# Statistical Frequency Reports for Pennsylvania 5/39 Lotto

## By Ion Saliu, Founder of: Lottery Mathematics, Lotto Programming Science

Software used to create the statistical reports: SkipDecaFreq5. The program also generates combinations based on such parameters as lotto number frequency, lotto decades and skips of lotto numbers. The application is a component of Bright5, the most powerful and comprehensive lotto software package for all 5-number lotto games. Actually, the Bright lottery software packages have been greatly upgraded and superseded by the Ultimate Lottery Software packages.

The following are real-life reports for Pennsylvania Lottery Cash 5 game (5 of 39 lotto). The reports show the influence of the parpaluck in the appearance of the lotto numbers based on frequency. The parpaluck is the range of analysis to determine the statistical frequency of the lotto numbers. The term parpaluck was introduced simply to… simplify! It's easier to use one word instead of range or span of statistical analysis or number of lottery drawings to analyze.

The parpaluck is to be calculated in conjunction with Ion Saliu's Paradox of N Trials. If the probability of an event is expressed as 1 in N, therefore p = 1/N, then the amount of the elements drawn can be calculated by the Fundamental Formula of Gambling (FFG). If we conduct N trials, then the old school told you that the probability of the event became p = 1 (certainty). NOT! The probability is clearly lower than 1. The paradox determines that such probability (called degree of certainty DC) tends to 1 – (1/e), or 63.2%, where e is the base of the natural logarithm: 2.718281828.....

The 5/39 lotto calculates the probability as 1 in 39/5, approximately 1 in 8 or p = 1/8. We can select parpalucks as multiples of the denominator (N = 8 in this case). It appears that parpalucks equal to N * 2 or N * 3 perform better than other parpalucks. The indicator is in Total combinations generated by various compositions of the lotto frequency groups.

