Passion of The Game of Bridge

Extended: 39 Type Of Possible Hands In Bridge Distribution

Extended: 39 Type Of Possible Hands In Bridge Distribution

In here , we learn that there are only 39 type of bridge distribution from possible 631 trillion possible hands. To study more advanced topic, it is necessary to breakdown further those 39 type of  distribution into below possibilities of hand distributions. The beauty of bridge distribution:
(For example: there are 12 hand distribution of 12-1-0-0, each has 169 combinations/variations)

13-0-0-0 S H D C Total Hands
1 13 0 0 0 1
2 0 13 0 0 1
3 0 0 13 0 1
4 0 0 0 13 1
12-1-0-0 S H D C Total Hands
1 12 0 0 1 169
2 12 0 1 0 169
3 12 1 0 0 169
4 1 0 0 12 169
5 1 0 12 0 169
6 1 12 0 0 169
7 0 0 1 12 169
8 0 0 12 1 169
9 0 1 0 12 169
10 0 1 12 0 169
11 0 12 0 1 169
12 0 12 1 0 169
11-2-0-0 S H D C Total Hands
1 11 2 0 0 6084
2 11 0 2 0 6084
3 11 0 0 2 6084
4 2 11 0 0 6084
5 2 0 11 0 6084
6 2 0 0 11 6084
7 0 11 2 0 6084
8 0 11 0 2 6084
9 0 2 11 0 6084
10 0 2 0 11 6084
11 0 0 11 2 6084
12 0 0 2 11 6084
11-1-1-0 S H D C Total Hands
1 11 1 1 0 13182
2 11 1 0 1 13182
3 11 0 1 1 13182
4 1 11 1 0 13182
5 1 11 0 1 13182
6 1 1 11 0 13182
7 1 1 0 11 13182
8 1 0 11 1 13182
9 1 0 1 11 13182
10 0 11 1 1 13182
11 0 1 11 1 13182
12 0 1 1 11 13182
10-3-0-0 S H D C Total Hands
1 10 3 0 0 81796
2 10 0 3 0 81796
3 10 0 0 3 81796
4 3 10 0 0 81796
5 3 0 10 0 81796
6 3 0 0 10 81796
7 0 10 3 0 81796
8 0 10 0 3 81796
9 0 3 10 0 81796
10 0 3 0 10 81796
11 0 0 10 3 81796
12 0 0 3 10 81796
10-2-1-0 S H D C Total Hands
1 10 2 1 0 290004
2 10 2 0 1 290004
3 10 1 2 0 290004
4 10 1 0 2 290004
5 10 0 2 1 290004
6 10 0 1 2 290004
7 2 10 0 1 290004
8 2 10 1 0 290004
9 2 1 0 10 290004
10 2 1 10 0 290004
11 2 0 1 10 290004
12 2 0 10 1 290004
13 1 10 2 0 290004
14 1 10 0 2 290004
15 1 2 10 0 290004
16 1 2 0 10 290004
17 1 0 10 2 290004
18 1 0 2 10 290004
19 0 10 1 2 290004
20 0 10 2 1 290004
21 0 2 1 10 290004
22 0 2 10 1 290004
23 0 1 2 10 290004
24 0 1 10 2 290004
10-1-1-1 S H D C Total Hands
1 10 1 1 1 628342
2 1 1 1 10 628342
3 1 1 10 1 628342
4 1 10 1 1 628342
5
9-4-0-0 S H D C Total Hands
1 9 0 0 4 511225
2 9 0 4 0 511225
3 9 4 0 0 511225
4 4 0 0 9 511225
5 4 0 9 0 511225
6 4 9 0 0 511225
7 0 0 4 9 511225
8 0 0 9 4 511225
9 0 4 0 9 511225
10 0 4 9 0 511225
11 0 9 0 4 511225
12 0 9 4 0 511225
9-3-1-0 S H D C Total Hands
1 9 3 1 0 2658370
2 9 3 0 1 2658370
3 9 1 3 0 2658370
4 9 1 0 3 2658370
5 9 0 3 1 2658370
6 9 0 1 3 2658370
7 3 9 0 1 2658370
8 3 9 1 0 2658370
9 3 1 0 9 2658370
