: 9.41% for 10. At least adds every count from that number up: 53.17% for 10 or more.
Use the at-least column for questions players really ask:
- How often can I open by points? At least 12: 34.8%, about one hand in three.
- How often do I hold an opening 1NT range or better? At least 15: 14.2%.
- How often is my hand big enough for a strong 2♣? At least 22: 0.42%.
Partner's points follow the same table before the auction starts. Once partner bids, the table shifts: an opening bid removes the low counts from partner's possible hands.
TipBefore the bidding starts, give each unseen hand 10 points. Then adjust the estimate after every bid you hear.
Why the Average Is Ten
The deck has 40 high-card points: 10 in each suit (4 + 3 + 2 + 1). Four hands share them, and the deal treats every seat the same, so each hand averages 40 / 4 = 10.
The most likely count is also 10, but 9 is almost as common (9.36% against 9.41%). The table is not symmetric: a hand can hold anywhere from 0 to 37, so the long tail is on the high side, and 9 points is more common than 11 (8.94%).
Points and Shape Together
Most bidding decisions need points and shape at once. Some exact joint figures:
| Hand type | Chance |
|---|---|
| Balanced, 12-14 HCP | 9.68% |
| Balanced, 15-17 HCP (a strong 1NT) | 4.87% |
| Balanced, 20-21 HCP (a 2NT opening) | 0.53% |
| Balanced, 22-24 HCP | 0.21% |
"Balanced" here means the 4-3-3-3, 4-4-3-2 and 5-3-3-2 patterns, which together make up about 47.6% of hands. The hand patterns table gives every shape.
For any other mix, the free BridgeDummy hand probability calculator gives the exact chance of a suit shape combined with any HCP range, and the bridge odds tables collect HCP frequencies, all 39 hand patterns and suit breaks on one page.
Practice: High-Card Points
Which high-card point count are you most likely to hold on any deal?
Read next: hand evaluation for turning points into a bid, counting points if you are new to the game, and the Rule of 20 for borderline openings.