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

Famous quotes containing the words probability of, probability, suit, hidden and/or hands:

    “Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.”
    —David Hume (1711–1776)

    “Crushed to earth and rising again is an author’s gymnastic. Once he fails to struggle to his feet and grab his pen, he will contemplate a fact he should never permit himself to face: that in all probability books have been written, are being written, will be written, better than anything he has done, is doing, or will do.”
    —Fannie Hurst (1889–1968)

    “Elyot: It doesn’t suit women to be promiscuous.
    Amanda: It doesn’t suit men for women to be promiscuous.”
    —Noël Coward (1899–1973)

    “And the unfailing sense of being young
    Spread out like a spring-woken tree, wherein
    That hidden freshness sung,
    That certainty of time laid up in store....”
    —Philip Larkin (1922–1986)

    “Criticism is often not a science; it is a craft, requiring more good health than wit, more hard work than talent, more habit than native genius. In the hands of a man who has read widely but lacks judgment, applied to certain subjects it can corrupt both its readers and the writer himself.”
    —Jean De La Bruyère (1645–1696)