10 3 1 9 0 2658370
11 3 0 1 9 2658370
12 3 0 9 1 2658370
13 1 9 3 0 2658370
14 1 9 0 3 2658370
15 1 3 9 0 2658370
16 1 3 0 9 2658370
17 1 0 9 3 2658370
18 1 0 3 9 2658370
19 0 9 1 3 2658370
20 0 9 3 1 2658370
21 0 3 1 9 2658370
22 0 3 9 1 2658370
23 0 1 3 9 2658370
24 0 1 9 3 2658370
9-2-2-0 S H D C Total Hands
1 9 2 2 0 4350060
2 9 2 0 2 4350060
3 9 0 2 2 4350060
4 2 9 2 0 4350060
5 2 9 0 2 4350060
6 2 2 9 0 4350060
7 2 2 0 9 4350060
8 2 0 9 2 4350060
9 2 0 2 9 4350060
10 0 9 2 2 4350060
11 0 2 9 2 4350060
12 0 2 2 9 4350060
9-2-1-1 S H D C Total Hands
1 9 2 1 1 9425130
2 9 1 2 1 9425130
3 9 1 1 2 9425130
4 2 9 1 1 9425130
5 2 1 9 1 9425130
6 2 1 1 9 9425130
7 1 9 2 1 9425130
8 1 9 1 2 9425130
9 1 2 9 1 9425130
10 1 2 1 9 9425130
11 1 1 9 2 9425130
12 1 1 2 9 9425130
8-5-0-0 S H D C Total Hands
1 8 5 0 0 1656369
2 8 0 5 0 1656369
3 8 0 0 5 1656369
4 5 8 0 0 1656369
5 5 0 8 0 1656369
6 5 0 0 8 1656369
7 0 8 5 0 1656369
8 0 8 0 5 1656369
9 0 5 8 0 1656369
10 0 5 0 8 1656369
11 0 0 8 5 1656369
12 0 0 5 8 1656369
8-4-1-0 S H D C Total Hands
1 8 4 1 0 11962665
2 8 4 0 1 11962665
3 8 1 4 0 11962665
4 8 1 0 4 11962665
5 8 0 4 1 11962665
6 8 0 1 4 11962665
7 4 8 0 1 11962665
8 4 8 1 0 11962665
9 4 1 0 8 11962665
10 4 1 8 0 11962665
11 4 0 1 8 11962665
12 4 0 8 1 11962665
13 1 8 4 0 11962665
14 1 8 0 4 11962665
15 1 4 8 0 11962665
16 1 4 0 8 11962665
17 1 0 8 4 11962665
18 1 0 4 8 11962665
19 0 8 1 4 11962665
20 0 8 4 1 11962665
21 0 4 1 8 11962665
22 0 4 8 1 11962665
23 0 1 4 8 11962665
24 0 1 8 4 11962665
8-3-2-0 S H D C Total Hands
1 8 3 2 0 28710396
2 8 3 0 2 28710396
3 8 2 3 0 28710396
4 8 2 0 3 28710396
5 8 0 3 2 28710396
6 8 0 2 3 28710396
7 3 8 0 2 28710396
8 3 8 2 0 28710396
9 3 2 0 8 28710396
10 3 2 8 0 28710396
11 3 0 2 8 28710396
12 3 0 8 2 28710396
13 2 8 3 0 28710396
14 2 8 0 3 28710396
15 2 3 8 0 28710396
16 2 3 0 8 28710396
17 2 0 8 3 28710396
18 2 0 3 8 28710396
19 0 8 2 3 28710396
20 0 8 3 2 28710396
21 0 3 2 8 28710396
22 0 3 8 2 28710396
23 0 2 3 8 28710396
24 0 2 8 3 28710396
8-3-1-1 S H D C Total Hands
1 8 3 1 1 62205858
2 8 1 3 1 62205858
3 8 1 1 3 62205858
4 3 8 1 1 62205858
5 3 1 8 1 62205858
6 3 1 1 8 62205858
7 1 8 3 1 62205858
8 1 8 1 3 62205858
9 1 3 8 1 62205858
10 1 3 1 8 62205858
11 1 1 8 3 62205858
12 1 1 3 8 62205858
8-2-2-1 S H D C Total Hands
1 8 2 2 1 101791404
2 8 2 1 2 101791404
3 8 1 2 2 101791404
4 2 8 2 1 101791404
5 2 8 1 2 101791404
6 2 2 8 1 101791404
7 2 2 1 8 101791404
8 2 1 8 2 101791404
9 2 1 2 8 101791404
10 1 8 2 2 101791404
11 1 2 8 2 101791404