Five reports were generated for the following parpaluck values: 8, 16, 24, 39 (total numbers in the lotto-5 game), and 78.

```
* Lotto 5/39 Frequencies Report by Draw
File: C:\LOTTERY\PA-5; Date: 12-16-2006
Draws Analyzed: 200 ~ Parpaluck: 8

The numbers in each column show how many numbers from the
frequency group came out in the corresponding drawing; e.g.
2 in the 1st col and 3 in 2nd col: 2 of the  numbers in the draw
came from group 1 (hot); 2 of numbers were from the 2nd group; etc.

Line    Draw                  Group #1    Group #2    Group #3       Total
no     ings                 5 numbers   14 numbers  20 numbers      combinations

1   8 23 24 27 37               1           3           1          36400
2   3 24 27 32 37               1           3           1          36400
3   8 13 22 30 39               1           2           2          86450
4   4  8 20 21 36               1           1           3          79800
5  15 29 32 36 37               2           2           1          18200
6  11 15 16 22 26               0           2           3          103740
7   1  4 10 15 31               0           1           4          67830
8   3  4 21 29 30               0           3           2          69160
9  14 15 22 24 32               0           3           2          69160
10  11 13 33 34 36               1           2           2          86450
...
40   1 16 20 32 34               0           2           3          103740
41   5 14 15 33 38               1           1           3          79800
42   6  7  9 19 38               1           0           4          24225
43  17 22 26 31 37               1           3           1          36400
44   2 14 20 33 37               1           1           3          79800
45   1 10 33 35 39               2           1           2          26600
46   7 15 19 24 26               0           2           3          103740
47   3  6 30 34 36               1           2           2          86450
48   3  5  8 19 28               0           1           4          67830
49   1  4 14 19 33               0           1           4          67830
50  20 27 31 35 36               2           2           1          18200
...
195   4  9 16 34 35               1           1           3          79800
196   1 22 25 26 32               0           4           1          20020
197   4  8 25 29 31               0           3           2          69160
198   2  8 10 15 27               0           1           4          67830
199   3 20 21 30 34               0           3           2          69160
200  21 23 32 38 39               2           3           0          3640

* Lotto-5 Frequencies Report by Draw
File: C:\LOTTERY\PA-5; Date: 12-16-2006
Draws Analyzed: 200 ~ Parpaluck: 16

The numbers in each column show how many numbers from the
frequency group came out in the corresponding drawing; e.g.
2 in the 1st col and 3 in 2nd col: 2 of the  numbers in the draw
came from group 1 (hot); 2 of numbers were from the 2nd group; etc.

Line    Draw                  Group #1    Group #2    Group #3       Total
no     ings                 5 numbers   14 numbers  20 numbers      combos

1   8 23 24 27 37               1           3           1          36400
2   3 24 27 32 37               1           3           1          36400
3   8 13 22 30 39               1           2           2          86450
4   4  8 20 21 36               1           1           3          79800
5  15 29 32 36 37               2           2           1          18200
6  11 15 16 22 26               0           2           3          103740
7   1  4 10 15 31               0           1           4          67830
8   3  4 21 29 30               0           3           2          69160
9  14 15 22 24 32               0           3           2          69160
10  11 13 33 34 36               1           2           2          86450
...
40   1 16 20 32 34               0           2           3          103740
41   5 14 15 33 38               1           1           3          79800
42   6  7  9 19 38               1           0           4          24225
43  17 22 26 31 37               1           3           1          36400
44   2 14 20 33 37               1           1           3          79800
45   1 10 33 35 39               2           1           2          26600
46   7 15 19 24 26               0           2           3          103740
47   3  6 30 34 36               1           2           2          86450
48   3  5  8 19 28               0           1           4          67830
49   1  4 14 19 33               0           1           4          67830
50  20 27 31 35 36               2           2           1          18200
...
195   4  9 16 34 35               1           1           3          79800
196   1 22 25 26 32               0           4           1          20020
197   4  8 25 29 31               0           3           2          69160
198   2  8 10 15 27               0           1           4          67830
199   3 20 21 30 34               0           3           2          69160
200  21 23 32 38 39               2           3           0          3640

* Lotto 5/39 Frequencies Report by Draw
File: C:\LOTTERY\PA-5; Date: 12-16-2006
Draws Analyzed: 200 ~ Parpaluck: 24

The numbers in each column show how many numbers from the
frequency group came out in the corresponding drawing; e.g.
2 in the 1st col and 3 in 2nd col: 2 of the  numbers in the draw
came from group 1 (hot); 2 of numbers were from the 2nd group; etc.

Line    Draw                  Group #1    Group #2    Group #3       Total
no     ings                 5 numbers   14 numbers  20 numbers      combinations

1   8 23 24 27 37               1           1           3          79800
2   3 24 27 32 37               1           2           2          86450
3   8 13 22 30 39               1           1           3          79800
4   4  8 20 21 36               1           1           3          79800
5  15 29 32 36 37               2           3           0          3640
6  11 15 16 22 26               0           1           4          67830
7   1  4 10 15 31               0           1           4          67830
8   3  4 21 29 30               0           3           2          69160
9  14 15 22 24 32               0           1           4          67830
10  11 13 33 34 36               1           2           2          86450
