Study 8J18   Main

Pavlicek Point Count Stats

by Richard Pavlicek

In any point-count system, HCP must be augmented by distributional factors to obtain a fair appraisal of a bridge hand. Many years ago I devised a method based on the ‘short-suit’ count but with a number of tweaks to improve accuracy. The complete structure is explained at Pavlicek Point Count and my study on Point Count Methods shows a comparison with other methods.

The purpose of this study is to determine the statistics of Pavlicek Point Count when applied to every possible bridge hand. The point-count rules for initial hand evaluation, assuming partner has not bid, are summarized below:

Ace = 4 King = 3 Queen = 2 Jack = 1

Void = 3 Singleton = 2 Doubleton = 1

Any four aces and/or 10s = 1

With singleton K, Q, J or doubleton KQ, KJ, QJ, Qx or Jx
count the greater of its HCP or shortness but not both.

The first table shows a summary of the statistics:

Statistic	Value
Hands evaluated	635,013,559,600
Unique values	39
Minimum	0
Maximum	38
Mode	11
Median	11
Mean	11.3682
Standard deviation	4.2781

The next table shows the number of hands and percent chance for each number of Pavlicek points. Percents are shown in three ways: for the specific number, at least that number, and at most that number. To find the chance of an interior range (e.g., 13-15 points) add the specific percents of each number in that range. Percents are rounded to the nearest 10,000th, except whole numbers are exact.

Points	Hands	Specific	At Least	At Most
0	293,805,568	0.0463	100	0.0463
1	1,766,279,872	0.2781	99.9537	0.3244
2	4,460,756,944	0.7025	99.6756	1.0269
3	8,243,807,120	1.2982	98.9731	2.3251
4	13,933,491,492	2.1942	97.6749	4.5193
5	21,764,214,176	3.4274	95.4807	7.9467
6	30,423,163,944	4.7909	92.0533	12.7376
7	38,944,701,748	6.1329	87.2624	18.8705
8	47,115,157,372	7.4196	81.1295	26.2900
9	53,631,235,236	8.4457	73.7100	34.7357
10	57,295,091,856	9.0227	65.2643	43.7584
11	58,143,902,808	9.1563	56.2416	52.9147
12	56,245,617,636	8.8574	47.0853	61.7721
13	51,805,296,432	8.1581	38.2279	69.9302
14	45,528,936,116	7.1698	30.0698	77.1000
15	38,297,308,552	6.0309	22.9000	83.1309
16	30,847,863,460	4.8578	16.8691	87.9888
17	23,818,563,824	3.7509	12.0112	91.7396
18	17,638,216,924	2.7776	8.2604	94.5173
19	12,512,959,412	1.9705	5.4827	96.4878
20	8,546,506,844	1.3459	3.5122	97.8336
21	5,599,172,640	0.8817	2.1664	98.7154
22	3,509,161,412	0.5526	1.2846	99.2680
23	2,112,451,680	0.3327	0.7320	99.6007
24	1,215,549,644	0.1914	0.3993	99.7921
25	665,258,884	0.1048	0.2079	99.8968
26	346,309,380	0.0545	0.1032	99.9514
27	171,594,884	0.0270	0.0486	99.9784
28	79,694,360	0.0126	0.0216	99.9909
29	35,006,360	0.0055	0.0091	99.9965
30	14,392,632	0.0023	0.0035	99.9987
31	5,429,168	0.0009	0.0013	99.9996
32	1,895,604	0.0003	0.0004	99.9999
33	574,548	0.0001	0.0001	100.0000
34	153,448	0.0000	0.0000	100.0000
35	31,924	0.0000	0.0000	100.0000
36	5172	0.0000	0.0000	100.0000
37	508	0.0000	0.0000	100.0000
38	16	0.0000	0.0000	100
Totals	635,013,559,600	100	4000*

*Columns 3 and 4 combined should add to 100×(U+1) where U = number of unique values.

Study 8J18   Main

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© 2012 Richard Pavlicek