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The statistics of the 39 types of hand distributions in Bridge are very important to get the best result for playing, bidding and defence in the long run. So, for a better Bridge player, it is a must to know them. You might not have to remember the exact number, however, getting to know the relative occurrences of each type will help to determine the best contract during bidding, help the declarer plays, even help the defence.

If you are wondering how it will help, to put it differently, Bridge players always make an educated guess of the hidden hand. So, for example, knowing that 7-2-2-2 are much less common than 6-3-3-2 will obviously help if the bidding shed no information.

Firstly, let us start with the fact that there are more than 600 trillion possibilities of getting a set of 13 cards when you play bridge. Hence, unless we already play much more than 600 trillion times, the chance is that we will never see most of them.

With that number in mind, it is a good thing that we don’t really have to deal with 650 trillion kinds of rules/guideline as they can be categorized into only 39 types of hands distribution.

Sorted by Distribution: The 39 Types of Hand Distributions

The table below is just showing you the systematic listing of all possible hand. So from the super rare 13-0-0-0 to the most balance hand 4-3-3-3. No need to remember anything from the table except that you are certain that there are indeed 39 types of hands.

With more than 7-cards in a suit

DistributionProbability Total Hands
1:13 – 0 – 0 – 0<0.1%4
2:12 – 1 – 0 – 0<0.1%2,028
3:11 – 2 – 0 – 0<0.1%73,008
4:11 – 1 – 1 – 0<0.1%158,184
5:10 – 3 – 0 – 0<0.1%981,552
6:10 – 2 – 1 – 0<0.1%6,960,096
7:10 – 1 – 1 – 1<0.1%2,513,368
8:9 – 4 – 0 – 0<0.1%6,134,700
9:9 – 3 – 1 – 0<0.1%63,800,880
10:9 – 2 – 2 – 0<0.1%52,200,720
11:9 – 2 – 1 – 1<0.1%113,101,560
12:8 – 5 – 0 – 0<0.1%19,876,428
13:8 – 4 – 1 – 0<0.1%287,103,960
14:8 – 3 – 2 – 00.1%689,049,504
15:8 – 3 – 1 – 10.1%746,470,296
16:8 – 2 – 2 – 10.2%1,221,496,848
17:7 – 6 – 0 – 0<0.1%35,335,872
18:7 – 5 – 1 – 00.1%689,049,504
19:7 – 4 – 2 – 00.4%2,296,831,680
20:7 – 4 – 1 – 10.4%2,488,234,320
21:7 – 3 – 3 – 00.3%1,684,343,232
22:7 – 3 – 2 – 11.9%11,943,524,736
23:7 – 2 – 2 – 20.5%3,257,324,928
Total:4%25,604,567,408

With less than 7-cards in a suit

DistributionProbability Total Hands
24:6 – 6 – 1 – 00.1%459,366,336
25:6 – 5 – 2 – 00.7%4,134,297,024
26:6 – 5 – 1 – 10.7%4,478,821,776
27:6 – 4 – 3 – 01.3%8,421,716,160
28:6 – 4 – 2 – 14.7%29,858,811,840
29:6 – 3 – 3 – 13.4%21,896,462,016
30:6 – 3 – 2 – 25.6%35,830,574,208
31:5 – 5 – 3 – 00.9%5,684,658,408
26:8 – 4 – 1 – 0<0.1%287,103,960
27:9 – 2 – 1 – 1<0.1%113,101,560
28:9 – 3 – 1 – 0<0.1%63,800,880
29:9 – 2 – 2 – 0<0.1%52,200,720
30:7 – 6 – 0 – 0<0.1%35,335,872
31:8 – 5 – 0 – 0<0.1%19,876,428
32:5 – 5 – 2 – 13.2%20,154,697,992
33:5 – 4 – 4 – 01.2%7,895,358,900
34:5 – 4 – 3 – 112.9%82,111,732,560
35:5 – 4 – 2 – 210.6%67,182,326,640
36:5 – 3 – 3 – 215.5%98,534,079,072
37:4 – 4 – 4 – 13.0%19,007,345,500
38:4 – 4 – 3 – 221.6%136,852,887,600
39:4 – 3 – 3 – 310.5%66,905,856,160
 Total96%609,408,992,192

Sorted by Percentage: The 39 Types of Hand Distributions

The tables below are more important. Basically it is the same as the above table, only it is sorted by the probability of occurring based on the possible combination. Try to remember the first part: The Top 10.

The Top-10

As you can see below, the top-10 of the distribution list made up of more than 90% of the whole combination. So, knowing what they are is very handy.