...
40   1 16 20 32 34               0           2           3          103740
41   5 14 15 33 38               1           2           2          86450
42   6  7  9 19 38               1           1           3          79800
43  17 22 26 31 37               1           2           2          86450
44   2 14 20 33 37               1           1           3          79800
45   1 10 33 35 39               2           2           1          18200
46   7 15 19 24 26               0           2           3          103740
47   3  6 30 34 36               1           2           2          86450
48   3  5  8 19 28               0           3           2          69160
49   1  4 14 19 33               0           2           3          103740
50  20 27 31 35 36               2           2           1          18200
...
195   4  9 16 34 35               1           2           2          86450
196   1 22 25 26 32               0           3           2          69160
197   4  8 25 29 31               0           3           2          69160
198   2  8 10 15 27               0           3           2          69160
199   3 20 21 30 34               0           2           3          103740
200  21 23 32 38 39               2           1           2          26600

* Lotto-5 Frequencies Report by Draw
File: C:\LOTTERY\PA-5; Date: 12-16-2006
Draws Analyzed: 200 ~ Parpaluck: 39

The numbers in each column show how many numbers from the
frequency group came out in the corresponding drawing; e.g.
2 in the 1st col and 3 in 2nd col: 2 of the numbers in the draw
came from group 1 (hot); 2 of numbers were from the 2nd group; etc.

Line    Draw                  Group #1    Group #2    Group #3       Total
no     ings                 5 numbers   14 numbers  20 numbers      combos

1   8 23 24 27 37               0           3           2          69160
2   3 24 27 32 37               0           3           2          69160
3   8 13 22 30 39               0           2           3          103740
4   4  8 20 21 36               0           4           1          20020
5  15 29 32 36 37               1           3           1          36400
6  11 15 16 22 26               1           0           4          24225
7   1  4 10 15 31               2           2           1          18200
8   3  4 21 29 30               0           3           2          69160
9  14 15 22 24 32               0           3           2          69160
10  11 13 33 34 36               1           1           3          79800
...
40   1 16 20 32 34               1           3           1          36400
41   5 14 15 33 38               0           3           2          69160
42   6  7  9 19 38               1           1           3          79800
43  17 22 26 31 37               1           0           4          24225
44   2 14 20 33 37               0           1           4          67830
45   1 10 33 35 39               2           1           2          26600
46   7 15 19 24 26               1           1           3          79800
47   3  6 30 34 36               0           2           3          103740
48   3  5  8 19 28               0           3           2          69160
49   1  4 14 19 33               1           2           2          86450
50  20 27 31 35 36               2           2           1          18200
...
195   4  9 16 34 35               1           0           4          24225
196   1 22 25 26 32               1           1           3          79800
197   4  8 25 29 31               1           3           1          36400
198   2  8 10 15 27               1           1           3          79800
199   3 20 21 30 34               0           1           4          67830
200  21 23 32 38 39               0           3           2          69160

* Lotto 5/39 Frequencies Report by Draw
File: C:\LOTTERY\PA-5; Date: 12-16-2006
Draws Analyzed: 200 ~ Parpaluck: 78

The numbers in each column show how many numbers from the
frequency group came out in the corresponding drawing; e.g.
2 in the 1st col and 3 in 2nd col: 2 of the numbers in the draw
came from group 1 (hot); 2 of numbers were from the 2nd group; etc.

Line    Draw                  Group #1    Group #2    Group #3       Total
no     ings                 5 numbers   14 numbers  20 numbers      combinations

1   8 23 24 27 37               0           2           3          103740
2   3 24 27 32 37               0           2           3          103740
3   8 13 22 30 39               0           1           4          67830
4   4  8 20 21 36               1           2           2          86450
5  15 29 32 36 37               1           3           1          36400
6  11 15 16 22 26               1           0           4          24225
7   1  4 10 15 31               2           3           0          3640
8   3  4 21 29 30               0           2           3          103740
9  14 15 22 24 32               0           2           3          103740
10  11 13 33 34 36               0           3           2          69160
...
40   1 16 20 32 34               1           3           1          36400
41   5 14 15 33 38               1           3           1          36400
42   6  7  9 19 38               0           2           3          103740
43  17 22 26 31 37               1           1           3          79800
44   2 14 20 33 37               1           1           3          79800
45   1 10 33 35 39               2           2           1          18200
46   7 15 19 24 26               0           2           3          103740
47   3  6 30 34 36               0           2           3          103740
48   3  5  8 19 28               0           1           4          67830
49   1  4 14 19 33               0           3           2          69160
50  20 27 31 35 36               2           1           2          26600
51  10 14 22 25 28               1           0           4          24225
...
195   4  9 16 34 35               1           1           3          79800
196   1 22 25 26 32               1           0           4          24225
197   4  8 25 29 31               1           3           1          36400
198   2  8 10 15 27               2           2           1          18200
199   3 20 21 30 34               0           0           5          15504
200  21 23 32 38 39               0           2           3          103740

```