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.
An excel spreadsheet that will compute precise probabilities of suit splits (suit splits tab) and probabilities for combinations (combinations tab) involving honors can be downloaded here.
The table information is from https://en.wikipedia.org/wiki/Contract_bridge_probabilities but rearranged to emphasize patterns.