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 |
|---|---|---|---|---|---|---|
| 1 | 13 | 0 | 0 | 0 | ~0% | 1 |
| 2 | 0 | 13 | 0 | 0 | ~0% | 1 |
| 3 | 0 | 0 | 13 | 0 | ~0% | 1 |
| 4 | 0 | 0 | 0 | 13 | ~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 |
|---|---|---|---|---|---|---|
| 1 | 12 | 0 | 0 | 1 | ≪0.001% | 169 |
| 2 | 12 | 0 | 1 | 0 | ≪0.001% | 169 |
| 3 | 12 | 1 | 0 | 0 | ≪0.001% | 169 |
| 4 | 1 | 0 | 0 | 12 | ≪0.001% | 169 |
| 5 | 1 | 0 | 12 | 0 | ≪0.001% | 169 |
| 6 | 1 | 12 | 0 | 0 | ≪0.001% | 169 |
| 7 | 0 | 0 | 1 | 12 | ≪0.001% | 169 |
| 8 | 0 | 0 | 12 | 1 | ≪0.001% | 169 |
| 9 | 0 | 1 | 0 | 12 | ≪0.001% | 169 |
| 10 | 0 | 1 | 12 | 0 | ≪0.001% | 169 |
| 11 | 0 | 12 | 0 | 1 | ≪0.001% | 169 |
| 12 | 0 | 12 | 1 | 0 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 11 | 2 | 0 | 0 | ≪0.001% | 6,084 |
| 2 | 11 | 0 | 2 | 0 | ≪0.001% | 6,084 |
| 3 | 11 | 0 | 0 | 2 | ≪0.001% | 6,084 |
| 4 | 2 | 11 | 0 | 0 | ≪0.001% | 6,084 |
| 5 | 2 | 0 | 11 | 0 | ≪0.001% | 6,084 |
| 6 | 2 | 0 | 0 | 11 | ≪0.001% | 6,084 |
| 7 | 0 | 11 | 2 | 0 | ≪0.001% | 6,084 |
| 8 | 0 | 11 | 0 | 2 | ≪0.001% | 6,084 |
| 9 | 0 | 2 | 11 | 0 | ≪0.001% | 6,084 |
| 10 | 0 | 2 | 0 | 11 | ≪0.001% | 6,084 |
| 11 | 0 | 0 | 11 | 2 | ≪0.001% | 6,084 |
| 12 | 0 | 0 | 2 | 11 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 11 | 1 | 1 | 0 | ≪0.001% | 13,182 |
| 2 | 11 | 1 | 0 | 1 | ≪0.001% | 13,182 |
| 3 | 11 | 0 | 1 | 1 | ≪0.001% | 13,182 |
| 4 | 1 | 11 | 1 | 0 | ≪0.001% | 13,182 |
| 5 | 1 | 11 | 0 | 1 | ≪0.001% | 13,182 |
| 6 | 1 | 1 | 11 | 0 | ≪0.001% | 13,182 |
| 7 | 1 | 1 | 0 | 11 | ≪0.001% | 13,182 |
| 8 | 1 | 0 | 11 | 1 | ≪0.001% | 13,182 |
| 9 | 1 | 0 | 1 | 11 | ≪0.001% | 13,182 |
| 10 | 0 | 11 | 1 | 1 | ≪0.001% | 13,182 |
| 11 | 0 | 1 | 11 | 1 | ≪0.001% | 13,182 |
| 12 | 0 | 1 | 1 | 11 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 10 | 3 | 0 | 0 | ≪0.001% | 81,796 |
| 2 | 10 | 0 | 3 | 0 | ≪0.001% | 81,796 |
| 3 | 10 | 0 | 0 | 3 | ≪0.001% | 81,796 |
| 4 | 3 | 10 | 0 | 0 | ≪0.001% | 81,796 |
| 5 | 3 | 0 | 10 | 0 | ≪0.001% | 81,796 |
| 6 | 3 | 0 | 0 | 10 | ≪0.001% | 81,796 |
| 7 | 0 | 10 | 3 | 0 | ≪0.001% | 81,796 |
| 8 | 0 | 10 | 0 | 3 | ≪0.001% | 81,796 |
| 9 | 0 | 3 | 10 | 0 | ≪0.001% | 81,796 |
| 10 | 0 | 3 | 0 | 10 | ≪0.001% | 81,796 |
| 11 | 0 | 0 | 10 | 3 | ≪0.001% | 81,796 |
| 12 | 0 | 0 | 3 | 10 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 10 | 2 | 1 | 0 | ≪0.001% | 290,004 |
| 2 | 10 | 2 | 0 | 1 | ≪0.001% | 290,004 |
| 3 | 10 | 1 | 2 | 0 | ≪0.001% | 290,004 |
| 4 | 10 | 1 | 0 | 2 | ≪0.001% | 290,004 |
| 5 | 10 | 0 | 2 | 1 | ≪0.001% | 290,004 |
| 6 | 10 | 0 | 1 | 2 | ≪0.001% | 290,004 |
| 7 | 2 | 10 | 0 | 1 | ≪0.001% | 290,004 |
| 8 | 2 | 10 | 1 | 0 | ≪0.001% | 290,004 |
| 9 | 2 | 1 | 0 | 10 | ≪0.001% | 290,004 |
| 10 | 2 | 1 | 10 | 0 | ≪0.001% | 290,004 |
| 11 | 2 | 0 | 1 | 10 | ≪0.001% | 290,004 |
| 12 | 2 | 0 | 10 | 1 | ≪0.001% | 290,004 |
| 13 | 1 | 10 | 2 | 0 | ≪0.001% | 290,004 |
| 14 | 1 | 10 | 0 | 2 | ≪0.001% | 290,004 |
| 15 | 1 | 2 | 10 | 0 | ≪0.001% | 290,004 |
| 16 | 1 | 2 | 0 | 10 | ≪0.001% | 290,004 |
| 17 | 1 | 0 | 10 | 2 | ≪0.001% | 290,004 |
| 18 | 1 | 0 | 2 | 10 | ≪0.001% | 290,004 |
| 19 | 0 | 10 | 1 | 2 | ≪0.001% | 290,004 |
| 20 | 0 | 10 | 2 | 1 | ≪0.001% | 290,004 |
| 21 | 0 | 2 | 1 | 10 | ≪0.001% | 290,004 |
| 22 | 0 | 2 | 10 | 1 | ≪0.001% | 290,004 |
| 23 | 0 | 1 | 2 | 10 | ≪0.001% | 290,004 |
