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Let us breakdown further all the 39 hand distributions in Bridge. While it is not as practical as the general knowledge, the topic in this article is handy for a bidding system improvement. For example, we can explore how many cards each suit has in each distribution and how many in total the possible combinations.

With that knowledge, we can then be able to answer the question “What is the odd to have at least x card in certain distribution. For example: what is the odd for your partner to have 4 cards Club in his/her hand.

The Breakdown of Each Of The 39 Hand Distributions

Here, we want to know the possible breakdown of each distribution. 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 to the 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 Distribution

#%# hands
113000~0%1
201300~0%1
300130~0%1
400013~0%1
Total:~0%4

This distribution is the easiest to understand. It has 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. However, the chance you will get this distribution is almost zero. The chance is 1 to 609 trillion.


12-1-0-0 Distribution

#%# hands
112001≪0.001%169
212010≪0.001%169
312100≪0.001%169
410012≪0.001%169
510120≪0.001%169
611200≪0.001%169
700112≪0.001%169
800121≪0.001%169
901012≪0.001%169
1001120≪0.001%169
1101201≪0.001%169
1201210≪0.001%169
Total:0.0000003%2028

This distribution has 4 groups corresponding to each suit. And in a group, there are 3 variations each with 12-cards in a suit plus a singleton of another suit. Therefore, there are a total of 12 kinds of hands.

Each variation has a total hands of: C(13,12) x 13 = 13 x 13 = 169


11-2-0-0 Distribution

#%# hands
111200≪0.001%6,084
211020≪0.001%6,084
311002≪0.001%6,084
421100≪0.001%6,084
520110≪0.001%6,084
620011≪0.001%6,084
701120≪0.001%6,084
801102≪0.001%6,084
902110≪0.001%6,084
1002011≪0.001%6,084
1100112≪0.001%6,084
1200211≪0.001%6,084
Total:0.0000115%73,008

Similar to 12-1-0-0 distribution, this distribution also has 4 groups corresponding to each suit. And in a group, there are 3 variations, each with 11-cards in a suit plus a doubleton of another suit. Therefore, there are also a total of 12 kinds of hands.

Each variation has a total hands of: C(13,11) x C(13,2) = 78 x 78 = 6,084


11-1-1-0 Distribution

#%# hands
111110≪0.001%13,182
211101≪0.001%13,182
311011≪0.001%13,182
411110≪0.001%13,182
511101≪0.001%13,182
611110≪0.001%13,182
711011≪0.001%13,182
810111≪0.001%13,182
910111≪0.001%13,182
1001111≪0.001%13,182
1101111≪0.001%13,182
1201111≪0.001%13,182
Total:0.0000245%158,184

This distribution has 4 groups corresponding to 10 cards of each suit. And in each group, there are 3 variations, each with 10-cards in a suit plus, a tripleton in one suit. Therefore, there are a total of 12 variations.

Each variation has a total hands of: C(13,11) x 13 x 13 = 286 x 13 x 13 = 13,182


10-3-0-0 Distribution

#%# hands
110300≪0.001%81,796
210030≪0.001%81,796
310003≪0.001%81,796
431000≪0.001%81,796
530100≪0.001%81,796
630010≪0.001%81,796
701030≪0.001%81,796
801003≪0.001%81,796
903100≪0.001%81,796
1003010≪0.001%81,796
1100103≪0.001%81,796
1200310≪0.001%81,796
Total:0.000155%981,552

This distribution has 4 groups corresponding to 11 cards of each suit. And in each group, there are 3 variations each, with 11-cards in a suit plus, a singleton for 2 suits and void in the other suit. Therefore, there are a total of 12 kinds of hands.

Each variation has a total hands of: C(13,10) x C(13,3) = 286 x 286 = 81,796


10-2-1-0 Distribution

#%# hands
110210≪0.001%290,004
210201≪0.001%290,004
310120≪0.001%290,004
410102≪0.001%290,004
510021≪0.001%290,004
610012≪0.001%290,004
721001≪0.001%290,004
821010≪0.001%290,004
921010≪0.001%290,004
1021100≪0.001%290,004
1120110≪0.001%290,004
1220101≪0.001%290,004
1311020≪0.001%290,004
1411002≪0.001%290,004
1512100≪0.001%290,004
1612010≪0.001%290,004
1710102≪0.001%290,004
1810210≪0.001%290,004
1901012≪0.001%290,004
2001021≪0.001%290,004
2102110≪0.001%290,004
2202101≪0.001%290,004
2301210≪0.001%290,004
2401102≪0.001%290,004
Total:0.0011%6,960,096

This distribution has 4 groups corresponding to 10 cards of each suit. And in each group, there are 6 variations, each with 10-cards in a suit plus, a doubleton in a suit, a singleton for another suit and void in the last suit. Therefore, there are a total of 24 variations.

