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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 will not 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 Cards |
Possible Holding |
Percentage |
Number of Hands |
Percent
Singleton
(Drop or Finesse) |
Percent
Doubleton |
Percent
Trebleton |
| 2 |
1-1
2-0, 0-2 |
52.0
48.0 |
2 |
52.0
Drop any, no finesse |
48.0 |
NA |
| 3 |
2-1,
1-2
3-0, 0-3 |
78.0
22.0 |
6
2 |
26.0
Finesse K but not QJ |
52.0 |
22.0 |
| 4 |
3-1, 1-3
2-2
4-0, 0-4 |
49.7
40.7
9.6 |
8
6
2 |
12.4
Finesse K but not QJ |
40.7 |
37.3 |
| 5 |
3-2,
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 |
27.1 |
40.7 |
| 6 |
4-2, 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) |
16.2 |
35.5 |
| 7 |
4-3,
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 |
.96 |
8.8 |
26.9 |
| 8 |
5-3, 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 |
.36 |
4.3 |
17.7 |
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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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