| 24 | 0 | 1 | 10 | 2 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 10 | 1 | 1 | 1 | ≪0.001% | 628,342 |
| 2 | 1 | 1 | 1 | 10 | ≪0.001% | 628,342 |
| 3 | 1 | 1 | 10 | 1 | ≪0.001% | 628,342 |
| 4 | 1 | 10 | 1 | 1 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 9 | 0 | 0 | 4 | ≪0.001% | 511,225 |
| 2 | 9 | 0 | 4 | 0 | ≪0.001% | 511,225 |
| 3 | 9 | 4 | 0 | 0 | ≪0.001% | 511,225 |
| 4 | 4 | 0 | 0 | 9 | ≪0.001% | 511,225 |
| 5 | 4 | 0 | 9 | 0 | ≪0.001% | 511,225 |
| 6 | 4 | 9 | 0 | 0 | ≪0.001% | 511,225 |
| 7 | 0 | 0 | 4 | 9 | ≪0.001% | 511,225 |
| 8 | 0 | 0 | 9 | 4 | ≪0.001% | 511,225 |
| 9 | 0 | 4 | 0 | 9 | ≪0.001% | 511,225 |
| 10 | 0 | 4 | 9 | 0 | ≪0.001% | 511,225 |
| 11 | 0 | 9 | 0 | 4 | ≪0.001% | 511,225 |
| 12 | 0 | 9 | 4 | 0 | ≪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 |
|---|---|---|---|---|---|---|
| 1 | 9 | 3 | 1 | 0 | 0.00042% | 2,658,370 |
| 2 | 9 | 3 | 0 | 1 | 0.00042% | 2,658,370 |
| 3 | 9 | 1 | 3 | 0 | 0.00042% | 2,658,370 |
| 4 | 9 | 1 | 0 | 3 | 0.00042% | 2,658,370 |
| 5 | 9 | 0 | 3 | 1 | 0.00042% | 2,658,370 |
| 6 | 9 | 0 | 1 | 3 | 0.00042% | 2,658,370 |
| 7 | 3 | 9 | 0 | 1 | 0.00042% | 2,658,370 |
| 8 | 3 | 9 | 1 | 0 | 0.00042% | 2,658,370 |
| 9 | 3 | 1 | 0 | 9 | 0.00042% | 2,658,370 |
| 10 | 3 | 1 | 9 | 0 | 0.00042% | 2,658,370 |
| 11 | 3 | 0 | 1 | 9 | 0.00042% | 2,658,370 |
| 12 | 3 | 0 | 9 | 1 | 0.00042% | 2,658,370 |
| 13 | 1 | 9 | 3 | 0 | 0.00042% | 2,658,370 |
| 14 | 1 | 9 | 0 | 3 | 0.00042% | 2,658,370 |
| 15 | 1 | 3 | 9 | 0 | 0.00042% | 2,658,370 |
| 16 | 1 | 3 | 0 | 9 | 0.00042% | 2,658,370 |
| 17 | 1 | 0 | 9 | 3 | 0.00042% | 2,658,370 |
| 18 | 1 | 0 | 3 | 9 | 0.00042% | 2,658,370 |
| 19 | 0 | 9 | 1 | 3 | 0.00042% | 2,658,370 |
| 20 | 0 | 9 | 3 | 1 | 0.00042% | 2,658,370 |
| 21 | 0 | 3 | 1 | 9 | 0.00042% | 2,658,370 |
| 22 | 0 | 3 | 9 | 1 | 0.00042% | 2,658,370 |
| 23 | 0 | 1 | 3 | 9 | 0.00042% | 2,658,370 |
| 24 | 0 | 1 | 9 | 3 | 0.00042% | 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 |
|---|---|---|---|---|---|---|
| 1 | 9 | 2 | 2 | 0 | 0.00069% | 4,350,060 |
| 2 | 9 | 2 | 0 | 2 | 0.00069% | 4,350,060 |
| 3 | 9 | 0 | 2 | 2 | 0.00069% | 4,350,060 |
| 4 | 2 | 9 | 2 | 0 | 0.00069% | 4,350,060 |
| 5 | 2 | 9 | 0 | 2 | 0.00069% | 4,350,060 |
| 6 | 2 | 2 | 9 | 0 | 0.00069% | 4,350,060 |
| 7 | 2 | 2 | 0 | 9 | 0.00069% | 4,350,060 |
| 8 | 2 | 0 | 9 | 2 | 0.00069% | 4,350,060 |
| 9 | 2 | 0 | 2 | 9 | 0.00069% | 4,350,060 |
| 10 | 0 | 9 | 2 | 2 | 0.00069% | 4,350,060 |
| 11 | 0 | 2 | 9 | 2 | 0.00069% | 4,350,060 |
| 12 | 0 | 2 | 2 | 9 | 0.00069% | 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 |
|---|---|---|---|---|---|---|
| 1 | 9 | 2 | 1 | 1 | 0.00148% | 9,425,130 |
| 2 | 9 | 1 | 2 | 1 | 0.00148% | 9,425,130 |
| 3 | 9 | 1 | 1 | 2 | 0.00148% | 9,425,130 |
| 4 | 2 | 9 | 1 | 1 | 0.00148% | 9,425,130 |
| 5 | 2 | 1 | 9 | 1 | 0.00148% | 9,425,130 |
| 6 | 2 | 1 | 1 | 9 | 0.00148% | 9,425,130 |
| 7 | 1 | 9 | 2 | 1 | 0.00148% | 9,425,130 |
| 8 | 1 | 9 | 1 | 2 | 0.00148% | 9,425,130 |
| 9 | 1 | 2 | 9 | 1 | 0.00148% | 9,425,130 |
| 10 | 1 | 2 | 1 | 9 | 0.00148% | 9,425,130 |
| 11 | 1 | 1 | 9 | 2 | 0.00148% | 9,425,130 |
| 12 | 1 | 1 | 2 | 9 | 0.00148% | 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 |
|---|---|---|---|---|---|---|
| 1 | 8 | 5 | 0 | 0 | 0.00026% | 1,656,369 |
| 2 | 8 | 0 | 5 | 0 | 0.00026% | 1,656,369 |
| 3 | 8 | 0 | 0 | 5 | 0.00026% | 1,656,369 |
