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In the game of bridge, mathematical probabilities play a significant role. To decide which strategy has the highest likelihood of success, the declarer needs to have at least an elementary knowledge of probabilities.
Best Probability of distributions in two hands 2 through 8 missing cards.
2 missing cards – 1-1
3 missing cards – 2-1
4 missing cards – 3-1
5 missing cards – 3-2
6 missing cards – 4-2
7 missing cards – 4-3
8 missing cards – 5-3
From Wikipedia:
This table represents the different ways that two to eight particular cards may be distributed or may lie or split, between two unknown 13-card hands (before the bidding and play, or a priori).
The table also shows the number of combinations of particular cards that match any numerical split and the probabilities for each combination.
| Number of cards missing from a partnership | Distribution | Probability | Combinations | Individual Probability |
|---|---|---|---|---|
| 2 | 1 – 1 | 0.52 | 2 | 0.26 |
| 2 – 0 | 0.48 | 2 | 0.24 | |
| 3 | 2 – 1 | 0.78 | 6 | 0.13 |
| 3 – 0 | 0.22 | 2 | 0.11 | |
| 4 | 2 – 2 | 0.40 | 6 | 0.0678~ |
| 3 – 1 | 0.50 | 8 | 0.0622~ | |
| 4 – 0 | 0.10 | 2 | 0.0478~ | |
| 5 | 3 – 2 | 0.68 | 20 | 0.0339~ |
| 4 – 1 | 0.28 | 10 | 0.02826~ | |
| 5 – 0 | 0.04 | 2 | 0.01956~ | |
| 6 | 3 – 3 | 0.36 | 20 | 0.01776~ |
| 4 – 2 | 0.48 | 30 | 0.01615~ | |
| 5 – 1 | 0.15 | 12 | 0.01211~ | |
| 6 – 0 | 0.01 | 2 | 0.00745~ | |
| 7 | 4 – 3 | 0.62 | 70 | 0.00888~ |
| 5 – 2 | 0.30 | 42 | 0.00727~ | |
| 6 – 1 | 0.07 | 14 | 0.00484~ | |
| 7 – 0 | 0.01 | 2 | 0.00261~ | |
| 8 | 4 – 4 | 0.33 | 70 | 0.00467~ |
| 5 – 3 | 0.47 | 112 | 0.00421~ | |
| 6 – 2 | 0.17 | 56 | 0.00306~ | |
| 7 – 1 | 0.03 | 16 | 0.00178~ | |
| 8 – 0 | 0.00 | 2 | 0.00082~ |
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