HIGH CARD POINT PROBABILITIES

The average high card point count for any hand is 10 and the average high card point count for any partnership is 20. Once a player has determined the high card point count in his holding, or x HCPs, then the assumption is made that the remaining high card points are distributed equally among the other three players, or 1/3 of 40 - x for each remaining player.

Probabilities can be calculated for the various possible high card point counts, since the individual holdings vary from the defined averages. The following charts are the calculations for these probabilities.

Probabilites Of High Card Points For One Hand

HCPs

   Percentage

HCPs

   Percentage

0

   .364  

19

   1.036

1

   .789  

20

   .644

2

   1.356  

21

   .378

3

   2.462  

22

   .210

4

   3.845  

23

   .112

5

   5.186  

24

   .056

6

   6.554  

25

   .026

7

   8.892  

26

   .012

8

   8.892  

27

   .0049

9

   9.356  

28

   .0019

10

   9.405  

29

   .00067

11

   9.945  

30

   .00022

12

   8.027  

31

   .00006

13

   6.914  

32

   .00002

14

   5.693  

33

   .000004

15

   4.424  

34

   .0000007

16

   3.311  

35

   .0000001

17

   2.362  

36

   .000000009

18

   1.605  

37

   .0000000006

 

No bridge hand of 13 cards can hold more than 37 high card points.

Probabilities Of High Card Points For A Partnership

HCPs

   Percentage

HCPs

   Percentage

0

   .00005  

21

   8.047

1

   .0005  

22

   7.566

2

   .002  

23

   6.831

3

   .006  

24

   5.907

4

   .018  

25

   4.892

5

   .043  

26

   3.883

6

   .093  

27

   2.943

7

   .196  

28

   2.124

8

   .341  

29

   1.463

9

   .588  

30

   .955

10

   .955  

31

   .588

11

   1.463  

32

   .341

12

   2.124  

33

   .186

13

   2.943  

34

   .093

14

   3.983  

35

   .043

15

   4.892  

36

   .018

16

   5.907  

37

   .006

17

   6.931  

38

   .002

18

   7.566  

39

   .0005

19

   8.047  

40

   .00005

20

   8.222  

 

    

 

 

If you wish to include this feature, or any other feature, of the game of bridge in your partnership agreement, then please make certain that the concept is understood by both partners. Be aware whether or not the feature is alertable or not and whether an announcement should or must be made. Check with the governing body and/or the bridge district and/or the bridge unit prior to the game to establish the guidelines applied. Please include the particular feature on your convention card in order that your opponents are also aware of this feature during the bidding process, since this information must be made known to them according to the Laws of Duplicate Contract Bridge. We do not always include the procedure regarding Alerts and/or Announcements, since these regulations are changed and revised during time by the governing body. It is our intention only to present the information as concisely and as accurately as possible.

 

 

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