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Exploring further all the 39 hand distributions in Bridge, we continue to make use of the knowledge of the 39 hand distributions into practical use. This time we do the odds of having at least x cards in a certain suit.

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

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

What is the Odd of Having At Least x Cards

Basically, we summarized the long table in this article to table below:

X Total Hands X or more Percentage
13 1 1 0.0000000002%
12 507 508 0.00000008%
11 57,798 58,306 0.0000092%
10 2,613,754 2,672,060 0.000423%
9 58,809,465 61,481,525 0.009743%
8 740,999,259 802,480,784 0.12717%
7 5,598,661,068 6,401,141,852 1.01438%
6 26,393,687,892 32,794,829,744 5.19696%
5 77,865,170,526 110,660,000,270 17.536%
4 149,531,979,655 260,191,979,925 41.232%
3 181,816,433,256 442,008,413,181 70.045%
2 130,725,621,432 572,734,034,613 90.76%
1 50,840,366,668 623,574,401,281 98.82%
0 7,464,478,869 631,038,880,150 100%
Sum: 631,038,880,150    

How to use the table above:

  • “X” is the number of cards that you want to check. For example, you want to know what is the chance of getting a hand with 7 cards of Spade. So, we set x=7
  • Then find the row “7” and lookup in the third column: 1.01 %. Therefore, the chance of getting 7 cards of Spade would be 1.01%
  • If you want to know what is the odds to get any 7 cards hand, then it is 4 x 1.01 = 4.04%

This will become handy to make an advanced analysis of particular bridge problems. For example: to consider which one is better: open with a better minor method or short club?

Knowing the statistic in bridge distribution will give you a sure advantage in the long run. This principle is the same that makes billions of dollars of profit in a casino. If the statistic is on your side, you surely will see the advantage (although sometimes it only becomes obvious in the extended time period).

Long live statistics – long live bridge distribution!

Back to the main articles: The 39 Types of hand Distribution in Bridge

odds of having at least x cards