| 4 | 5 | 8 | 0 | 0 | 0.00026% | 1,656,369 |
| 5 | 5 | 0 | 8 | 0 | 0.00026% | 1,656,369 |
| 6 | 5 | 0 | 0 | 8 | 0.00026% | 1,656,369 |
| 7 | 0 | 8 | 5 | 0 | 0.00026% | 1,656,369 |
| 8 | 0 | 8 | 0 | 5 | 0.00026% | 1,656,369 |
| 9 | 0 | 5 | 8 | 0 | 0.00026% | 1,656,369 |
| 10 | 0 | 5 | 0 | 8 | 0.00026% | 1,656,369 |
| 11 | 0 | 0 | 8 | 5 | 0.00026% | 1,656,369 |
| 12 | 0 | 0 | 5 | 8 | 0.00026% | 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 |
|---|---|---|---|---|---|---|
| 1 | 8 | 4 | 1 | 0 | 0.00188% | 11,962,665 |
| 2 | 8 | 4 | 0 | 1 | 0.00188% | 11,962,665 |
| 3 | 8 | 1 | 4 | 0 | 0.00188% | 11,962,665 |
| 4 | 8 | 1 | 0 | 4 | 0.00188% | 11,962,665 |
| 5 | 8 | 0 | 4 | 1 | 0.00188% | 11,962,665 |
| 6 | 8 | 0 | 1 | 4 | 0.00188% | 11,962,665 |
| 7 | 4 | 8 | 0 | 1 | 0.00188% | 11,962,665 |
| 8 | 4 | 8 | 1 | 0 | 0.00188% | 11,962,665 |
| 9 | 4 | 1 | 0 | 8 | 0.00188% | 11,962,665 |
| 10 | 4 | 1 | 8 | 0 | 0.00188% | 11,962,665 |
| 11 | 4 | 0 | 1 | 8 | 0.00188% | 11,962,665 |
| 12 | 4 | 0 | 8 | 1 | 0.00188% | 11,962,665 |
| 13 | 1 | 8 | 4 | 0 | 0.00188% | 11,962,665 |
| 14 | 1 | 8 | 0 | 4 | 0.00188% | 11,962,665 |
| 15 | 1 | 4 | 8 | 0 | 0.00188% | 11,962,665 |
| 16 | 1 | 4 | 0 | 8 | 0.00188% | 11,962,665 |
| 17 | 1 | 0 | 8 | 4 | 0.00188% | 11,962,665 |
| 18 | 1 | 0 | 4 | 8 | 0.00188% | 11,962,665 |
| 19 | 0 | 8 | 1 | 4 | 0.00188% | 11,962,665 |
| 20 | 0 | 8 | 4 | 1 | 0.00188% | 11,962,665 |
| 21 | 0 | 4 | 1 | 8 | 0.00188% | 11,962,665 |
| 22 | 0 | 4 | 8 | 1 | 0.00188% | 11,962,665 |
| 23 | 0 | 1 | 4 | 8 | 0.00188% | 11,962,665 |
| 24 | 0 | 1 | 8 | 4 | 0.00188% | 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 |
|---|---|---|---|---|---|---|
| 1 | 8 | 3 | 2 | 0 | 0.0045% | 28,710,396 |
| 2 | 8 | 3 | 0 | 2 | 0.0045% | 28,710,396 |
| 3 | 8 | 2 | 3 | 0 | 0.0045% | 28,710,396 |
| 4 | 8 | 2 | 0 | 3 | 0.0045% | 28,710,396 |
| 5 | 8 | 0 | 3 | 2 | 0.0045% | 28,710,396 |
| 6 | 8 | 0 | 2 | 3 | 0.0045% | 28,710,396 |
| 7 | 3 | 8 | 0 | 2 | 0.0045% | 28,710,396 |
| 8 | 3 | 8 | 2 | 0 | 0.0045% | 28,710,396 |
| 9 | 3 | 2 | 0 | 8 | 0.0045% | 28,710,396 |
| 10 | 3 | 2 | 8 | 0 | 0.0045% | 28,710,396 |
| 11 | 3 | 0 | 2 | 8 | 0.0045% | 28,710,396 |
| 12 | 3 | 0 | 8 | 2 | 0.0045% | 28,710,396 |
| 13 | 2 | 8 | 3 | 0 | 0.0045% | 28,710,396 |
| 14 | 2 | 8 | 0 | 3 | 0.0045% | 28,710,396 |
| 15 | 2 | 3 | 8 | 0 | 0.0045% | 28,710,396 |
| 16 | 2 | 3 | 0 | 8 | 0.0045% | 28,710,396 |
| 17 | 2 | 0 | 8 | 3 | 0.0045% | 28,710,396 |
| 18 | 2 | 0 | 3 | 8 | 0.0045% | 28,710,396 |
| 19 | 0 | 8 | 2 | 3 | 0.0045% | 28,710,396 |
| 20 | 0 | 8 | 3 | 2 | 0.0045% | 28,710,396 |
| 21 | 0 | 3 | 2 | 8 | 0.0045% | 28,710,396 |
| 22 | 0 | 3 | 8 | 2 | 0.0045% | 28,710,396 |
| 23 | 0 | 2 | 3 | 8 | 0.0045% | 28,710,396 |
| 24 | 0 | 2 | 8 | 3 | 0.0045% | 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 |
|---|---|---|---|---|---|---|
| 1 | 8 | 3 | 1 | 1 | 0.098% | 62,205,858 |
| 2 | 8 | 1 | 3 | 1 | 0.098% | 62,205,858 |
| 3 | 8 | 1 | 1 | 3 | 0.098% | 62,205,858 |
| 4 | 3 | 8 | 1 | 1 | 0.098% | 62,205,858 |
| 5 | 3 | 1 | 8 | 1 | 0.098% | 62,205,858 |
| 6 | 3 | 1 | 1 | 8 | 0.098% | 62,205,858 |
| 7 | 1 | 8 | 3 | 1 | 0.098% | 62,205,858 |
| 8 | 1 | 8 | 1 | 3 | 0.098% | 62,205,858 |
| 9 | 1 | 3 | 8 | 1 | 0.098% | 62,205,858 |
| 10 | 1 | 3 | 1 | 8 | 0.098% | 62,205,858 |
| 11 | 1 | 1 | 8 | 3 | 0.098% | 62,205,858 |
| 12 | 1 | 1 | 3 | 8 | 0.098% | 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 |