DistributionProbability Total Hands
1:4 – 4 – 3 – 221.6%132,852,887,600
2:5 – 3 – 3 – 215.5%98,534,079,072
3:5 – 4 – 3 – 112.9%82,111,732,560
4:5 – 4 – 2 – 210.6%67,182,326,640
5:4 – 3 – 3 – 310.5%66,905,856,160
6:6 – 3 – 2 – 25.6%35,830,574,208
7;6 – 4 – 2 – 14.7%29,858,811,840
8;6 – 3 – 3 – 13.4%21,896,462,016
9:5 – 5 – 2 – 13.2%20,154,697,992
10:4 – 4 – 4 – 13.0%19,007,345,500
 Total90.4%574,334,773,588

The Rest

The rest of the distribution is quite rare. So, just be aware of the trend, not the actual number.

DistributionProbability Total Hands
11:7 – 3 – 2 – 11.9%11,943,524,736
12:6 – 4 – 3 – 01.3%8,421,716,160
13:5 – 4 – 4 – 01.2%7,895,358,900
14:5 – 5 – 3 – 00.9%5,684,658,408
15:6 – 5 – 1 – 10.7%4,478,821,776
16:6 – 5 – 2 – 00.7%4,134,297,024
17:7 – 2 – 2 – 20.5%3,257,324,928
18:7 – 4 – 1 – 10.4%2,488,234,320
19:7 – 4 – 2 – 00.4%2,296,831,680
20:7 – 3 – 3 – 00.3%1,684,343,232
21:8 – 2 – 2 – 10.2%1,221,496,848
22:8 – 3 – 1 – 10.1%746,470,296
23:8 – 3 – 2 – 00.1%689,049,504
24:7 – 5 – 1 – 00.1%689,049,504
25:6 – 6 – 1 – 00.1%459,366,336
32:10 – 2 – 1 – 0<0.1%6,960,096
33:9 – 4 – 0 – 0<0.1%6,134,700
34:10 – 1 – 1 – 1<0.1%2,513,368
35;10 – 3 – 0 – 0<0.1%981,552
36:11 – 1 – 1 – 0<0.1%158,184
37:11 – 2 – 0 – 0<0.1%73,008
38:12 – 1 – 0 – 0<0.1%2,028
39:13 – 0 – 0 – 0<0.1%4
 Total9.6%60,678,786,012

References: The Most Important Formula In Bridge

Important Takeout:

From the tables above, we can observe some of the important facts:

  • The most common distribution is 4-4-3-2 with 21.6% probability.
  • Despite the flattest, 4-3-3-3 distribution in only the fifth most common distribution with 10.5% odds.
  • Hands with longer suit will be less likely than the shorter one
  • But hand with a void is also less likely than the one without void
  • The probability is higher toward “flatness”, i.e: make it more even, but not to even.

The 39 Types of Hand Distributions Into 5 Groups

Don’t feel overwhelmed! To make it even easier, we can manage the 39 types of hand distribution into 5 groups categories. In no particular order, they are:

1. Balanced hand (Total 47.6%)

DistributionProbability Total Hands
1:5 – 3 – 3 – 215.5%98,534,079,072
2:4 – 4 – 3 – 221.6%136,852,887,600
3:4 – 3 – 3 – 310.5%66,905,856,160
TOTAL:47.6% 

You probably argue that 5-3-3-2 is not balanced. Yes, it’s more accurate to be defined as “semi-balanced”. But what you rebid with that hand? We need to treat 5-3-3-2 as balanced as you cannot really re-bid with another suit.

A rebid of the same suit should promise at least an additional card of that suit. But there is no other 4-cards suit to bid. Hence, treating it as balanced similar to 4-3-3-3 is probably the best treatment.

This category is the biggest group of all. It accounts of almost half of all the hand that you play. So, very familiar with the bidding for balanced hand should be the priority of your bidding system. If you do that first , at least 1 out of 2 hands that you play will be covered.

Please note that the highest hand probability of distribution is not 4-3-3-3 (only 10.5%) but 4-4-3-2 (21.6%). So, start your bidding system discussion with your partner on balanced hand sequence first!

Note that category (3.3.1) below (5422 distribution) may have similarity in regard to bidding the distribution.

2. Three Suiter Hand (Total 4.24%)

DistributionProbability Total Hands
1:5 – 4 – 4 – 01.2%7,895,358,900
2:4 – 4 – 4 – 13.0%19,007,345,500
TOTAL:4.24% 

Three suiters hands are quite notoriously difficult to bid/rebid during “normal” bidding and sometimes the partnership may miss the fit on the third suits. Therefore, some bidding system is actually treating this distribution seriously and creating a special opening bid or sequence just to cater to this type of distribution.

