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
| Distribution | Probability | 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 – 0 | 0.1% | 689,049,504 |
| 15: | 8 – 3 – 1 – 1 | 0.1% | 746,470,296 |
| 16: | 8 – 2 – 2 – 1 | 0.2% | 1,221,496,848 |
| 17: | 7 – 6 – 0 – 0 | <0.1% | 35,335,872 |
| 18: | 7 – 5 – 1 – 0 | 0.1% | 689,049,504 |
| 19: | 7 – 4 – 2 – 0 | 0.4% | 2,296,831,680 |
| 20: | 7 – 4 – 1 – 1 | 0.4% | 2,488,234,320 |
| 21: | 7 – 3 – 3 – 0 | 0.3% | 1,684,343,232 |
| 22: | 7 – 3 – 2 – 1 | 1.9% | 11,943,524,736 |
| 23: | 7 – 2 – 2 – 2 | 0.5% | 3,257,324,928 |
| Total: | 4% | 25,604,567,408 | |
With less than 7-cards in a suit
| Distribution | Probability | Total Hands | |
| 24: | 6 – 6 – 1 – 0 | 0.1% | 459,366,336 |
| 25: | 6 – 5 – 2 – 0 | 0.7% | 4,134,297,024 |
| 26: | 6 – 5 – 1 – 1 | 0.7% | 4,478,821,776 |
| 27: | 6 – 4 – 3 – 0 | 1.3% | 8,421,716,160 |
| 28: | 6 – 4 – 2 – 1 | 4.7% | 29,858,811,840 |
| 29: | 6 – 3 – 3 – 1 | 3.4% | 21,896,462,016 |
| 30: | 6 – 3 – 2 – 2 | 5.6% | 35,830,574,208 |
| 31: | 5 – 5 – 3 – 0 | 0.9% | 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 – 1 | 3.2% | 20,154,697,992 |
| 33: | 5 – 4 – 4 – 0 | 1.2% | 7,895,358,900 |
| 34: | 5 – 4 – 3 – 1 | 12.9% | 82,111,732,560 |
| 35: | 5 – 4 – 2 – 2 | 10.6% | 67,182,326,640 |
| 36: | 5 – 3 – 3 – 2 | 15.5% | 98,534,079,072 |
| 37: | 4 – 4 – 4 – 1 | 3.0% | 19,007,345,500 |
| 38: | 4 – 4 – 3 – 2 | 21.6% | 136,852,887,600 |
| 39: | 4 – 3 – 3 – 3 | 10.5% | 66,905,856,160 |
| Total | 96% | 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.
| Distribution | Probability | Total Hands | |
| 1: | 4 – 4 – 3 – 2 | 21.6% | 132,852,887,600 |
| 2: | 5 – 3 – 3 – 2 | 15.5% | 98,534,079,072 |
| 3: | 5 – 4 – 3 – 1 | 12.9% | 82,111,732,560 |
| 4: | 5 – 4 – 2 – 2 | 10.6% | 67,182,326,640 |
| 5: | 4 – 3 – 3 – 3 | 10.5% | 66,905,856,160 |
| 6: | 6 – 3 – 2 – 2 | 5.6% | 35,830,574,208 |
| 7; | 6 – 4 – 2 – 1 | 4.7% | 29,858,811,840 |
| 8; | 6 – 3 – 3 – 1 | 3.4% | 21,896,462,016 |
| 9: | 5 – 5 – 2 – 1 | 3.2% | 20,154,697,992 |
| 10: | 4 – 4 – 4 – 1 | 3.0% | 19,007,345,500 |
| Total | 90.4% | 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.