Each variation has a total hands of: C(13,10) x C(13,2) x 13 = 286 x 78 x 13 = 290,004


10-1-1-1 Distribution

#%# hands
110111≪0.001%628,342
211110≪0.001%628,342
311101≪0.001%628,342
411011≪0.001%628,342
Total:0.000396%2,513,368

This distribution has 4 groups corresponding to 10 cards of each suit. And in each group, there are 6 variations, each with 10-cards in a suit plus, a doubleton in a suit, a singleton for another suit and void in the last suit. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,10) x 13 x 13 x 13 = 286 x 13 x 13 x 13 = 628,342


9-4-0-0 Distribution

#%# hands
19004≪0.001%511,225
29040≪0.001%511,225
39400≪0.001%511,225
44009≪0.001%511,225
54090≪0.001%511,225
64900≪0.001%511,225
70049≪0.001%511,225
80094≪0.001%511,225
90409≪0.001%511,225
100490≪0.001%511,225
110904≪0.001%511,225
120940≪0.001%511,225
Total:0.00097%62,880,675

This distribution has 4 groups corresponding to 9 cards of each suit. And in each group, there are 3 variations, each with 4-cards in a suit. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,9) x C(13,4) = 286 x 13 x 13 x 13 = 511,225


9-3-1-0 Distribution

#%# hands
193100.00042%2,658,370
293010.00042%2,658,370
391300.00042%2,658,370
491030.00042%2,658,370
590310.00042%2,658,370
690130.00042%2,658,370
739010.00042%2,658,370
839100.00042%2,658,370
931090.00042%2,658,370
1031900.00042%2,658,370
1130190.00042%2,658,370
1230910.00042%2,658,370
1319300.00042%2,658,370
1419030.00042%2,658,370
1513900.00042%2,658,370
1613090.00042%2,658,370
1710930.00042%2,658,370
1810390.00042%2,658,370
1909130.00042%2,658,370
2009310.00042%2,658,370
2103190.00042%2,658,370
2203910.00042%2,658,370
2301390.00042%2,658,370
2401930.00042%2,658,370
Total:0.01%63,800,880

This distribution has 4 groups corresponding to 9 cards of each suit. And in each group, there are 6 variations, each with 3-cards in a suit, plus a singleton in another suit and void in the other suit. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,9) x C(13,3) x 13 = 715 x 286 x 13 = 2,658,370


9-2-2-0 Distribution

#%# hands
192200.00069%4,350,060
292020.00069%4,350,060
390220.00069%4,350,060
429200.00069%4,350,060
529020.00069%4,350,060
622900.00069%4,350,060
722090.00069%4,350,060
820920.00069%4,350,060
920290.00069%4,350,060
1009220.00069%4,350,060
1102920.00069%4,350,060
1202290.00069%4,350,060
Total:0.082%52,200,720

This distribution has 4 groups corresponding to 9 cards of each suit. And in each group, there are 3 variations, each with a doubleton in a suit, plus another doubleton in another suit and void in the other suit. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,9) x C(13,2) x C(13,2) = 715 x 78 x 78 = 52,200,720


9-2-1-1 Distribution

#%# hands
192110.00148%9,425,130
291210.00148%9,425,130
391120.00148%9,425,130
429110.00148%9,425,130
521910.00148%9,425,130
621190.00148%9,425,130
719210.00148%9,425,130
819120.00148%9,425,130
912910.00148%9,425,130
1012190.00148%9,425,130
1111920.00148%9,425,130
1211290.00148%9,425,130
Total:0.018%113,101,560

This distribution has 4 groups corresponding to 9 cards of each suit. And in each group, there are 3 variations, each with a singleton in a suit, plus another singleton in another suit and a doubleton in the other suit. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,9) x C(13,2) x 13 x 13 = 715 x 78 x 78 = 9,425,130


