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Let us breakdown further all the 39 hand distributions in Bridge. This seemingly useless topic is quite handy in both practical situation and system design. Many articles on this website will refer to this page.

Firstly, here in part A, we want to see what makes up all the 39 hand distributions. How many Spade, Heart, Diamond or Club in each distribution and how many in total the possible combinations.

In part B, we will compile a table to answer the question “What is the odd to have at least x card in certain distribution among all the 39 hand distributions. For example: what is the odd for your partner to have 3 cards Club in his/her hand.

Part A: The Breakdown of Each Of The 39 Hand Distributions

Here, we want to know the possible breakdown of each distribution for all the 39 Hand Distributions. For example:

  • The 13-0-0-0 distribution. This distribution is the easiest to understand. There are only 4 possible hands. They are a hand with 13 cards of Spade, a hand with 13 cards of Heart, a hand with 13 cards of Diamond and a hand with 13 cards of Club.
  • For the 12-1-0-0 distribution, there are 4 groups of variations. The first group is all the hands of 12 cards Spade with singleton Club, all the hands of 12 cards Spade with singleton Diamond and all the hands of 12 cards Spade with singleton Heart. So, as each group has 3 variations, the total is 12 variations.
  • In 11-2-0-0 distribution, there are also each a total of 12 variations similar like above ( 11 cards in a suit with a doubleton in another suit)
  • For 11-1-1-0 distribution, the 12 variations make up of 11 cards in a suit with a void in another suit.
  • We do all the 39 distributions just like the above.

The last columns below, “Total Hands” is all the possible specific card distribution for that specific variation.

For example, we know the distribution 12-0-1-0 would have a singleton from Diamond and 12 cards from Spade. Meanings there are 13 ways to choose the Diamond (singleton Ace or Singleton King or singleton Queen, etc)

But then, there are also 13 ways for the longer suit: missing Ace or missing King or missing Queen, etc.

Therefore, there are a total of 13 x 13 = 169 hands for every 12-1-0-0 variations as part of the 39 Hand Distributions.

13-0-0-0

Total Hands
                           1130001
2013001
3001301
4000131
 

12-1-0-0

Total Hands
112001169
212010169
312100169
410012169
510120169
611200169
700112169
800121169
901012169
1001120169
1101201169
1201210169
 

11-2-0-0

Total Hands
1112006084
2110206084
3110026084
4211006084
5201106084
6200116084
7011206084
8011026084
9021106084
10020116084
11001126084
12002116084
 

11-1-1-0

Total Hands
11111013182
21110113182
31101113182
41111013182
51110113182
61111013182
71101113182
81011113182
91011113182
100111113182
110111113182
120111113182
 

10-3-0-0

Total Hands
11030081796
21003081796
31000381796
43100081796
53010081796
63001081796
70103081796
80100381796
90310081796
100301081796
110010381796
120031081796
 

10-2-1-0

Total Hands
110210290004
210201290004
310120290004
410102290004
510021290004
610012290004
721001290004
821010290004
921010290004
1021100290004
1120110290004
1220101290004
1311020290004
1411002290004
1512100290004
1612010290004
1710102290004
1810210290004
1901012290004
2001021290004
2102110290004
2202101290004
2301210290004
2401102290004
 

10-1-1-1

Total Hands
110111628342
211110628342
311101628342
411011628342
5     
 

9-4-0-0

Total Hands
19004511225
29040511225
39400511225
44009511225
54090511225
64900511225
70049511225
80094511225
90409511225
100490511225
110904511225
120940511225
 

9-3-1-0

Total Hands
193102658370
293012658370
391302658370
491032658370
590312658370
690132658370
739012658370
839102658370
931092658370
1031902658370
1130192658370
1230912658370
1319302658370
1419032658370
1513902658370
1613092658370
1710932658370
1810392658370
1909132658370
2009312658370
2103192658370
2203912658370
2301392658370
2401932658370
 

9-2-2-0

Total Hands
192204350060
292024350060
390224350060
429204350060
529024350060
622904350060
722094350060
820924350060
920294350060
1009224350060
1102924350060
1202294350060
 