|---|---|---|---|---|---|---|
| 1 | 8 | 2 | 2 | 1 | 0.016% | 101,791,404 |
| 2 | 8 | 2 | 1 | 2 | 0.016% | 101,791,404 |
| 3 | 8 | 1 | 2 | 2 | 0.016% | 101,791,404 |
| 4 | 2 | 8 | 2 | 1 | 0.016% | 101,791,404 |
| 5 | 2 | 8 | 1 | 2 | 0.016% | 101,791,404 |
| 6 | 2 | 2 | 8 | 1 | 0.016% | 101,791,404 |
| 7 | 2 | 2 | 1 | 8 | 0.016% | 101,791,404 |
| 8 | 2 | 1 | 8 | 2 | 0.016% | 101,791,404 |
| 9 | 2 | 1 | 2 | 8 | 0.016% | 101,791,404 |
| 10 | 1 | 8 | 2 | 2 | 0.016% | 101,791,404 |
| 11 | 1 | 2 | 8 | 2 | 0.016% | 101,791,404 |
| 12 | 1 | 2 | 2 | 8 | 0.016% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 6 | 0 | 0 | 0.00046% | 2,944,656 |
| 2 | 7 | 0 | 6 | 0 | 0.00046% | 2,944,656 |
| 3 | 7 | 0 | 0 | 6 | 0.00046% | 2,944,656 |
| 4 | 6 | 7 | 0 | 0 | 0.00046% | 2,944,656 |
| 5 | 6 | 0 | 7 | 0 | 0.00046% | 2,944,656 |
| 6 | 6 | 0 | 0 | 7 | 0.00046% | 2,944,656 |
| 7 | 0 | 7 | 6 | 0 | 0.00046% | 2,944,656 |
| 8 | 0 | 7 | 0 | 6 | 0.00046% | 2,944,656 |
| 9 | 0 | 6 | 7 | 0 | 0.00046% | 2,944,656 |
| 10 | 0 | 6 | 0 | 7 | 0.00046% | 2,944,656 |
| 11 | 0 | 0 | 7 | 6 | 0.00046% | 2,944,656 |
| 12 | 0 | 0 | 6 | 7 | 0.00046% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 5 | 1 | 0 | 0.0045% | 28,710,396 |
| 2 | 7 | 5 | 0 | 1 | 0.0045% | 28,710,396 |
| 3 | 7 | 1 | 5 | 0 | 0.0045% | 28,710,396 |
| 4 | 7 | 1 | 0 | 5 | 0.0045% | 28,710,396 |
| 5 | 7 | 0 | 5 | 1 | 0.0045% | 28,710,396 |
| 6 | 7 | 0 | 1 | 5 | 0.0045% | 28,710,396 |
| 7 | 5 | 7 | 0 | 1 | 0.0045% | 28,710,396 |
| 8 | 5 | 7 | 1 | 0 | 0.0045% | 28,710,396 |
| 9 | 5 | 1 | 0 | 7 | 0.0045% | 28,710,396 |
| 10 | 5 | 1 | 7 | 0 | 0.0045% | 28,710,396 |
| 11 | 5 | 0 | 1 | 7 | 0.0045% | 28,710,396 |
| 12 | 5 | 0 | 7 | 1 | 0.0045% | 28,710,396 |
| 13 | 1 | 7 | 5 | 0 | 0.0045% | 28,710,396 |
| 14 | 1 | 7 | 0 | 5 | 0.0045% | 28,710,396 |
| 15 | 1 | 5 | 7 | 0 | 0.0045% | 28,710,396 |
| 16 | 1 | 5 | 0 | 7 | 0.0045% | 28,710,396 |
| 17 | 1 | 0 | 7 | 5 | 0.0045% | 28,710,396 |
| 18 | 1 | 0 | 5 | 7 | 0.0045% | 28,710,396 |
| 19 | 0 | 7 | 1 | 5 | 0.0045% | 28,710,396 |
| 20 | 0 | 7 | 5 | 1 | 0.0045% | 28,710,396 |
| 21 | 0 | 5 | 1 | 7 | 0.0045% | 28,710,396 |
| 22 | 0 | 5 | 7 | 1 | 0.0045% | 28,710,396 |
| 23 | 0 | 1 | 5 | 7 | 0.0045% | 28,710,396 |
| 24 | 0 | 1 | 7 | 5 | 0.0045% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 4 | 2 | 0 | 0.015% | 95,701,320 |
| 2 | 7 | 4 | 0 | 2 | 0.015% | 95,701,320 |
| 3 | 7 | 2 | 4 | 0 | 0.015% | 95,701,320 |
| 4 | 7 | 2 | 0 | 4 | 0.015% | 95,701,320 |
| 5 | 7 | 0 | 4 | 2 | 0.015% | 95,701,320 |
| 6 | 7 | 0 | 2 | 4 | 0.015% | 95,701,320 |
| 7 | 4 | 7 | 0 | 2 | 0.015% | 95,701,320 |
| 8 | 4 | 7 | 2 | 0 | 0.015% | 95,701,320 |
| 9 | 4 | 2 | 0 | 7 | 0.015% | 95,701,320 |
| 10 | 4 | 2 | 7 | 0 | 0.015% | 95,701,320 |
| 11 | 4 | 0 | 2 | 7 | 0.015% | 95,701,320 |
| 12 | 4 | 0 | 7 | 2 | 0.015% | 95,701,320 |
| 13 | 2 | 7 | 4 | 0 | 0.015% | 95,701,320 |
| 14 | 2 | 7 | 0 | 4 | 0.015% | 95,701,320 |
| 15 | 2 | 4 | 7 | 0 | 0.015% | 95,701,320 |
| 16 | 2 | 4 | 0 | 7 | 0.015% | 95,701,320 |
| 17 | 2 | 0 | 7 | 4 | 0.015% | 95,701,320 |
| 18 | 2 | 0 | 4 | 7 | 0.015% | 95,701,320 |
| 19 | 0 | 7 | 2 | 4 | 0.015% | 95,701,320 |
| 20 | 0 | 7 | 4 | 2 | 0.015% | 95,701,320 |
| 21 | 0 | 4 | 2 | 7 | 0.015% | 95,701,320 |
| 22 | 0 | 4 | 7 | 2 | 0.015% | 95,701,320 |
| 23 | 0 | 2 | 4 | 7 | 0.015% | 95,701,320 |
