High Card Point Distributions

The following table defines the odds of picking up a certain number of high card points (HCP). The most common holding is 10 HCP (9.405%). Note: If you own a copy of the Encyclopedia of Bridge, it may have a typo saying that 11 HCP is the most common ("9.945%"). Cross that out and write "8.945%" in the margin. :-)

The highest possible point count is 37 HCP, like so:

AKQ

AKQJ

# HCP	Probability %	Context
0	0.364%
1	0.789%	Odds of being born a fraternal twin (1 in 125).
2	1.356%
3	2.462%
4	3.845%
5	5.186%
6	6.554%
7	8.028%
8	8.892%
9	9.356%
10	9.405%
11	8.945%
12	8.027%
13	6.914%
14	5.693%
15	4.424%
16	3.311%
17	2.362%
18	1.605%
19	1.036%
20	0.644%
21	0.378%
22	0.210%
23	0.112%
24	0.056%
25	0.026%
26	0.012%
27	0.0049%
28	0.0019%
29	0.00067%	Roughly 1 in every 149,253 hands.
30	0.00022%
31	0.00006%
32	0.00002%
33	0.000004%	Roughly 1 in every 25 million hands.
34	0.0000007%
35	0.0000001%
36	0.000000009%
37	0.0000000006%	This is a crazy number... akin to winning your state lottery multiple times. Good luck!

See also

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