8-5-0-0 Distribution

#%# hands
185000.00026%1,656,369
280500.00026%1,656,369
380050.00026%1,656,369
458000.00026%1,656,369
550800.00026%1,656,369
650080.00026%1,656,369
708500.00026%1,656,369
808050.00026%1,656,369
905800.00026%1,656,369
1005080.00026%1,656,369
1100850.00026%1,656,369
1200580.00026%1,656,369
Total:0.0031%19,876,428

This distribution has 4 groups corresponding to 8 cards of each suit. And in each group, there are 3 variations, each with 5-cards in a suit and void for the other two suits. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,8) x C(13,5) = 1287 x 1287 = 1,656,369


8-4-1-0 Distribution

#%# hands
184100.00188%11,962,665
284010.00188%11,962,665
381400.00188%11,962,665
481040.00188%11,962,665
580410.00188%11,962,665
680140.00188%11,962,665
748010.00188%11,962,665
848100.00188%11,962,665
941080.00188%11,962,665
1041800.00188%11,962,665
1140180.00188%11,962,665
1240810.00188%11,962,665
1318400.00188%11,962,665
1418040.00188%11,962,665
1514800.00188%11,962,665
1614080.00188%11,962,665
1710840.00188%11,962,665
1810480.00188%11,962,665
1908140.00188%11,962,665
2008410.00188%11,962,665
2104180.00188%11,962,665
2204810.00188%11,962,665
2301480.00188%11,962,665
2401840.00188%11,962,665
Total:0.045%143,551,980

This distribution has 4 groups corresponding to 8 cards of each suit. And in each group, there are 6 variations, each with 4-cards in a suit, a singleton in another suit and void for the other suit. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,8) x C(13,4) x 13 = 1287 x 1287 = 11962665


8-3-2-0 Distribution

#%# hands
183200.0045%28,710,396
283020.0045%28,710,396
382300.0045%28,710,396
482030.0045%28,710,396
580320.0045%28,710,396
680230.0045%28,710,396
738020.0045%28,710,396
838200.0045%28,710,396
932080.0045%28,710,396
1032800.0045%28,710,396
1130280.0045%28,710,396
1230820.0045%28,710,396
1328300.0045%28,710,396
1428030.0045%28,710,396
1523800.0045%28,710,396
1623080.0045%28,710,396
1720830.0045%28,710,396
1820380.0045%28,710,396
1908230.0045%28,710,396
2008320.0045%28,710,396
2103280.0045%28,710,396
2203820.0045%28,710,396
2302380.0045%28,710,396
2402830.0045%28,710,396
Total:0.1085%344,524,752

This distribution has 4 groups corresponding to 8 cards of each suit. And in each group, there are 6 variations, each with 3-cards in a suit, a doubleton in another suit and void for the other suit. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,8) x C(13,3) x C(13,2) = 1287 x 286 x 78 = 28,710,396


8-3-1-1 Distribution

#%# hands
183110.098%62,205,858
281310.098%62,205,858
381130.098%62,205,858
438110.098%62,205,858
531810.098%62,205,858
631180.098%62,205,858
718310.098%62,205,858
818130.098%62,205,858
913810.098%62,205,858
1013180.098%62,205,858
1111830.098%62,205,858
1211380.098%62,205,858
Total:0.12%746,470,296

This distribution has 4 groups corresponding to 8 cards of each suit. And in each group, there are 3 variations, each with 3-cards in a suit, singleton for the other two suits. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,8) x C(13,3) x 13 x 13 = 1287 x 286 x 78 = 62,205,858


8-2-2-1 Distribution

#%# hands
182210.016%101,791,404
282120.016%101,791,404
381220.016%101,791,404
428210.016%101,791,404
528120.016%101,791,404
622810.016%101,791,404
722180.016%101,791,404
821820.016%101,791,404
921280.016%101,791,404
1018220.016%101,791,404
1112820.016%101,791,404
1212280.016%101,791,404
Total:0.19%1,221,496,848

This distribution has 4 groups corresponding to 8 cards of each suit. And in each group, there are 3 variations, each with a singleton in a suit, and doubleton for the other two suits. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,8) x C(13,2) x C(13,2) x 13 = 1287 x 78 x 78 13 = 101,791,404


7-6-0-0 Distribution

#%# hands
176000.00046%2,944,656
270600.00046%2,944,656
370060.00046%2,944,656
467000.00046%2,944,656
560700.00046%2,944,656
660070.00046%2,944,656
707600.00046%2,944,656
807060.00046%2,944,656
906700.00046%2,944,656
1006070.00046%2,944,656
1100760.00046%2,944,656
1200670.00046%2,944,656
Total:0.0556%35,335,872