| 24 | 0 | 2 | 7 | 4 | 0.015% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 4 | 1 | 1 | 0.033% | 207,352,860 |
| 2 | 7 | 1 | 4 | 1 | 0.033% | 207,352,860 |
| 3 | 7 | 1 | 1 | 4 | 0.033% | 207,352,860 |
| 4 | 4 | 7 | 1 | 1 | 0.033% | 207,352,860 |
| 5 | 4 | 1 | 7 | 1 | 0.033% | 207,352,860 |
| 6 | 4 | 1 | 1 | 7 | 0.033% | 207,352,860 |
| 7 | 1 | 7 | 4 | 1 | 0.033% | 207,352,860 |
| 8 | 1 | 7 | 1 | 4 | 0.033% | 207,352,860 |
| 9 | 1 | 4 | 7 | 1 | 0.033% | 207,352,860 |
| 10 | 1 | 4 | 1 | 7 | 0.033% | 207,352,860 |
| 11 | 1 | 1 | 7 | 4 | 0.033% | 207,352,860 |
| 12 | 1 | 1 | 4 | 7 | 0.033% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 3 | 3 | 0 | 0.022% | 140,361,936 |
| 2 | 7 | 3 | 0 | 3 | 0.022% | 140,361,936 |
| 3 | 7 | 0 | 3 | 3 | 0.022% | 140,361,936 |
| 4 | 3 | 7 | 3 | 0 | 0.022% | 140,361,936 |
| 5 | 3 | 7 | 0 | 3 | 0.022% | 140,361,936 |
| 6 | 3 | 3 | 7 | 0 | 0.022% | 140,361,936 |
| 7 | 3 | 3 | 0 | 7 | 0.022% | 140,361,936 |
| 8 | 3 | 0 | 7 | 3 | 0.022% | 140,361,936 |
| 9 | 3 | 0 | 3 | 7 | 0.022% | 140,361,936 |
| 10 | 0 | 7 | 3 | 3 | 0.022% | 140,361,936 |
| 11 | 0 | 3 | 7 | 3 | 0.022% | 140,361,936 |
| 12 | 0 | 3 | 3 | 7 | 0.022% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 3 | 2 | 1 | 0.078% | 497,646,864 |
| 2 | 7 | 3 | 1 | 2 | 0.078% | 497,646,864 |
| 3 | 7 | 2 | 3 | 1 | 0.078% | 497,646,864 |
| 4 | 7 | 2 | 1 | 3 | 0.078% | 497,646,864 |
| 5 | 7 | 1 | 3 | 2 | 0.078% | 497,646,864 |
| 6 | 7 | 1 | 2 | 3 | 0.078% | 497,646,864 |
| 7 | 3 | 7 | 1 | 2 | 0.078% | 497,646,864 |
| 8 | 3 | 7 | 2 | 1 | 0.078% | 497,646,864 |
| 9 | 3 | 2 | 1 | 7 | 0.078% | 497,646,864 |
| 10 | 3 | 2 | 7 | 1 | 0.078% | 497,646,864 |
| 11 | 3 | 1 | 2 | 7 | 0.078% | 497,646,864 |
| 12 | 3 | 1 | 7 | 2 | 0.078% | 497,646,864 |
| 13 | 2 | 7 | 3 | 1 | 0.078% | 497,646,864 |
| 14 | 2 | 7 | 1 | 3 | 0.078% | 497,646,864 |
| 15 | 2 | 3 | 7 | 1 | 0.078% | 497,646,864 |
| 16 | 2 | 3 | 1 | 7 | 0.078% | 497,646,864 |
| 17 | 2 | 1 | 7 | 3 | 0.078% | 497,646,864 |
| 18 | 2 | 1 | 3 | 7 | 0.078% | 497,646,864 |
| 19 | 1 | 7 | 2 | 3 | 0.078% | 497,646,864 |
| 20 | 1 | 7 | 3 | 2 | 0.078% | 497,646,864 |
| 21 | 1 | 3 | 2 | 7 | 0.078% | 497,646,864 |
| 22 | 1 | 3 | 7 | 2 | 0.078% | 497,646,864 |
| 23 | 1 | 2 | 3 | 7 | 0.078% | 497,646,864 |
| 24 | 1 | 2 | 7 | 3 | 0.078% | 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 |
|---|---|---|---|---|---|---|
| 1 | 7 | 2 | 2 | 2 | 0.128% | 814,331,232 |
| 2 | 2 | 7 | 2 | 2 | 0.128% | 814,331,232 |
| 3 | 2 | 2 | 7 | 2 | 0.128% | 814,331,232 |
| 4 | 2 | 2 | 2 | 7 | 0.128% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 6 | 1 | 0 | 0.006% | 38,280,528 |
| 2 | 6 | 6 | 0 | 1 | 0.006% | 38,280,528 |
| 3 | 6 | 1 | 6 | 0 | 0.006% | 38,280,528 |
| 4 | 6 | 1 | 0 | 6 | 0.006% | 38,280,528 |
| 5 | 6 | 0 | 6 | 1 | 0.006% | 38,280,528 |
| 6 | 6 | 0 | 1 | 6 | 0.006% | 38,280,528 |
| 7 | 1 | 6 | 6 | 0 | 0.006% | 38,280,528 |
| 8 | 1 | 6 | 0 | 6 | 0.006% | 38,280,528 |
| 9 | 1 | 0 | 6 | 6 | 0.006% | 38,280,528 |
| 10 | 0 | 6 | 6 | 1 | 0.006% | 38,280,528 |
| 11 | 0 | 6 | 1 | 6 | 0.006% | 38,280,528 |
| 12 | 0 | 1 | 6 | 6 | 0.006% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 5 | 2 | 0 | 0.027% | 172,262,376 |
| 2 | 6 | 5 | 0 | 2 | 0.027% | 172,262,376 |
| 3 | 6 | 2 | 5 | 0 | 0.027% | 172,262,376 |
| 4 | 6 | 2 | 0 | 5 | 0.027% | 172,262,376 |
| 5 | 6 | 0 | 5 | 2 | 0.027% | 172,262,376 |
| 6 | 6 | 0 | 2 | 5 | 0.027% | 172,262,376 |