9-2-1-1

Total Hands
192119425130
291219425130
391129425130
429119425130
521919425130
621199425130
719219425130
819129425130
912919425130
1012199425130
1111929425130
1211299425130
 

8-5-0-0

Total Hands
185001656369
280501656369
380051656369
458001656369
550801656369
650081656369
708501656369
808051656369
905801656369
1005081656369
1100851656369
1200581656369
 

8-4-1-0

Total Hands
1841011962665
2840111962665
3814011962665
4810411962665
5804111962665
6801411962665
7480111962665
8481011962665
9410811962665
10418011962665
11401811962665
12408111962665
13184011962665
14180411962665
15148011962665
16140811962665
17108411962665
18104811962665
19081411962665
20084111962665
21041811962665
22048111962665
23014811962665
24018411962665
 

8-3-2-0

Total Hands
1832028710396
2830228710396
3823028710396
4820328710396
5803228710396
6802328710396
7380228710396
8382028710396
9320828710396
10328028710396
11302828710396
12308228710396
13283028710396
14280328710396
15238028710396
16230828710396
17208328710396
18203828710396
19082328710396
20083228710396
21032828710396
22038228710396
23023828710396
24028328710396
 

8-3-1-1

Total Hands
1831162205858
2813162205858
3811362205858
4381162205858
5318162205858
6311862205858
7183162205858
8181362205858
9138162205858
10131862205858
11118362205858
12113862205858
 

8-2-2-1

Total Hands
18221101791404
28212101791404
38122101791404
42821101791404
52812101791404
62281101791404
72218101791404
82182101791404
92128101791404
101822101791404
111282101791404
121228101791404
 

7-6-0-0

Total Hands
176002944656
270602944656
370062944656
467002944656
560702944656
660072944656
707602944656
807062944656
906702944656
1006072944656
1100762944656
1200672944656
 

7-5-1-0

Total Hands
1751028710396
2750128710396
3715028710396
4710528710396
5705128710396
6701528710396
7570128710396
8571028710396
9510728710396
10517028710396
11501728710396
12507128710396
13175028710396
14170528710396
15157028710396
16150728710396
17107528710396
18105728710396
19071528710396
20075128710396
21051728710396
22057128710396
23015728710396
24017528710396
 

7-4-2-0

Total Hands
1742095701320
2740295701320
3724095701320
4720495701320
5704295701320
6702495701320
7470295701320
8472095701320
9420795701320
10427095701320
11402795701320
12407295701320
13274095701320
14270495701320
15247095701320
16240795701320
17207495701320
18204795701320
19072495701320
20074295701320
21042795701320
22047295701320
23024795701320
24027495701320
 

7-4-1-1

Total Hands
17411207352860
27141207352860
37114207352860
44711207352860
54171207352860
64117207352860
71741207352860
81714207352860
91471207352860
101417207352860
111174207352860
121147207352860
 

7-3-3-0

Total Hands
17330140361936
27303140361936
37033140361936
43730140361936
53703140361936
63370140361936
73307140361936
83073140361936
93037140361936
100733140361936
110373140361936
120337140361936
 

7-3-2-1

Total Hands
17321497646864
27312497646864
37231497646864
47213497646864
57132497646864
67123497646864
73712497646864
83721497646864
93217497646864
103271497646864
113127497646864
123172497646864
132731497646864
142713497646864
152371497646864
162317497646864
172173497646864
182137497646864
191723497646864
201732497646864
211327497646864
221372497646864
231237497646864
241273497646864
 

7-2-2-2

Total Hands
17222814331232
22722814331232
32272814331232
42227814331232
 

6-6-1-0

Total Hands
1661038280528
2660138280528
3616038280528
4610638280528
5606138280528
6601638280528
7166038280528
8160638280528
9106638280528
10066138280528
11061638280528
12016638280528
 

6-5-2-0

Total Hands
16520172262376
26502172262376
36250172262376
46205172262376
56052172262376
66025172262376
75602172262376
85620172262376
95206172262376
105260172262376
115026172262376
125062172262376
132650172262376
142605172262376
152560172262376
162506172262376
172065172262376
182056172262376
190625172262376
200652172262376
210526172262376
220562172262376
230256172262376
240265172262376
 