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a 6-cards second suit. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,6) = 1716 x 1716 = 2,944,656


7-5-1-0 Distribution

#%# hands
175100.0045%28,710,396
275010.0045%28,710,396
371500.0045%28,710,396
471050.0045%28,710,396
570510.0045%28,710,396
670150.0045%28,710,396
757010.0045%28,710,396
857100.0045%28,710,396
951070.0045%28,710,396
1051700.0045%28,710,396
1150170.0045%28,710,396
1250710.0045%28,710,396
1317500.0045%28,710,396
1417050.0045%28,710,396
1515700.0045%28,710,396
1615070.0045%28,710,396
1710750.0045%28,710,396
1810570.0045%28,710,396
1907150.0045%28,710,396
2007510.0045%28,710,396
2105170.0045%28,710,396
2205710.0045%28,710,396
2301570.0045%28,710,396
2401750.0045%28,710,396
Total:0.1085%689,049,504

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a 5-cards second suit and a singleton. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,5) x 13 = 1716 x 1287 x 13 = 28,710,396


7-4-2-0 Distribution

#%# hands
174200.015%95,701,320
274020.015%95,701,320
372400.015%95,701,320
472040.015%95,701,320
570420.015%95,701,320
670240.015%95,701,320
747020.015%95,701,320
847200.015%95,701,320
942070.015%95,701,320
1042700.015%95,701,320
1140270.015%95,701,320
1240720.015%95,701,320
1327400.015%95,701,320
1427040.015%95,701,320
1524700.015%95,701,320
1624070.015%95,701,320
1720740.015%95,701,320
1820470.015%95,701,320
1907240.015%95,701,320
2007420.015%95,701,320
2104270.015%95,701,320
2204720.015%95,701,320
2302470.015%95,701,320
2402740.015%95,701,320
Total:0.1808%1,148,415,840

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a 4-cards second suit void in one suit and a doubleton in other. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,4) x C(13,2) = 1716 x 715 x 78 =95,701,320


7-4-1-1 Distribution

#%# hands
174110.033%207,352,860
271410.033%207,352,860
371140.033%207,352,860
447110.033%207,352,860
541710.033%207,352,860
641170.033%207,352,860
717410.033%207,352,860
817140.033%207,352,860
914710.033%207,352,860
1014170.033%207,352,860
1111740.033%207,352,860
1211470.033%207,352,860
Total:0.39%2,488,234,320

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a 4-cards second suit and two doubletons. Therefore, there are a total of 24 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,4) x 13 x 13 = 1716 x 715 x 13 x 13 =207,352,860


7-3-3-0 Distribution

#%# hands
173300.022%140,361,936
273030.022%140,361,936
370330.022%140,361,936
437300.022%140,361,936
537030.022%140,361,936
633700.022%140,361,936
733070.022%140,361,936
830730.022%140,361,936
930370.022%140,361,936
1007330.022%140,361,936
1103730.022%140,361,936
1203370.022%140,361,936
Total:0.265%1,684,343,232

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a void in one suit and two tripletons. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,3) x C(13,3) = 1716 x 286 x 286 =140,361,936


7-3-2-1 Distribution

#%# hands
173210.078%497,646,864
273120.078%497,646,864
372310.078%497,646,864
472130.078%497,646,864
571320.078%497,646,864
671230.078%497,646,864
737120.078%497,646,864
837210.078%497,646,864
932170.078%497,646,864
1032710.078%497,646,864
1131270.078%497,646,864
1231720.078%497,646,864
1327310.078%497,646,864
1427130.078%497,646,864
1523710.078%497,646,864
1623170.078%497,646,864
1721730.078%497,646,864
1821370.078%497,646,864
1917230.078%497,646,864
2017320.078%497,646,864
2113270.078%497,646,864
2213720.078%497,646,864
2312370.078%497,646,864
2412730.078%497,646,864
Total:1.88%11,943,524,736

This distribution has 4 groups corresponding to 7 cards of each suit. And in each group, there are 3 variations, each with a 4-cards second suit and two singletons. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,4) x 13 x 13 = 1716 x 715 x 13 x 13 =497,646,864


7-2-2-2 Distribution

#%# hands
172220.128%814,331,232
227220.128%814,331,232
322720.128%814,331,232
422270.128%814,331,232
Total:0.513%3,257,324,928

This distribution has 4 groups corresponding to 7 cards in one suit and doubleton in three other suits. Therefore, there are a total of 4 variations.