| 7 | 5 | 6 | 0 | 2 | 0.027% | 172,262,376 |
| 8 | 5 | 6 | 2 | 0 | 0.027% | 172,262,376 |
| 9 | 5 | 2 | 0 | 6 | 0.027% | 172,262,376 |
| 10 | 5 | 2 | 6 | 0 | 0.027% | 172,262,376 |
| 11 | 5 | 0 | 2 | 6 | 0.027% | 172,262,376 |
| 12 | 5 | 0 | 6 | 2 | 0.027% | 172,262,376 |
| 13 | 2 | 6 | 5 | 0 | 0.027% | 172,262,376 |
| 14 | 2 | 6 | 0 | 5 | 0.027% | 172,262,376 |
| 15 | 2 | 5 | 6 | 0 | 0.027% | 172,262,376 |
| 16 | 2 | 5 | 0 | 6 | 0.027% | 172,262,376 |
| 17 | 2 | 0 | 6 | 5 | 0.027% | 172,262,376 |
| 18 | 2 | 0 | 5 | 6 | 0.027% | 172,262,376 |
| 19 | 0 | 6 | 2 | 5 | 0.027% | 172,262,376 |
| 20 | 0 | 6 | 5 | 2 | 0.027% | 172,262,376 |
| 21 | 0 | 5 | 2 | 6 | 0.027% | 172,262,376 |
| 22 | 0 | 5 | 6 | 2 | 0.027% | 172,262,376 |
| 23 | 0 | 2 | 5 | 6 | 0.027% | 172,262,376 |
| 24 | 0 | 2 | 6 | 5 | 0.027% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 5 | 1 | 1 | 0.059% | 373,235,148 |
| 2 | 6 | 1 | 5 | 1 | 0.059% | 373,235,148 |
| 3 | 6 | 1 | 1 | 5 | 0.059% | 373,235,148 |
| 4 | 5 | 6 | 1 | 1 | 0.059% | 373,235,148 |
| 5 | 5 | 1 | 6 | 1 | 0.059% | 373,235,148 |
| 6 | 5 | 1 | 1 | 6 | 0.059% | 373,235,148 |
| 7 | 1 | 6 | 5 | 1 | 0.059% | 373,235,148 |
| 8 | 1 | 6 | 1 | 5 | 0.059% | 373,235,148 |
| 9 | 1 | 5 | 6 | 1 | 0.059% | 373,235,148 |
| 10 | 1 | 5 | 1 | 6 | 0.059% | 373,235,148 |
| 11 | 1 | 1 | 6 | 5 | 0.059% | 373,235,148 |
| 12 | 1 | 1 | 5 | 6 | 0.059% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 4 | 3 | 0 | 0.055% | 350,904,840 |
| 2 | 6 | 4 | 0 | 3 | 0.055% | 350,904,840 |
| 3 | 6 | 3 | 4 | 0 | 0.055% | 350,904,840 |
| 4 | 6 | 3 | 0 | 4 | 0.055% | 350,904,840 |
| 5 | 6 | 0 | 4 | 3 | 0.055% | 350,904,840 |
| 6 | 6 | 0 | 3 | 4 | 0.055% | 350,904,840 |
| 7 | 4 | 6 | 0 | 3 | 0.055% | 350,904,840 |
| 8 | 4 | 6 | 3 | 0 | 0.055% | 350,904,840 |
| 9 | 4 | 3 | 0 | 6 | 0.055% | 350,904,840 |
| 10 | 4 | 3 | 6 | 0 | 0.055% | 350,904,840 |
| 11 | 4 | 0 | 3 | 6 | 0.055% | 350,904,840 |
| 12 | 4 | 0 | 6 | 3 | 0.055% | 350,904,840 |
| 13 | 3 | 6 | 4 | 0 | 0.055% | 350,904,840 |
| 14 | 3 | 6 | 0 | 4 | 0.055% | 350,904,840 |
| 15 | 3 | 4 | 6 | 0 | 0.055% | 350,904,840 |
| 16 | 3 | 4 | 0 | 6 | 0.055% | 350,904,840 |
| 17 | 3 | 0 | 6 | 4 | 0.055% | 350,904,840 |
| 18 | 3 | 0 | 4 | 6 | 0.055% | 350,904,840 |
| 19 | 0 | 6 | 3 | 4 | 0.055% | 350,904,840 |
| 20 | 0 | 6 | 4 | 3 | 0.055% | 350,904,840 |
| 21 | 0 | 4 | 3 | 6 | 0.055% | 350,904,840 |
| 22 | 0 | 4 | 6 | 3 | 0.055% | 350,904,840 |
| 23 | 0 | 3 | 4 | 6 | 0.055% | 350,904,840 |
| 24 | 0 | 3 | 6 | 4 | 0.055% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 4 | 2 | 1 | 0.196% | 1,244,117,160 |
| 2 | 6 | 4 | 1 | 2 | 0.196% | 1,244,117,160 |
| 3 | 6 | 2 | 4 | 1 | 0.196% | 1,244,117,160 |
| 4 | 6 | 2 | 1 | 4 | 0.196% | 1,244,117,160 |
| 5 | 6 | 1 | 4 | 2 | 0.196% | 1,244,117,160 |
| 6 | 6 | 1 | 2 | 4 | 0.196% | 1,244,117,160 |
| 7 | 4 | 6 | 1 | 2 | 0.196% | 1,244,117,160 |
| 8 | 4 | 6 | 2 | 1 | 0.196% | 1,244,117,160 |
| 9 | 4 | 2 | 1 | 6 | 0.196% | 1,244,117,160 |
| 10 | 4 | 2 | 6 | 1 | 0.196% | 1,244,117,160 |
| 11 | 4 | 1 | 2 | 6 | 0.196% | 1,244,117,160 |
| 12 | 4 | 1 | 6 | 2 | 0.196% | 1,244,117,160 |
| 13 | 2 | 6 | 4 | 1 | 0.196% | 1,244,117,160 |
| 14 | 2 | 6 | 1 | 4 | 0.196% | 1,244,117,160 |
| 15 | 2 | 4 | 6 | 1 | 0.196% | 1,244,117,160 |
| 16 | 2 | 4 | 1 | 6 | 0.196% | 1,244,117,160 |
| 17 | 2 | 1 | 6 | 4 | 0.196% | 1,244,117,160 |
| 18 | 2 | 1 | 4 | 6 | 0.196% | 1,244,117,160 |
