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 Actually, the **Bright** lottery software packages have been greatly upgraded and superseded by the ** Ultimate Lottery Software** packages.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

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.

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* 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

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