For each variation, we can calculate the total hands as follows: C(13,7) x C(13,2) x C(13,2) x C(13,2) = 1716 x 78 x 78 x 78 =814,331,232


6-6-1-0 Distribution

#%# hands
166100.006%38,280,528
266010.006%38,280,528
361600.006%38,280,528
461060.006%38,280,528
560610.006%38,280,528
660160.006%38,280,528
716600.006%38,280,528
816060.006%38,280,528
910660.006%38,280,528
1006610.006%38,280,528
1106160.006%38,280,528
1201660.006%38,280,528
Total:0.0723%459,366,336

This distribution has 6 groups corresponding to 2-suiter 6 cards. Each group has 2 variations. Each of a singleton in one suit and void in the other suit. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,6) x 13 = 1716 x 1716 x 13 =38,280,528


6-5-2-0 Distribution

#%# hands
165200.027%172,262,376
265020.027%172,262,376
362500.027%172,262,376
462050.027%172,262,376
560520.027%172,262,376
660250.027%172,262,376
756020.027%172,262,376
856200.027%172,262,376
952060.027%172,262,376
1052600.027%172,262,376
1150260.027%172,262,376
1250620.027%172,262,376
1326500.027%172,262,376
1426050.027%172,262,376
1525600.027%172,262,376
1625060.027%172,262,376
1720650.027%172,262,376
1820560.027%172,262,376
1906250.027%172,262,376
2006520.027%172,262,376
2105260.027%172,262,376
2205620.027%172,262,376
2302560.027%172,262,376
2402650.027%172,262,376
Total:0.651%4,134,297,024

This distribution has six groups corresponding to 2-suiter 6-5 cards. Each group has four variations. Each of a doubleton in one suit and void in the other suit. Therefore, there are a total of 24 varieties.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,5) x C(13,2) = 1716 x 1287 x 78 =172,262,376


6-5-1-1 Distribution

#%# hands
165110.059%373,235,148
261510.059%373,235,148
361150.059%373,235,148
456110.059%373,235,148
551610.059%373,235,148
651160.059%373,235,148
716510.059%373,235,148
816150.059%373,235,148
915610.059%373,235,148
1015160.059%373,235,148
1111650.059%373,235,148
1211560.059%373,235,148
Total:0.705%4,478,821,776

This distribution has six groups corresponding to 2-suiter 6-5 cards. Each group has two variations. Each consists of two doubletons. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,5) x 13 x 13 = 1716 x 1287 x 78 =373,235,148


6-4-3-0 Distribution

#%# hands
164300.055%350,904,840
264030.055%350,904,840
363400.055%350,904,840
463040.055%350,904,840
560430.055%350,904,840
660340.055%350,904,840
746030.055%350,904,840
846300.055%350,904,840
943060.055%350,904,840
1043600.055%350,904,840
1140360.055%350,904,840
1240630.055%350,904,840
1336400.055%350,904,840
1436040.055%350,904,840
1534600.055%350,904,840
1634060.055%350,904,840
1730640.055%350,904,840
1830460.055%350,904,840
1906340.055%350,904,840
2006430.055%350,904,840
2104360.055%350,904,840
2204630.055%350,904,840
2303460.055%350,904,840
2403640.055%350,904,840
Total:1.33%8,421,716,160

This distribution has for groups corresponding to 6 cards in a suit. Each group has four variations. Each consists of a 4-cards, a tripleton and void. Therefore, there are a total of 24 variety.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,4) x C(13,3) = 1716 x 715 x 286 =350,904,840


6-4-2-1 Distribution

#%# hands
164210.196%1,244,117,160
264120.196%1,244,117,160
362410.196%1,244,117,160
462140.196%1,244,117,160
561420.196%1,244,117,160
661240.196%1,244,117,160
746120.196%1,244,117,160
846210.196%1,244,117,160
942160.196%1,244,117,160
1042610.196%1,244,117,160
1141260.196%1,244,117,160
1241620.196%1,244,117,160
1326410.196%1,244,117,160
1426140.196%1,244,117,160
1524610.196%1,244,117,160
1624160.196%1,244,117,160
1721640.196%1,244,117,160
1821460.196%1,244,117,160
1916240.196%1,244,117,160
2016420.196%1,244,117,160
2114260.196%1,244,117,160
2214620.196%1,244,117,160
2312460.196%1,244,117,160
2412640.196%1,244,117,160
Total:4.7%29,858,811,840