| 19 | 1 | 6 | 2 | 4 | 0.196% | 1,244,117,160 |
| 20 | 1 | 6 | 4 | 2 | 0.196% | 1,244,117,160 |
| 21 | 1 | 4 | 2 | 6 | 0.196% | 1,244,117,160 |
| 22 | 1 | 4 | 6 | 2 | 0.196% | 1,244,117,160 |
| 23 | 1 | 2 | 4 | 6 | 0.196% | 1,244,117,160 |
| 24 | 1 | 2 | 6 | 4 | 0.196% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 3 | 3 | 1 | 0.287% | 1,824,705,168 |
| 2 | 6 | 3 | 1 | 3 | 0.287% | 1,824,705,168 |
| 3 | 6 | 1 | 3 | 3 | 0.287% | 1,824,705,168 |
| 4 | 3 | 6 | 3 | 1 | 0.287% | 1,824,705,168 |
| 5 | 3 | 6 | 1 | 3 | 0.287% | 1,824,705,168 |
| 6 | 3 | 3 | 6 | 1 | 0.287% | 1,824,705,168 |
| 7 | 3 | 3 | 1 | 6 | 0.287% | 1,824,705,168 |
| 8 | 3 | 1 | 6 | 3 | 0.287% | 1,824,705,168 |
| 9 | 3 | 1 | 3 | 6 | 0.287% | 1,824,705,168 |
| 10 | 1 | 6 | 3 | 3 | 0.287% | 1,824,705,168 |
| 11 | 1 | 3 | 6 | 3 | 0.287% | 1,824,705,168 |
| 12 | 1 | 3 | 3 | 6 | 0.287% | 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 |
|---|---|---|---|---|---|---|
| 1 | 6 | 3 | 2 | 2 | 0.47% | 2,985,881,184 |
| 2 | 6 | 2 | 3 | 2 | 0.47% | 2,985,881,184 |
| 3 | 6 | 2 | 2 | 3 | 0.47% | 2,985,881,184 |
| 4 | 3 | 6 | 2 | 2 | 0.47% | 2,985,881,184 |
| 5 | 3 | 2 | 6 | 2 | 0.47% | 2,985,881,184 |
| 6 | 3 | 2 | 2 | 6 | 0.47% | 2,985,881,184 |
| 7 | 2 | 6 | 3 | 2 | 0.47% | 2,985,881,184 |
| 8 | 2 | 6 | 2 | 3 | 0.47% | 2,985,881,184 |
| 9 | 2 | 3 | 6 | 2 | 0.47% | 2,985,881,184 |
| 10 | 2 | 3 | 2 | 6 | 0.47% | 2,985,881,184 |
| 11 | 2 | 2 | 6 | 3 | 0.47% | 2,985,881,184 |
| 12 | 2 | 2 | 3 | 6 | 0.47% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 5 | 3 | 0 | 0.075% | 473,721,534 |
| 2 | 5 | 5 | 0 | 3 | 0.075% | 473,721,534 |
| 3 | 5 | 3 | 5 | 0 | 0.075% | 473,721,534 |
| 4 | 5 | 3 | 0 | 5 | 0.075% | 473,721,534 |
| 5 | 5 | 0 | 5 | 3 | 0.075% | 473,721,534 |
| 6 | 5 | 0 | 3 | 5 | 0.075% | 473,721,534 |
| 7 | 3 | 5 | 5 | 0 | 0.075% | 473,721,534 |
| 8 | 3 | 5 | 0 | 5 | 0.075% | 473,721,534 |
| 9 | 3 | 0 | 5 | 5 | 0.075% | 473,721,534 |
| 10 | 0 | 5 | 5 | 3 | 0.075% | 473,721,534 |
| 11 | 0 | 5 | 3 | 5 | 0.075% | 473,721,534 |
| 12 | 0 | 3 | 5 | 5 | 0.075% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 5 | 2 | 1 | 0.264% | 1,679,558,166 |
| 2 | 5 | 5 | 1 | 2 | 0.264% | 1,679,558,166 |
| 3 | 5 | 2 | 5 | 1 | 0.264% | 1,679,558,166 |
| 4 | 5 | 2 | 1 | 5 | 0.264% | 1,679,558,166 |
| 5 | 5 | 1 | 5 | 2 | 0.264% | 1,679,558,166 |
| 6 | 5 | 1 | 2 | 5 | 0.264% | 1,679,558,166 |
| 7 | 2 | 5 | 5 | 1 | 0.264% | 1,679,558,166 |
| 8 | 2 | 5 | 1 | 5 | 0.264% | 1,679,558,166 |
| 9 | 2 | 1 | 5 | 5 | 0.264% | 1,679,558,166 |
| 10 | 1 | 5 | 5 | 2 | 0.264% | 1,679,558,166 |
| 11 | 1 | 5 | 2 | 5 | 0.264% | 1,679,558,166 |
| 12 | 1 | 2 | 5 | 5 | 0.264% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 4 | 4 | 0 | 0.1% | 657,946,575 |
| 2 | 5 | 4 | 0 | 4 | 0.1% | 657,946,575 |
| 3 | 5 | 0 | 4 | 4 | 0.1% | 657,946,575 |
| 4 | 4 | 5 | 4 | 0 | 0.1% | 657,946,575 |
| 5 | 4 | 5 | 0 | 4 | 0.1% | 657,946,575 |
| 6 | 4 | 4 | 5 | 0 | 0.1% | 657,946,575 |
| 7 | 4 | 4 | 0 | 5 | 0.1% | 657,946,575 |
| 8 | 4 | 0 | 5 | 4 | 0.1% | 657,946,575 |
| 9 | 4 | 0 | 4 | 5 | 0.1% | 657,946,575 |
| 10 | 0 | 5 | 4 | 4 | 0.1% | 657,946,575 |
| 11 | 0 | 4 | 5 | 4 | 0.1% | 657,946,575 |
| 12 | 0 | 4 | 4 | 5 | 0.1% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 4 | 3 | 1 | 0.54% | 3,421,322,190 |
| 2 | 5 | 4 | 1 | 3 | 0.54% | 3,421,322,190 |
| 3 | 5 | 3 | 4 | 1 | 0.54% | 3,421,322,190 |