| Distribution | Probability | Total Hands | |
| 11: | 7 – 3 – 2 – 1 | 1.9% | 11,943,524,736 |
| 12: | 6 – 4 – 3 – 0 | 1.3% | 8,421,716,160 |
| 13: | 5 – 4 – 4 – 0 | 1.2% | 7,895,358,900 |
| 14: | 5 – 5 – 3 – 0 | 0.9% | 5,684,658,408 |
| 15: | 6 – 5 – 1 – 1 | 0.7% | 4,478,821,776 |
| 16: | 6 – 5 – 2 – 0 | 0.7% | 4,134,297,024 |
| 17: | 7 – 2 – 2 – 2 | 0.5% | 3,257,324,928 |
| 18: | 7 – 4 – 1 – 1 | 0.4% | 2,488,234,320 |
| 19: | 7 – 4 – 2 – 0 | 0.4% | 2,296,831,680 |
| 20: | 7 – 3 – 3 – 0 | 0.3% | 1,684,343,232 |
| 21: | 8 – 2 – 2 – 1 | 0.2% | 1,221,496,848 |
| 22: | 8 – 3 – 1 – 1 | 0.1% | 746,470,296 |
| 23: | 8 – 3 – 2 – 0 | 0.1% | 689,049,504 |
| 24: | 7 – 5 – 1 – 0 | 0.1% | 689,049,504 |
| 25: | 6 – 6 – 1 – 0 | 0.1% | 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 |
| Total | 9.6% | 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%)
| Distribution | Probability | Total Hands | |
| 1: | 5 – 3 – 3 – 2 | 15.5% | 98,534,079,072 |
| 2: | 4 – 4 – 3 – 2 | 21.6% | 136,852,887,600 |
| 3: | 4 – 3 – 3 – 3 | 10.5% | 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%)
| Distribution | Probability | Total Hands | |
| 1: | 5 – 4 – 4 – 0 | 1.2% | 7,895,358,900 |
| 2: | 4 – 4 – 4 – 1 | 3.0% | 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%)
| Distribution | Probability | 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 – 0 | 0.1% | 689,049,504 |
| 6: | 7 – 4 – 2 – 0 | 0.4% | 2,296,831,680 |
| 7: | 7 – 4 – 1 – 1 | 0.4% | 2,488,234,320 |
| 8: | 6 – 6 – 1 – 0 | 0.1% | 459,366,336 |
| 9: | 6 – 5 – 2 – 0 | 0.7% | 4,134,297,024 |
| 10: | 6 – 5 – 1 – 1 | 0.7% | 4,478,821,776 |
| 11: | 6 – 4 – 3 – 0 | 1.3% | 8,421,716,160 |
| 12: | 6 – 4 – 2 – 1 | 4.7% | 29,858,811,840 |
| 13: | 5 – 5 – 3 – 0 | 0.9% | 5,684,658,408 |
| 14: | 5 – 5 – 2 – 1 | 3.2% | 20,154,697,992 |
| 15: | 5 – 4 – 3 – 1 | 12.9% | 82,111,732,560 |
| 16: | 5 – 4 – 2 – 2 | 10.6% | 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+%)
| Distribution | Probability | 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 – 0 | 0.1% | 689,049,504 |
| 4: | 6 – 6 – 1 – 0 | 0.1% | 459,366,336 |
| 5: | 6 – 5 – 2 – 0 | 0.7% | 4,134,297,024 |
| 6: | 6 – 5 – 1 – 1 | 0.7% | 4,478,821,776 |
| 7: | 5 – 5 – 3 – 0 | 0.9% | 5,684,658,408 |
| 8: | 5 – 5 – 2 – 1 | 3.2% | 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:
- (5422) can be grouped as (semi) balanced (Total: 10.6%)
- (5431) can be grouped as (almost) 3-suiter (Total: 12.9%)
- (6+4xx) can be grouped as 1-suiter (Total: 6.9%)
4. One-Suiter Hand (Total: 12.17%)
| Distribution | Probability | Total Hands | |
| 1: | 8 – 3 – 2 – 0 | 0.1% | 689,049,504 |
| 2: | 8 – 3 – 1 – 1 | 0.1% | 746,470,296 |
| 3: | 8 – 2 – 2 – 1 | 0.2% | 1,221,496,848 |
| 4: | 7 – 3 – 3 – 0 | 0.3% | 1,684,343,232 |
| 5: | 7 – 3 – 2 – 1 | 1.9% | 11,943,524,736 |
| 6: | 7 – 2 – 2 – 2 | 0.5% | 3,257,324,928 |
| 7: | 6 – 3 – 3 – 1 | 3.4% | 21,896,462,016 |
| 8: | 6 – 3 – 2 – 2 | 5.6% | 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%)
| Distribution | Probability | 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:
- The Extended Details. of the 39-types.
- The Odds of Having at least x cards
- The Spectrum of level-1 opening
