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 |
Read more about this topic: Bridge Probabilities
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