This distribution has for groups corresponding to 6 cards in a suit. Each group has four variations. Each consists of a 4-cards, a doubleton and a singleton. Therefore, there are a total of 24 variety.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,4) x C(13,2) x 13= 1716 x 715 x 78 x 13 =1,244,117,160


6-3-3-1 Distribution

#%# hands
163310.287%1,824,705,168
263130.287%1,824,705,168
361330.287%1,824,705,168
436310.287%1,824,705,168
536130.287%1,824,705,168
633610.287%1,824,705,168
733160.287%1,824,705,168
831630.287%1,824,705,168
931360.287%1,824,705,168
1016330.287%1,824,705,168
1113630.287%1,824,705,168
1213360.287%1,824,705,168
Total:3.45%21,896,462,016

This distribution has for groups corresponding to 6 cards in a suit. Each group has four variations. Each consists of two 3-cards and a singleton. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,3) x C(13,3) x 13= 1716 x 286 x 286 x 13 =1,824,705,168


6-3-2-2 Distribution

#%# hands
163220.47%2,985,881,184
262320.47%2,985,881,184
362230.47%2,985,881,184
436220.47%2,985,881,184
532620.47%2,985,881,184
632260.47%2,985,881,184
726320.47%2,985,881,184
826230.47%2,985,881,184
923620.47%2,985,881,184
1023260.47%2,985,881,184
1122630.47%2,985,881,184
1222360.47%2,985,881,184
Total:5.6%35,830,574,208

This distribution has for groups corresponding to 6 cards in a suit. Each group has four variations. Each consists of a 3-cards and two doubletons. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,6) x C(13,3) x C(13,2) x C(13,2)= 1716 x 286 x 78 x 78 =2,985,881,184


5-5-3-0 Distribution

#%# hands
155300.075%473,721,534
255030.075%473,721,534
353500.075%473,721,534
453050.075%473,721,534
550530.075%473,721,534
650350.075%473,721,534
735500.075%473,721,534
835050.075%473,721,534
930550.075%473,721,534
1005530.075%473,721,534
1105350.075%473,721,534
1203550.075%473,721,534
Total:0.9%5,684,658,408

This distribution has for 6 groups corresponding to a 5-5 2-suiter. Each group has two variations. Each consists of a 3-cards and void. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,5) x C(13,5) x C(13,3) = 1287 x 1287 x 286 =473,721,534


5-5-2-1 Distribution

#%# hands
155210.264%1,679,558,166
255120.264%1,679,558,166
352510.264%1,679,558,166
452150.264%1,679,558,166
551520.264%1,679,558,166
651250.264%1,679,558,166
725510.264%1,679,558,166
825150.264%1,679,558,166
921550.264%1,679,558,166
1015520.264%1,679,558,166
1115250.264%1,679,558,166
1212550.264%1,679,558,166
Total:3.17%20,154,697,992

This distribution has for 6 groups corresponding to a 5-5 2-suiter. Each group has two variations. Each consists of a doubleton and a singleton. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,5) x C(13,5) x C(13,2) x 13= 1287 x 1287 x 78 x 13=1,679,558,166


5-5-4-0 Distribution

#%# hands
154400.1%657,946,575
254040.1%657,946,575
350440.1%657,946,575
445400.1%657,946,575
545040.1%657,946,575
644500.1%657,946,575
744050.1%657,946,575
840540.1%657,946,575
940450.1%657,946,575
1005440.1%657,946,575
1104540.1%657,946,575
1204450.1%657,946,575
Total:1.24%7,895,358,900

This distribution is a 3-suiter 5-4-4-0. There are a total of 12 variety. For each variation, we can calculate the total hands as follows: C(13,5) x C(13,5) x C(13,4) = 1287 x 715 x 715=657,946,575