12 1 2 2 8 101791404
7-6-0-0 S H D C Total Hands
1 7 6 0 0 2944656
2 7 0 6 0 2944656
3 7 0 0 6 2944656
4 6 7 0 0 2944656
5 6 0 7 0 2944656
6 6 0 0 7 2944656
7 0 7 6 0 2944656
8 0 7 0 6 2944656
9 0 6 7 0 2944656
10 0 6 0 7 2944656
11 0 0 7 6 2944656
12 0 0 6 7 2944656
7-5-1-0 S H D C Total Hands
1 7 5 1 0 28710396
2 7 5 0 1 28710396
3 7 1 5 0 28710396
4 7 1 0 5 28710396
5 7 0 5 1 28710396
6 7 0 1 5 28710396
7 5 7 0 1 28710396
8 5 7 1 0 28710396
9 5 1 0 7 28710396
10 5 1 7 0 28710396
11 5 0 1 7 28710396
12 5 0 7 1 28710396
13 1 7 5 0 28710396
14 1 7 0 5 28710396
15 1 5 7 0 28710396
16 1 5 0 7 28710396
17 1 0 7 5 28710396
18 1 0 5 7 28710396
19 0 7 1 5 28710396
20 0 7 5 1 28710396
21 0 5 1 7 28710396
22 0 5 7 1 28710396
23 0 1 5 7 28710396
24 0 1 7 5 28710396
7-4-2-0 S H D C Total Hands
1 7 4 2 0 95701320
2 7 4 0 2 95701320
3 7 2 4 0 95701320
4 7 2 0 4 95701320
5 7 0 4 2 95701320
6 7 0 2 4 95701320
7 4 7 0 2 95701320
8 4 7 2 0 95701320
9 4 2 0 7 95701320
10 4 2 7 0 95701320
11 4 0 2 7 95701320
12 4 0 7 2 95701320
13 2 7 4 0 95701320
14 2 7 0 4 95701320
15 2 4 7 0 95701320
16 2 4 0 7 95701320
17 2 0 7 4 95701320
18 2 0 4 7 95701320
19 0 7 2 4 95701320
20 0 7 4 2 95701320
21 0 4 2 7 95701320
22 0 4 7 2 95701320
23 0 2 4 7 95701320
24 0 2 7 4 95701320
7-4-1-1 S H D C Total Hands
1 7 4 1 1 207352860
2 7 1 4 1 207352860
3 7 1 1 4 207352860
4 4 7 1 1 207352860
5 4 1 7 1 207352860
6 4 1 1 7 207352860
7 1 7 4 1 207352860
8 1 7 1 4 207352860
9 1 4 7 1 207352860
10 1 4 1 7 207352860
11 1 1 7 4 207352860
12 1 1 4 7 207352860
7-3-3-0 S H D C Total Hands
1 7 3 3 0 140361936
2 7 3 0 3 140361936
3 7 0 3 3 140361936
4 3 7 3 0 140361936
5 3 7 0 3 140361936
6 3 3 7 0 140361936
7 3 3 0 7 140361936
8 3 0 7 3 140361936
9 3 0 3 7 140361936
10 0 7 3 3 140361936
11 0 3 7 3 140361936
12 0 3 3 7 140361936
7-3-2-1 S H D C Total Hands
1 7 3 2 1 497646864
2 7 3 1 2 497646864
3 7 2 3 1 497646864
4 7 2 1 3 497646864
5 7 1 3 2 497646864
6 7 1 2 3 497646864
7 3 7 1 2 497646864
8 3 7 2 1 497646864
9 3 2 1 7 497646864
10 3 2 7 1 497646864
11 3 1 2 7 497646864
12 3 1 7 2 497646864
13 2 7 3 1 497646864
14 2 7 1 3 497646864
15 2 3 7 1 497646864
16 2 3 1 7 497646864
17 2 1 7 3 497646864
18 2 1 3 7 497646864
19 1 7 2 3 497646864
20 1 7 3 2 497646864
21 1 3 2 7 497646864
22 1 3 7 2 497646864
23 1 2 3 7 497646864
24 1 2 7 3 497646864
7-2-2-2 S H D C Total Hands
1 7 2 2 2 814331232
2 2 7 2 2 814331232
3 2 2 7 2 814331232
4 2 2 2 7 814331232
6-6-1-0 S H D C Total Hands
1 6 6 1 0 38280528
2 6 6 0 1 38280528
3 6 1 6 0 38280528
4 6 1 0 6 38280528