The odds of happening is one for every 25 boards.

Note that category (3.3.2) below (5431 distribution) may have similarity in regard to bidding the distribution.

3. Two-Suiter Hand

3.1. Two-suiter hand with 54+ (Total: 35.90%)

DistributionProbability Total Hands
1:9 – 4 – 0 – 0<0.1%6,134,700
2:8 – 5 – 0 – 0<0.1%19,876,428
3:8 – 4 – 1 – 0<0.1%287,103,960
4:7 – 6 – 0 – 0<0.1%35,335,872
5:7 – 5 – 1 – 00.1%689,049,504
6:7 – 4 – 2 – 00.4%2,296,831,680
7:7 – 4 – 1 – 10.4%2,488,234,320
8:6 – 6 – 1 – 00.1%459,366,336
9:6 – 5 – 2 – 00.7%4,134,297,024
10:6 – 5 – 1 – 10.7%4,478,821,776
11:6 – 4 – 3 – 01.3%8,421,716,160
12:6 – 4 – 2 – 14.7%29,858,811,840
13:5 – 5 – 3 – 00.9%5,684,658,408
14:5 – 5 – 2 – 13.2%20,154,697,992
15:5 – 4 – 3 – 112.9%82,111,732,560
16:5 – 4 – 2 – 210.6%67,182,326,640
TOTAL:35.90% 

Any hand distribution with 5+cards in 1 suit and 4+ cards in another suit, I consider them as two-suiter hand.

This group is responsible for more than 1/3 of all hand that you play. Hence, careful bidding as to how to rebid both suits is very important to make sure you play at the correct level. 

3.2. Two-Suiter hand with 55+ (Total: 5.7+%)

DistributionProbability Total Hands
1:8 – 5 – 0 – 0<0.1%19,876,428
2:7 – 6 – 0 – 0<0.1%35,335,872
3:7 – 5 – 1 – 00.1%689,049,504
4:6 – 6 – 1 – 00.1%459,366,336
5:6 – 5 – 2 – 00.7%4,134,297,024
6:6 – 5 – 1 – 10.7%4,478,821,776
7:5 – 5 – 3 – 00.9%5,684,658,408
8:5 – 5 – 2 – 13.2%20,154,697,992
TOTAL:>5.7% 

If we narrow down the 2-suiter hand to have a minimum of 5-5 suit, the table would be as on the right.

3.3. Two-Suiter hand with 5+4

The distribution with 4-cards second suit and longer first suit can be re-group as follows:

  1. (5422) can be grouped as (semi) balanced (Total: 10.6%)
  2. (5431) can be grouped as (almost) 3-suiter (Total: 12.9%)
  3. (6+4xx) can be grouped as 1-suiter (Total: 6.9%)

4. One-Suiter Hand (Total: 12.17%)

DistributionProbability Total Hands
1:8 – 3 – 2 – 00.1%689,049,504
2:8 – 3 – 1 – 10.1%746,470,296
3:8 – 2 – 2 – 10.2%1,221,496,848
4:7 – 3 – 3 – 00.3%1,684,343,232
5:7 – 3 – 2 – 11.9%11,943,524,736
6:7 – 2 – 2 – 20.5%3,257,324,928
7:6 – 3 – 3 – 13.4%21,896,462,016
8:6 – 3 – 2 – 25.6%35,830,574,208
TOTAL:12.17% 

One-suiter hand with 6 to 8 cards in one hand account for 12.17% of the possibility. That’s roughly 1 for every 8 boards.

Note that category (3.3.3) above (6+4xx distribution) may have similarity in regard to bidding the distribution.

5. Extreme 1 Suiter (Total: 0.04%)

DistributionProbability Total Hands
1:13 – 0 – 0 – 0<0.1%4
2:12 – 1 – 0 – 0<0.1%2,028
3:11 – 2 – 0 – 0<0.1%73,008
4:11 – 1 – 1 – 0<0.1%158,184
5:10 – 3 – 0 – 0<0.1%981,552
6:10 – 2 – 1 – 0<0.1%6,960,096
7:10 – 1 – 1 – 1<0.1%2,513,368
8:9 – 3 – 1 – 0<0.1%63,800,880
9:9 – 2 – 2 – 0<0.1%52,200,720
10:9 – 2 – 1 – 1<0.1%113,101,560
TOTAL:0.04% 

There are 10 types of distribution that include a nine-carder hand. The statistical probability is similar to play 2500 boards before you meet one.

There is more to the 39 types of hand distributions

Further detail of what presented here can be further explored and study. You might not see the importance now. But in one of those moments in the future, you will just know:

39 types of hand distributions