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:
“The probability of learning something unusual from a newspaper is far greater than that of experiencing it; in other words, it is in the realm of the abstract that the more important things happen in these times, and it is the unimportant that happens in real life.”
—Robert Musil (1880–1942)
“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical probability provides loopholes, and discrepancies are expunged by Faith.”
—Ursula K. Le Guin (b. 1929)
“Every people have gods to suit their circumstances.”
—Henry David Thoreau (1817–1862)
“It is a hidden fear that somehow, if they are only given a chance, women will suddenly do as they have been done by.”
—Eva Figes (b. 1932)
“O kinsmen of the Three in One,
O kinsmen, bless the hands that play.
The notes they waken shall live on
When all this heavy history’s done;
Our hands, our hands must ebb away.”
—William Butler Yeats (1865–1939)