5 6 0 6 1 38280528
6 6 0 1 6 38280528
7 1 6 6 0 38280528
8 1 6 0 6 38280528
9 1 0 6 6 38280528
10 0 6 6 1 38280528
11 0 6 1 6 38280528
12 0 1 6 6 38280528
6-5-2-0 S H D C Total Hands
1 6 5 2 0 172262376
2 6 5 0 2 172262376
3 6 2 5 0 172262376
4 6 2 0 5 172262376
5 6 0 5 2 172262376
6 6 0 2 5 172262376
7 5 6 0 2 172262376
8 5 6 2 0 172262376
9 5 2 0 6 172262376
10 5 2 6 0 172262376
11 5 0 2 6 172262376
12 5 0 6 2 172262376
13 2 6 5 0 172262376
14 2 6 0 5 172262376
15 2 5 6 0 172262376
16 2 5 0 6 172262376
17 2 0 6 5 172262376
18 2 0 5 6 172262376
19 0 6 2 5 172262376
20 0 6 5 2 172262376
21 0 5 2 6 172262376
22 0 5 6 2 172262376
23 0 2 5 6 172262376
24 0 2 6 5 172262376
6-5-1-1 S H D C Total Hands
1 6 5 1 1 373235148
2 6 1 5 1 373235148
3 6 1 1 5 373235148
4 5 6 1 1 373235148
5 5 1 6 1 373235148
6 5 1 1 6 373235148
7 1 6 5 1 373235148
8 1 6 1 5 373235148
9 1 5 6 1 373235148
10 1 5 1 6 373235148
11 1 1 6 5 373235148
12 1 1 5 6 373235148
6-4-3-0 S H D C Total Hands
1 6 4 3 0 350904840
2 6 4 0 3 350904840
3 6 3 4 0 350904840
4 6 3 0 4 350904840
5 6 0 4 3 350904840
6 6 0 3 4 350904840
7 4 6 0 3 350904840
8 4 6 3 0 350904840
9 4 3 0 6 350904840
10 4 3 6 0 350904840
11 4 0 3 6 350904840
12 4 0 6 3 350904840
13 3 6 4 0 350904840
14 3 6 0 4 350904840
15 3 4 6 0 350904840
16 3 4 0 6 350904840
17 3 0 6 4 350904840
18 3 0 4 6 350904840
19 0 6 3 4 350904840
20 0 6 4 3 350904840
21 0 4 3 6 350904840
22 0 4 6 3 350904840
23 0 3 4 6 350904840
24 0 3 6 4 350904840
6-4-2-1 S H D C Total Hands
1 6 4 2 1 1244117160
2 6 4 1 2 1244117160
3 6 2 4 1 1244117160
4 6 2 1 4 1244117160
5 6 1 4 2 1244117160
6 6 1 2 4 1244117160
7 4 6 1 2 1244117160
8 4 6 2 1 1244117160
9 4 2 1 6 1244117160
10 4 2 6 1 1244117160
11 4 1 2 6 1244117160
12 4 1 6 2 1244117160
13 2 6 4 1 1244117160
14 2 6 1 4 1244117160
15 2 4 6 1 1244117160
16 2 4 1 6 1244117160
17 2 1 6 4 1244117160
18 2 1 4 6 1244117160
19 1 6 2 4 1244117160
20 1 6 4 2 1244117160
21 1 4 2 6 1244117160
22 1 4 6 2 1244117160
23 1 2 4 6 1244117160
24 1 2 6 4 1244117160
6-3-3-1 S H D C Total Hands
1 6 3 3 1 1824705168
2 6 3 1 3 1824705168
3 6 1 3 3 1824705168
4 3 6 3 1 1824705168
5 3 6 1 3 1824705168
6 3 3 6 1 1824705168
7 3 3 1 6 1824705168
8 3 1 6 3 1824705168
9 3 1 3 6 1824705168
10 1 6 3 3 1824705168
11 1 3 6 3 1824705168
12 1 3 3 6 1824705168
6-3-2-2 S H D C Total Hands
1 6 3 2 2 2985881184
2 6 2 3 2 2985881184
3 6 2 2 3 2985881184
4 3 6 2 2 2985881184
5 3 2 6 2 2985881184
6 3 2 2 6 2985881184
7 2 6 3 2 2985881184
8 2 6 2 3 2985881184
9 2 3 6 2 2985881184