5-4-3-1 Distribution

#%# hands
154310.54%3,421,322,190
254130.54%3,421,322,190
353410.54%3,421,322,190
453140.54%3,421,322,190
551430.54%3,421,322,190
651340.54%3,421,322,190
745130.54%3,421,322,190
845310.54%3,421,322,190
943150.54%3,421,322,190
1043510.54%3,421,322,190
1141350.54%3,421,322,190
1241530.54%3,421,322,190
1335410.54%3,421,322,190
1435140.54%3,421,322,190
1534510.54%3,421,322,190
1634150.54%3,421,322,190
1731540.54%3,421,322,190
1831450.54%3,421,322,190
1915340.54%3,421,322,190
2015430.54%3,421,322,190
2114350.54%3,421,322,190
2214530.54%3,421,322,190
2313450.54%3,421,322,190
2413540.54%3,421,322,190
Total:12.9%82,111,732,560

This distribution has for 4 groups corresponding to a 5-cards in each suit. Each group has six variations. Each consists of a 4-cards, a tripleton and a singleton. Therefore, there are a total of 24 variety.

For each variation, we can calculate the total hands as follows: C(13,5) x C(13,4) x C(13,3) x 13= 1287 x 715 x 286 x 13=3,421,322,190


5-4-2-2 Distribution

#%# hands
154220.88%5,598,527,220
252420.88%5,598,527,220
352240.88%5,598,527,220
445220.88%5,598,527,220
542520.88%5,598,527,220
642250.88%5,598,527,220
725420.88%5,598,527,220
825240.88%5,598,527,220
924520.88%5,598,527,220
1024250.88%5,598,527,220
1122540.88%5,598,527,220
1222450.88%5,598,527,220
Total:10.56%67,182,326,640

This distribution has for 4 groups corresponding to a 5-cards in each suit. Each group has three variations. Each consists of a 4-cards, and two doubletons. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,5) x C(13,4) x C(13,2) x C(13,2)= 1287 x 715 x 78 x 78=5,598,527,220


5-3-2-2 Distribution

#%# hands
153321.29%8,211,173,256
253231.29%8,211,173,256
352331.29%8,211,173,256
435321.29%8,211,173,256
535231.29%8,211,173,256
633521.29%8,211,173,256
733251.29%8,211,173,256
832531.29%8,211,173,256
932351.29%8,211,173,256
1025331.29%8,211,173,256
1123531.29%8,211,173,256
1223351.29%8,211,173,256
Total:15.5%98,534,079,072

This distribution has for 4 groups corresponding to a 5-cards in each suit. Each group has three variations. Each consists of two tripletons and a doubleton. Therefore, there are a total of 12 variety.

For each variation, we can calculate the total hands as follows: C(13,5) x C(13,3) x C(13,3) x C(13,2)= 1287 x 286 x 286 x 78=8,211,173,256


4-4-4-1 Distribution

#%# hands
141440.75%4,751,836,375
244140.75%4,751,836,375
344410.75%4,751,836,375
414440.75%4,751,836,375
Total:2.99%19,007,345,500

This distribution has for 4 groups corresponding to a 3-suiter with a singleton and three 4-cards. Therefore, there are a total of 4 variations.

For each variation, we can calculate the total hands as follows: C(13,4) x C(13,4) x C(13,4) x 13= 715 x 715 x 715 x 13=4,751,836,375


4-4-3-2 Distribution

#%# hands
144321.796%11,404,407,300
244231.796%11,404,407,300
343421.796%11,404,407,300
443241.796%11,404,407,300
542431.796%11,404,407,300
642341.796%11,404,407,300
734421.796%11,404,407,300
834241.796%11,404,407,300
932441.796%11,404,407,300
1024431.796%11,404,407,300
1124341.796%11,404,407,300
1223441.796%11,404,407,300
Total:21.55%136,852,887,600

This distribution has 4 groups corresponding to a 2-suiter of 44 with a tripleton and a doubleton. Therefore, there are a total of 12 variations.

For each variation, we can calculate the total hands as follows: C(13,4) x C(13,4) x C(13,3) x C(13,2)= 715 x 715 x 286 x 78=11,404,407,300


4-3-3-3 Distribution

#%# hands
143332.63%16,726,464,040
234332.63%16,726,464,040
333432.63%16,726,464,040
433342.63%16,726,464,040
Total:10.5%66,905,856,160

This distribution is a flat 4-3-3-3. So, there are only 4 variations.

For each variation, we can calculate the total hands as follows: C(13,4) x C(13,3) x C(13,3) x C(13,3)= 715 x 286 x 286 x 286=16,726,464,040


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.

Next: Odd of having x number of card -or- Back to the general stats : The 39 Types of hand Distribution in Bridge

The 39 hand distributions