High-Card Point Distribution
The high-card point distribution tells you how often a hand holds each count from 0 to 37. The average is exactly 10 points, 10 is also the single most common count at 9.4 percent of hands, and a 1NT opening of 15 to 17 is dealt to one hand in twenty. The table gives every count with its cumulative chance.
Updated 13 October 2026
Ten points is the single likeliest count, held in 9.41 percent of hands, and it is also the exact average. The table lists every count from 0 to 25, the chance of holding exactly that many, and the chance of holding at least that many. Counts of 26 and above are gathered into a final row.
| Points | Exactly | At least |
|---|---|---|
| 0 | 0.36% | 100.00% |
| 1 | 0.79% | 99.64% |
| 2 | 1.36% | 98.85% |
| 3 | 2.46% | 97.49% |
| 4 | 3.85% | 95.03% |
| 5 | 5.19% | 91.18% |
| 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% |
| 19 | 1.04% | 2.48% |
| 20 | 0.64% | 1.45% |
| 21 | 0.38% | 0.80% |
| 22 | 0.21% | 0.42% |
| 23 | 0.11% | 0.21% |
| 24 | 0.06% | 0.10% |
| 25 | 0.03% | 0.05% |
| 26 or more | 0.019% | 0.019% |
Exactly and at least
The Exactly column answers how often a hand holds one precise count. Thirteen points, a sound opening hand, comes up 6.91 percent of the time, and a hand with no honors at all only 0.36 percent.
The At least column adds everything from that row down, and it is usually the more useful one when planning an agreement. Fifteen or more points, the floor of a strong notrump, comes to 14.18 percent, about one hand in seven. A 20-count or better drops to 1.45 percent. Openings reserved for big hands are rare for that reason, and most partnerships accept that their strong bids will sit unused for long stretches.
Why the average is ten
Each suit holds an ace, king, queen and jack, worth 4, 3, 2 and 1. That makes 10 points a suit and 40 in the deck. Four hands share those 40, so the average hand holds exactly 10. The distribution is a little lopsided, because a hand can hold as many as 37 but never fewer than 0.
Points and shape together
Points alone say nothing about shape. The bridge odds calculator combines the two, and a balanced 15 to 17, the strong 1NT opening, comes out at 4.87 percent. The hand patterns table gives the shape side on its own. For adjusting a raw count to a hand's real playing strength, see hand evaluation and the rule of 20.
Frequently asked questions
- What is the average number of high-card points in a bridge hand?
- The average is exactly 10 points. The deck holds 40 high-card points and they are shared among four hands.
- How often do you hold 15 or more points?
- A hand holds 15 or more high-card points 14.18 percent of the time, roughly once in seven deals.
- How rare is a 20-point hand?
- A hand of 20 or more points is dealt 1.45 percent of the time. Exactly 10 points, the likeliest count, is held in 9.41 percent of hands.
- What are the odds of a hand with no points?
- A hand with no ace, king, queen or jack is dealt 0.36 percent of the time.
The odds calculator combines a point range with a pattern and gives the chance of that exact hand.
Price any shape and point range- Bridge Odds CalculatorA bridge probability calculator: pick a shape and a point range and see how often a hand like it is dealt, computed over all 635 billion bridge hands.
- Bridge Hand PatternsEvery one of the 39 bridge hand patterns and how often each is dealt: 4-4-3-2 leads at 21.6 percent, balanced hands make up 47.6 percent, and a void appears in one hand in twenty.
- Hand Evaluation in BridgeHow to count a bridge hand: high-card points, length and shortness points, quick tricks, the adjustments experts make, and how many points game and slam need.
- The Rule of 20The rule of 20 says open the bidding when your high-card points plus the lengths of your two longest suits reach 20. How it works, the rule of 22 refinement, and hands at the border.