10 2 3 2 6 2985881184
11 2 2 6 3 2985881184
12 2 2 3 6 2985881184
5-5-3-0 S H D C Total Hands
1 5 5 3 0 473721534
2 5 5 0 3 473721534
3 5 3 5 0 473721534
4 5 3 0 5 473721534
5 5 0 5 3 473721534
6 5 0 3 5 473721534
7 3 5 5 0 473721534
8 3 5 0 5 473721534
9 3 0 5 5 473721534
10 0 5 5 3 473721534
11 0 5 3 5 473721534
12 0 3 5 5 473721534
5-5-2-1 S H D C Total Hands
1 5 5 2 1 1679558166
2 5 5 1 2 1679558166
3 5 2 5 1 1679558166
4 5 2 1 5 1679558166
5 5 1 5 2 1679558166
6 5 1 2 5 1679558166
7 2 5 5 1 1679558166
8 2 5 1 5 1679558166
9 2 1 5 5 1679558166
10 1 5 5 2 1679558166
11 1 5 2 5 1679558166
12 1 2 5 5 1679558166
5-4-4-0 S H D C Total Hands
1 5 4 4 0 657946575
2 5 4 0 4 657946575
3 5 0 4 4 657946575
4 4 5 4 0 657946575
5 4 5 0 4 657946575
6 4 4 5 0 657946575
7 4 4 0 5 657946575
8 4 0 5 4 657946575
9 4 0 4 5 657946575
10 0 5 4 4 657946575
11 0 4 5 4 657946575
12 0 4 4 5 657946575
5-4-3-1 S H D C Total Hands
1 5 4 3 1 3421322190
2 5 4 1 3 3421322190
3 5 3 4 1 3421322190
4 5 3 1 4 3421322190
5 5 1 4 3 3421322190
6 5 1 3 4 3421322190
7 4 5 1 3 3421322190
8 4 5 3 1 3421322190
9 4 3 1 5 3421322190
10 4 3 5 1 3421322190
11 4 1 3 5 3421322190
12 4 1 5 3 3421322190
13 3 5 4 1 3421322190
14 3 5 1 4 3421322190
15 3 4 5 1 3421322190
16 3 4 1 5 3421322190
17 3 1 5 4 3421322190
18 3 1 4 5 3421322190
19 1 5 3 4 3421322190
20 1 5 4 3 3421322190
21 1 4 3 5 3421322190
22 1 4 5 3 3421322190
23 1 3 4 5 3421322190
24 1 3 5 4 3421322190
5-4-2-2 S H D C Total Hands
1 5 4 2 2 5598527220
2 5 2 4 2 5598527220
3 5 2 2 4 5598527220
4 4 5 2 2 5598527220
5 4 2 5 2 5598527220
6 4 2 2 5 5598527220
7 2 5 4 2 5598527220
8 2 5 2 4 5598527220
9 2 4 5 2 5598527220
10 2 4 2 5 5598527220
11 2 2 5 4 5598527220
12 2 2 4 5 5598527220
5-3-3-2 S H D C Total Hands
1 5 3 3 2 8211173256
2 5 3 2 3 8211173256
3 5 2 3 3 8211173256
4 3 5 3 2 8211173256
5 3 5 2 3 8211173256
6 3 3 5 2 8211173256
7 3 3 2 5 8211173256
8 3 2 5 3 8211173256
9 3 2 3 5 8211173256
10 2 5 3 3 8211173256
11 2 3 5 3 8211173256
12 2 3 3 5 8211173256
4-4-4-1 S H D C Total Hands
1 4 1 4 4 4751836375
2 4 4 1 4 4751836375
3 4 4 4 1 4751836375
4 1 4 4 4 4751836375
4-4-3-2 S H D C Total Hands
1 4 4 3 2 11402157300
2 4 4 2 3 11402157300
3 4 3 4 2 11402157300
4 4 3 2 4 11402157300
5 4 2 4 3 11402157300
6 4 2 3 4 11402157300
7 3 4 4 2 11402157300
8 3 4 2 4 11402157300
9 3 2 4 4 11402157300
10 2 4 4 3 11402157300
11 2 4 3 4 11402157300
12 2 3 4 4 11402157300
4-3-3-3 S H D C Total Hands
1 4 3 3 3 16726464040
2 3 4 3 3 16726464040
3 3 3 4 3 16726464040
4 3 3 3 4 16726464040
634986559600

