Probability of Bridge Hand Distributions
Cumulative
No.
Distribution
Combinations
Probability
Probability
1
4
4
3
2
136,852,887,600
0.21551176
0.2155118
2
5
3
3
2
98,534,079,072
0.15516846
0.3706802
3
5
4
3
1
82,111,732,560
0.12930705
0.4999873
4
5
4
2
2
67,182,326,640
0.10579668
0.6057840
5
4
3
3
3
66,905,856,160
0.10536130
0.7111453
6
6
3
2
2
35,830,574,208
0.05642490
0.7675702
7
6
4
2
1
29,858,811,840
0.04702075
0.8145909
8
6
3
3
1
21,896,462,016
0.03448188
0.8490728
9
5
5
2
1
20,154,697,992
0.03173900
0.8808118
10
4
4
4
1
19,007,345,500
0.02993219
0.9107440
11
7
3
2
1
11,943,524,736
0.01880830
0.9295523
12
6
4
3
0
8,421,716,160
0.01326226
0.9428145
13
5
4
4
0
7,895,358,900
0.01243337
0.9552479
14
5
5
3
0
5,684,658,408
0.00895203
0.9641999
15
6
5
1
1
4,478,821,776
0.00705311
0.9712530
16
6
5
2
0
4,134,297,024
0.00651056
0.97776361
17
7
2
2
2
3,257,324,928
0.00512954
0.98289315
18
7
4
1
1
2,488,234,320
0.00391840
0.98681154
19
7
4
2
0
2,296,831,680
0.00361698
0.99042852
20
7
3
3
0
1,684,343,232
0.00265245
0.99308097
21
8
2
2
1
1,221,496,848
0.00192358
0.99500455
22
8
3
1
1
746,470,296
0.00117552
0.99618007
23
8
3
2
0
689,049,504
0.00108509
0.99726516
24
7
5
1
0
689,049,504
0.00108509
0.99835026
25
6
6
1
0
459,366,336
0.00072340
0.99907365
26
8
4
1
0
287,103,960
0.00045212
0.99952578
27
9
2
1
1
113,101,560
0.00017811
0.99970389
28
9
3
1
0
63,800,880
0.00010047
0.99980436
29
9
2
2
0
52,200,720
0.00008220
0.99988656
30
7
6
0
0
35,335,872
0.00005565
0.99994221
31
8
5
0
0
19,876,428
0.00003130
0.99997351
32
10
2
1
0
6,960,096
1.09605E-05
0.99998447
33
9
4
0
0
6,134,700
9.66074E-06
0.99999413
34
10
1
1
1
2,513,368
3.95798E-06
0.99999809
35
10
3
0
0
981,552
1.54572E-06
0.99999963
36
11
1
1
0
158,184
2.49103E-07
0.99999988
37
11
2
0
0
73,008
1.14971E-07
1.00000000
38
12
1
0
0
2,028
3.19363E-09
1.00000000
39
13
0
0
0
4
6.29908E-12
1.00000000
Totals
635,013,559,600
1.00000000