Bridge Probabilities - Probability of HCP Distribution

Probability of HCP Distribution

High card points (HCP) are usually counted using the Milton Work scale of 4/3/2/1 points for each Ace/King/Queen/Jack respectively. The a priori probabilities that a given hand contains no more than a specified number of HCP is given in the table below. To find the likelihood of a certain point range, one simply subtracts the two relevant cumulative probabilities. So, the likelihood of being dealt a 12-19 HCP hand (ranges inclusive) is the probability of having at most 19 HCP minus the probability of having at most 11 hcp, or: 0.986 − 0.652 = 0.334.

HCP Probability HCP Probability HCP Probability HCP Probability HCP Probability
0 0.0036 8 0.3748 16 0.9355 24 0.9995 32 1.0000
1 0.0115 9 0.4683 17 0.9591 25 0.9998 33 1.0000
2 0.0251 10 0.5624 18 0.9752 26 0.9999 34 1.0000
3 0.0497 11 0.6518 19 0.9855 27 1.0000 35 1.0000
4 0.0882 12 0.7321 20 0.9920 28 1.0000 36 1.0000
5 0.1400 13 0.8012 21 0.9958 29 1.0000 37 1.0000
6 0.2056 14 0.8582 22 0.9979 30 1.0000
7 0.2858 15 0.9024 23 0.9990 31 1.0000

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