 

Then we summarized the long table above into this handy summary: X=number of card in a suit

X Total Hands X or more Percentage
13 1 1 0.0000000002%
12 507 508 0.0000000805%
11 57,798 58,306 0.0000092397%
10 2,613,754 2,672,060 0.0004234383%
9 58,809,465 61,481,525 0.0097429060%
8 740,999,259 802,480,784 0.1271681998%
7 5,598,661,068 6,401,141,852 1.0143815307%
6 26,393,687,892 32,794,829,744 5.1969586622%
5 77,865,170,526 110,660,000,270 17.5361619943%
4 149,531,979,655 260,191,979,925 41.2323215113%
3 181,816,433,256 442,008,413,181 70.0445609747%
2 130,725,621,432 572,734,034,613 90.7604986997%
1 50,840,366,668 623,574,401,281 98.8171126845%
0 7,464,478,869 631,038,880,150 100.0000000000%
Sum: 631,038,880,150

Meaning:

  1. If we want to know the possible hand of having 0 or more card of Spade, for example – we know it is 631,038,880,150 possible hand – or 100%
  2. How about the possibility of having 3 cards or more of Club? It is 442,008,413,181 possible hands -or- a mere 70.04% of what possible.

This will become handy to make advanced analysis of particular bridge problems. For example: to consider which one is better: open with better minor method or short club?

Knowing the statistic in bridge distribution will give you a sure advantage in the long run. This principle is the same that makes billions of dollars of profit in casino. If the statistic is on your side, you surely will see the advantage (although it is only become obvious in the extended time period).

Long live statistics – long live bridge distribution…. 🙂

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