6-5-1-1

Total Hands
16511373235148
26151373235148
36115373235148
45611373235148
55161373235148
65116373235148
71651373235148
81615373235148
91561373235148
101516373235148
111165373235148
121156373235148
 

6-4-3-0

Total Hands
16430350904840
26403350904840
36340350904840
46304350904840
56043350904840
66034350904840
74603350904840
84630350904840
94306350904840
104360350904840
114036350904840
124063350904840
133640350904840
143604350904840
153460350904840
163406350904840
173064350904840
183046350904840
190634350904840
200643350904840
210436350904840
220463350904840
230346350904840
240364350904840
 

6-4-2-1

Total Hands
164211244117160
264121244117160
362411244117160
462141244117160
561421244117160
661241244117160
746121244117160
846211244117160
942161244117160
1042611244117160
1141261244117160
1241621244117160
1326411244117160
1426141244117160
1524611244117160
1624161244117160
1721641244117160
1821461244117160
1916241244117160
2016421244117160
2114261244117160
2214621244117160
2312461244117160
2412641244117160
 

6-3-3-1

Total Hands
163311824705168
263131824705168
361331824705168
436311824705168
536131824705168
633611824705168
733161824705168
831631824705168
931361824705168
1016331824705168
1113631824705168
1213361824705168
 

6-3-2-2

Total Hands
163222985881184
262322985881184
362232985881184
436222985881184
532622985881184
632262985881184
726322985881184
826232985881184
923622985881184
1023262985881184
1122632985881184
1222362985881184
 

5-5-3-0

Total Hands
15530473721534
25503473721534
35350473721534
45305473721534
55053473721534
65035473721534
73550473721534
83505473721534
93055473721534
100553473721534
110535473721534
120355473721534
 

5-5-2-1

Total Hands
155211679558166
255121679558166
352511679558166
452151679558166
551521679558166
651251679558166
725511679558166
825151679558166
921551679558166
1015521679558166
1115251679558166
1212551679558166
 

5-4-4-0

Total Hands
15440657946575
25404657946575
35044657946575
44540657946575
54504657946575
64450657946575
74405657946575
84054657946575
94045657946575
100544657946575
110454657946575
120445657946575
 

5-4-3-1

Total Hands
154313421322190
254133421322190
353413421322190
453143421322190
551433421322190
651343421322190
745133421322190
845313421322190
943153421322190
1043513421322190
1141353421322190
1241533421322190
1335413421322190
1435143421322190
1534513421322190
1634153421322190
1731543421322190
1831453421322190
1915343421322190
2015433421322190
2114353421322190
2214533421322190
2313453421322190
2413543421322190
 

5-4-2-2

Total Hands
154225598527220
252425598527220
352245598527220
445225598527220
542525598527220
642255598527220
725425598527220
825245598527220
924525598527220
1024255598527220
1122545598527220
1222455598527220
 

5-3-3-2

Total Hands
153328211173256
253238211173256
352338211173256
435328211173256
535238211173256
633528211173256
733258211173256
832538211173256
932358211173256
1025338211173256
1123538211173256
1223358211173256
 

4-4-4-1

Total Hands
141444751836375
244144751836375
344414751836375
414444751836375
 

4-4-3-2

Total Hands
1443211402157300
2442311402157300
3434211402157300
4432411402157300
5424311402157300
6423411402157300
7344211402157300
8342411402157300
9324411402157300
10244311402157300
11243411402157300
12234411402157300
 

4-3-3-3

Total Hands
1433316726464040
2343316726464040
3334316726464040
4333416726464040
 634986559600

The 39 hand distributions statistics as reference.

There you have it. All the 39 Hand Distributions specific details are presented above. Use this page as your reference.

For example, you know that if you are dealing with 8-5-0-0 distribution, you need to look after all its 12 variations/combination.

Let’s move on to Part B -or- Back to the main articles: The 39 Types of hand Distribution in Bridge

The 39 hand distributions