Bridge Odds Tables
Exact reference numbers computed from combinatorics: suit breaks, HCP frequencies and every hand pattern.
Suit breaks
Probability of each split by number of missing cards. Open the interactive calculator
2 missing
| 1-1 | 52.00% |
| 2-0 | 48.00% |
3 missing
| 2-1 | 78.00% |
| 3-0 | 22.00% |
4 missing
| 2-2 | 40.70% |
| 3-1 | 49.74% |
| 4-0 | 9.57% |
5 missing
| 3-2 | 67.83% |
| 4-1 | 28.26% |
| 5-0 | 3.91% |
6 missing
| 3-3 | 35.53% |
| 4-2 | 48.45% |
| 5-1 | 14.53% |
| 6-0 | 1.49% |
7 missing
| 4-3 | 62.17% |
| 5-2 | 30.52% |
| 6-1 | 6.78% |
| 7-0 | 0.52% |
8 missing
| 4-4 | 32.72% |
| 5-3 | 47.12% |
| 6-2 | 17.14% |
| 7-1 | 2.86% |
| 8-0 | 0.16% |
High-card points
Probability of holding a given HCP count in 13 cards (A=4, K=3, Q=2, J=1).
| HCP | Exactly | At least |
|---|---|---|
| 0 | 0.364% | 100.000% |
| 1 | 0.788% | 99.636% |
| 2 | 1.356% | 98.848% |
| 3 | 2.462% | 97.492% |
| 4 | 3.845% | 95.029% |
| 5 | 5.186% | 91.184% |
| 6 | 6.554% | 85.998% |
| 7 | 8.028% | 79.443% |
| 8 | 8.892% | 71.415% |
| 9 | 9.356% | 62.523% |
| 10 | 9.405% | 53.167% |
| 11 | 8.945% | 43.762% |
| 12 | 8.027% | 34.817% |
| 13 | 6.914% | 26.790% |
| 14 | 5.693% | 19.876% |
| 15 | 4.424% | 14.183% |
| 16 | 3.311% | 9.759% |
| 17 | 2.362% | 6.448% |
| 18 | 1.605% | 4.086% |
| 19 | 1.036% | 2.481% |
| 20 | 0.644% | 1.445% |
| 21 | 0.378% | 0.802% |
| 22 | 0.210% | 0.424% |
| 23 | 0.112% | 0.214% |
| 24 | 0.056% | 0.102% |
| 25 | 0.026% | 0.046% |
| 26+ | 0.0194% | - |
Hand patterns
All 39 possible suit-length patterns, most common first.
| # | Pattern | Probability |
|---|---|---|
| 1 | 4-4-3-2 | 21.55% |
| 2 | 5-3-3-2 | 15.52% |
| 3 | 5-4-3-1 | 12.93% |
| 4 | 5-4-2-2 | 10.58% |
| 5 | 4-3-3-3 | 10.54% |
| 6 | 6-3-2-2 | 5.64% |
| 7 | 6-4-2-1 | 4.70% |
| 8 | 6-3-3-1 | 3.45% |
| 9 | 5-5-2-1 | 3.17% |
| 10 | 4-4-4-1 | 2.99% |
FAQ
What is the average number of HCP in a bridge hand?
Exactly 10: the deck holds 40 high-card points split among four hands. The most likely single count is also 10 HCP, at about 9.4% of hands.
How often is a hand balanced?
The three balanced patterns together (4-3-3-3, 4-4-3-2, 5-3-3-2) cover about 47.6% of all hands.
Where do these numbers come from?
All tables are computed exactly from combinatorics over the 52-card deck: no simulation, no rounding beyond display precision.