| 4 | 5 | 3 | 1 | 4 | 0.54% | 3,421,322,190 |
| 5 | 5 | 1 | 4 | 3 | 0.54% | 3,421,322,190 |
| 6 | 5 | 1 | 3 | 4 | 0.54% | 3,421,322,190 |
| 7 | 4 | 5 | 1 | 3 | 0.54% | 3,421,322,190 |
| 8 | 4 | 5 | 3 | 1 | 0.54% | 3,421,322,190 |
| 9 | 4 | 3 | 1 | 5 | 0.54% | 3,421,322,190 |
| 10 | 4 | 3 | 5 | 1 | 0.54% | 3,421,322,190 |
| 11 | 4 | 1 | 3 | 5 | 0.54% | 3,421,322,190 |
| 12 | 4 | 1 | 5 | 3 | 0.54% | 3,421,322,190 |
| 13 | 3 | 5 | 4 | 1 | 0.54% | 3,421,322,190 |
| 14 | 3 | 5 | 1 | 4 | 0.54% | 3,421,322,190 |
| 15 | 3 | 4 | 5 | 1 | 0.54% | 3,421,322,190 |
| 16 | 3 | 4 | 1 | 5 | 0.54% | 3,421,322,190 |
| 17 | 3 | 1 | 5 | 4 | 0.54% | 3,421,322,190 |
| 18 | 3 | 1 | 4 | 5 | 0.54% | 3,421,322,190 |
| 19 | 1 | 5 | 3 | 4 | 0.54% | 3,421,322,190 |
| 20 | 1 | 5 | 4 | 3 | 0.54% | 3,421,322,190 |
| 21 | 1 | 4 | 3 | 5 | 0.54% | 3,421,322,190 |
| 22 | 1 | 4 | 5 | 3 | 0.54% | 3,421,322,190 |
| 23 | 1 | 3 | 4 | 5 | 0.54% | 3,421,322,190 |
| 24 | 1 | 3 | 5 | 4 | 0.54% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 4 | 2 | 2 | 0.88% | 5,598,527,220 |
| 2 | 5 | 2 | 4 | 2 | 0.88% | 5,598,527,220 |
| 3 | 5 | 2 | 2 | 4 | 0.88% | 5,598,527,220 |
| 4 | 4 | 5 | 2 | 2 | 0.88% | 5,598,527,220 |
| 5 | 4 | 2 | 5 | 2 | 0.88% | 5,598,527,220 |
| 6 | 4 | 2 | 2 | 5 | 0.88% | 5,598,527,220 |
| 7 | 2 | 5 | 4 | 2 | 0.88% | 5,598,527,220 |
| 8 | 2 | 5 | 2 | 4 | 0.88% | 5,598,527,220 |
| 9 | 2 | 4 | 5 | 2 | 0.88% | 5,598,527,220 |
| 10 | 2 | 4 | 2 | 5 | 0.88% | 5,598,527,220 |
| 11 | 2 | 2 | 5 | 4 | 0.88% | 5,598,527,220 |
| 12 | 2 | 2 | 4 | 5 | 0.88% | 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 |
|---|---|---|---|---|---|---|
| 1 | 5 | 3 | 3 | 2 | 1.29% | 8,211,173,256 |
| 2 | 5 | 3 | 2 | 3 | 1.29% | 8,211,173,256 |
| 3 | 5 | 2 | 3 | 3 | 1.29% | 8,211,173,256 |
| 4 | 3 | 5 | 3 | 2 | 1.29% | 8,211,173,256 |
| 5 | 3 | 5 | 2 | 3 | 1.29% | 8,211,173,256 |
| 6 | 3 | 3 | 5 | 2 | 1.29% | 8,211,173,256 |
| 7 | 3 | 3 | 2 | 5 | 1.29% | 8,211,173,256 |
| 8 | 3 | 2 | 5 | 3 | 1.29% | 8,211,173,256 |
| 9 | 3 | 2 | 3 | 5 | 1.29% | 8,211,173,256 |
| 10 | 2 | 5 | 3 | 3 | 1.29% | 8,211,173,256 |
| 11 | 2 | 3 | 5 | 3 | 1.29% | 8,211,173,256 |
| 12 | 2 | 3 | 3 | 5 | 1.29% | 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 |
|---|---|---|---|---|---|---|
| 1 | 4 | 1 | 4 | 4 | 0.75% | 4,751,836,375 |
| 2 | 4 | 4 | 1 | 4 | 0.75% | 4,751,836,375 |
| 3 | 4 | 4 | 4 | 1 | 0.75% | 4,751,836,375 |
| 4 | 1 | 4 | 4 | 4 | 0.75% | 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 |
|---|---|---|---|---|---|---|
| 1 | 4 | 4 | 3 | 2 | 1.796% | 11,404,407,300 |
| 2 | 4 | 4 | 2 | 3 | 1.796% | 11,404,407,300 |
| 3 | 4 | 3 | 4 | 2 | 1.796% | 11,404,407,300 |
| 4 | 4 | 3 | 2 | 4 | 1.796% | 11,404,407,300 |
| 5 | 4 | 2 | 4 | 3 | 1.796% | 11,404,407,300 |
| 6 | 4 | 2 | 3 | 4 | 1.796% | 11,404,407,300 |
| 7 | 3 | 4 | 4 | 2 | 1.796% | 11,404,407,300 |
| 8 | 3 | 4 | 2 | 4 | 1.796% | 11,404,407,300 |
| 9 | 3 | 2 | 4 | 4 | 1.796% | 11,404,407,300 |
| 10 | 2 | 4 | 4 | 3 | 1.796% | 11,404,407,300 |
| 11 | 2 | 4 | 3 | 4 | 1.796% | 11,404,407,300 |
| 12 | 2 | 3 | 4 | 4 | 1.796% | 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 |
|---|---|---|---|---|---|---|
| 1 | 4 | 3 | 3 | 3 | 2.63% | 16,726,464,040 |
| 2 | 3 | 4 | 3 | 3 | 2.63% | 16,726,464,040 |
| 3 | 3 | 3 | 4 | 3 | 2.63% | 16,726,464,040 |
| 4 | 3 | 3 | 3 | 4 | 2.63% | 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
