Bridge Probabilities - Probability of Suit Distributions in Two Hidden Hands

Probability of Suit Distributions in Two Hidden Hands

This table represents the different ways that two to thirteen 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.

These probabilities follow directly from the law of Vacant Places.

Number
of Cards		 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 0.41 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 0.31 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~

Read more about this topic:  Bridge Probabilities

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