This is an excerpt from a lengthy post titled “Basic Bridge Odds.” The main purpose is to suggest useful approximations to use at the table: Also, the Individual probability entry can be multiplied by the number of combinations* in a given hand to obtain a probability for the holding.
1)Missing an odd number of cards, they will divide evenly 2/3 of the time and one step from evenly 1/3 of the time. (Ignore greater steps.) Exception: Three missing cards divide 2-1 about 3/4 of the time and 3-0 about 1/4 of the time.
2)Missing an even number of cards, they will divide evenly 1/3 of the time, one step from evenly ½ of the time and two steps from evenly 1/6 of the time, seldom worse. Exception: Two missing cards divide 2-0 vs 1-1 about 1/2 of the time.
Suit Splits
| Number of Cards | Distribu-tion | Proba-bility | Combin-ations* | Individual Probability | Approxim-ation |
| 2 | 1 – 1 | 0.52 | 2 | 0.2600 | 1/2 |
| 2 – 0 | 0.48 | 2 | 0.2400 | 1/2 | |
| 4 | 2 – 2 | 0.40 | 6 | 0.0678 | 1/3 |
| 3 – 1 | 0.5 | 8 | 0.0622 | 1/2 | |
| 4 – 0 | 0.1 | 2 | 0.0478 | 1/6 | |
| 6 | 3 – 3 | 0.36 | 20 | 0.0178 | 1/3 |
| 4 – 2 | 0.48 | 30 | 0.0162 | 1/2 | |
| 5 – 1 | 0.15 | 12 | 0.0121 | 1/6 | |
| 6 – 0 | 0.01 | 2 | 0.0075 | 0 | |
| 8 | 4 – 4 | 0.33 | 70 | 0.0047 | 1/3 |
| 5 – 3 | 0.47 | 112 | 0.0042 | 1/2 | |
| 6 – 2 | 0.17 | 56 | 0.0031 | 1/6 | |
| 7 – 1 | 0.03 | 16 | 0.0018 | 0 | |
| 8 – 0 | 0 | 2 | 0.0008 | 0 |
| Number of Cards | Distribu-tion | Proba-bility | Combin-ations | Individual Probability | Approxim-ation |
| 3 | 2 – 1 | 0.78 | 6 | 0.1300 | 3/4 |
| 3 – 0 | 0.22 | 2 | 0.1100 | 1/4 | |
| 5 | 3 – 2 | 0.68 | 20 | 0.0339 | 2/3 |
| 4 – 1 | 0.28 | 10 | 0.0283 | 1/3 | |
| 5 – 0 | 0.04 | 2 | 0.0196 | 0 | |
| 4 – 3 | 0.62 | 70 | 0.0089 | 2/3 | |
| 7 | 5 – 2 | 0.31 | 42 | 0.0073 | 1/3 |
| 6 – 1 | 0.07 | 14 | 0.0048 | 0 | |
| 7 – 0 | 0.01 | 2 | 0.0026 | 0 | |
| 5-4 | 0.59 | 252 | 0.00234 | 2/3 | |
| 9 | 6-3 | 0.31 | 168 | 0.00187 | 1/3 |
| 7-2 | 0.086 | 72 | 0.00119 | 0 | |
| 8-1 | 0.107 | 18 | 0.0006 | 0 |
* To illustrate “combinations,” consider a five card suit containing H1,H2,x1,x2,x3. For a 2-3 split, ask how many combinations there are in Hxx — Hx. The doubleton could be either of H1 or H2, together with any one of x1,x2, or x3. That makes six combinations for Hx or for Hxx. Swapping the sides gives a total of 12, for a probability of .0339*12 = 0.407. XX offers 3 combinations and HH is one combination. Swapping sides makes it 6 and 2. Therefore the total number of combinations for a 3-2 split is 20.
The table information is from https://en.wikipedia.org/wiki/Contract_bridge_probabilities but rearranged to emphasize patterns.