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Probability of Card Distribution - The priori probability of a player holding a certain card distribution based on mathematical odds. Aspiring Bridge players make mental references to the distribution when bidding or determining the best line of play, particularly the most probable line of distribution.

Generally, when opponents hold an even number of cards, the number of cards held willnot break evenly between the opponents. When opponents hold an odd number of cards, the number of cards held will break evenly.
Also see Suit Combinations

Outstanding CardsPossible HoldingPercentageNumber of HandsPercent
Singleton
(Drop or Finesse)		Percent
Doubleton		Percent
Trebleton
21-1
2-0, 0-2		52.0
48.0		252.0
Drop any, no finesse		48.0NA
32-1, 1-2
3-0, 0-3		78.0
22.0		6
2		26.0
Finesse K but not QJ		52.022.0
43-1, 1-3
2-2
4-0, 0-4		49.7
40.7
9.6		8
6
2		12.4
Finesse K but not QJ		40.737.3
53-2, 2-3
4-1, 1-4
5-0, 0-5		67.8
28.3
3.9		20
10
2		5.7
Finesse KQ not J		27.140.7
64-2, 2-4
3-3
5-1, 1-5
6-0, 0-6		48.5
35.5
14.5
1.5		30
20
12
2		2.4
Finesse KQ not J
(see note below)		16.235.5
74-3, 3-4
5-2, 2-5
6-1, 1-6
7-0, 0-7		62.2
30.5
6.8
.5		70
42
14
2		.968.826.9
85-3, 3-5
4-4
6-2, 2-6
7-1, 1-7
8-0, 0-8		47.1
32.7
17.1
2.9
.16		112
70
56
16
2		.364.317.7
NOTE: In some situations, we may wish to consider a finesse such as case #6 above.
With AK10x and Qxx we make 4 tricks 60.9%. Of course we should play the Queen first,
just in case there is a 6-0 split with LHO holding Jxxxxx (0.75)
or there is a 5-1 split with LHO holding Jxxxx (6.1%) so we play A or K, then the Q
watching to see if RHO shows out with a void or singleton.

With AKxx and Qxx (w/o 10 or 9), we make 4 tricks 35.5%

With AK98 and Q10x, we make 4 tricks 61.6%

With AK10xx and Qx, we make 4 tricks 93.2% or
5 tricks 51.7 if we finesse after playing the Queen.

With AKxxx and Qx (w/o 10 or 9), we make 4 tricks 84%
or 5 tricks 35.5% if we finesse.

For more details, please see Suit Combinations

Card Distribution (remaining two hands)
Hand Distribution (suits within a hand)
High Card Point Count (HCPs in one hand)
Miscellaneous Probabilities (assorted interesting odds)
Number of Cards (card quantity in a suit)
Posteriori Probability (example when additional information is known)
Suit Combinations (best lead and plays)
Expected Controls (based on HCP)
Also see books on Probabilities

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