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.

### Statistics

The following table summarizes the data of the Pavlicek Point Count:

StatisticValue
Hands evaluated635,013,559,600
Unique values39
Minimum0
Maximum38
Mode11
Median11
Mean11.3682
Standard deviation4.2781

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.

PointsHandsSpecificAt LeastAt Most
0293,805,5680.04631000.0463
11,766,279,8720.278199.95370.3244
24,460,756,9440.702599.67561.0269
38,243,807,1201.298298.97312.3251
413,933,491,4922.194297.67494.5193
521,764,214,1763.427495.48077.9467
630,423,163,9444.790992.053312.7376
738,944,701,7486.132987.262418.8705
847,115,157,3727.419681.129526.2900
953,631,235,2368.445773.710034.7357
1057,295,091,8569.022765.264343.7584
1158,143,902,8089.156356.241652.9147
1256,245,617,6368.857447.085361.7721
1351,805,296,4328.158138.227969.9302
1445,528,936,1167.169830.069877.1000
1538,297,308,5526.030922.900083.1309
1630,847,863,4604.857816.869187.9888
1723,818,563,8243.750912.011291.7396
1817,638,216,9242.77768.260494.5173
1912,512,959,4121.97055.482796.4878
208,546,506,8441.34593.512297.8336
215,599,172,6400.88172.166498.7154
223,509,161,4120.55261.284699.2680
232,112,451,6800.33270.732099.6007
241,215,549,6440.19140.399399.7921
25665,258,8840.10480.207999.8968
26346,309,3800.05450.103299.9514
27171,594,8840.02700.048699.9784
2879,694,3600.01260.021699.9909
2935,006,3600.00550.009199.9965
3014,392,6320.00230.003599.9987
315,429,1680.00090.001399.9996
321,895,6040.00030.000499.9999
33574,5480.00010.0001100.0000
34153,4480.00000.0000100.0000
3531,9240.00000.0000100.0000
3651720.00000.0000100.0000
375080.00000.0000100.0000
38160.00000.0000100
U=39635,013,559,6001004000*

*Columns 3 and 4 check total = 100×(U+1)

 Study 8J18 Main Top Pavlicek Point Count Stats