# ToolsLotto6: Special upgrade to the lottery utility software for 6-number lotto games

## By Ion Saliu, Founder of Lottery Mathematics

ToolsLotto6, special upgrade to Util632, the lottery utility software that crunches the lotto-6 (drawing 6 winning lotto numbers).

This special upgrade to Util632, ToolsLotto6, has two new functions:
~ Triplets Rundown (3-number lotto groups);

The Triplets Rundown has some powerful capabilities:
~ calculates the frequency of every triplet in a 6-number lotto game;
~ sorts the lotto triplets by frequency in descending order;
~ creates a 'least triplets file' the same way as 'least pairings' for a 6-number lotto game.

The Quadruplets function does not provide a 'least quadruplets file'. Such a file would be very large and not usable at this time. I do not provide lotto software to crunch the least quadruplets.

This is the main menu. You can see the same functions present in Util-632, plus the two new lotto functions. I will analyze here only the new functions (triplets and quadruplets). For te rest of the functions, I will refer you back to the material that presents the entire collection of lottery utility software:

Don't sit back, but still enjoy it!

Triplets or triples: Groups of 3 lotto numbers

A lotto game such as '6 from 49' has a total of C(49, 3) = (49 * 48 * 47) / (1 * 2 * 3) = 18424 triplets.

I ran the frequency reporting for triplets using a real-drawing data file in Pennsylvania lottery, the 6-49 lotto game. The first frequency report is in sequential order, from
1-2-3 to 47-48-49.

```
Lotto-6 Triplets
Data file analyzed: C:\LOTTERY\PA-6
Total drawings analyzed:  464

Lotto-6 Triplet         Total hits

1  2  3                   1
1  2  4                   1
1  2  5                   0
....
45  48  49                1
46  47  48                0
46  47  49                0
46  48  49                0
47  48  49                0

```

The second report is sorted on frequency, in descending order, from the most frequent triplet to the least frequent.

```
SORTED Lotto-6 Triplets
Data file analyzed: C:\LOTTERY\PA-6
Total drawings analyzed:  464

Lotto-6 Triplet         Total hits

11  18  36                5
36  37  48                5
1  19  33                 4
2  11  39                 4
2  13  45                 4
....
46  47  48                0
46  47  49                0
46  48  49                0
47  48  49                0

```

Will you notice, please, something significant? Of course, my plea will fall on deaf ears, insofar as my googoos are concerned (fierce enemies). But they are insignificant in numbers and effect. My plea will be consequential to the overwhelming majority of guests and readers. My plea: Let's not overlook standard deviation. Clearly, the standard deviation is larger in the first lotto triple group, as compared to the last group! Something to always keep in mind. Remember the 1-2-3-4-5-6 lotto combination heated debates? I mean, such "scientific" debates are still steaming! Many people with real brains still aren't capable of distinguishing between probability and degree of certainty! How much clearer can I be...can any human be...

A lotto game such as '6 from 49' has a total of C(49, 4) = (49 * 48 * 47 * 46) / (1 * 2 * 3 * 4) = 211876 quadruplets.

I ran the frequency reporting for quadruplets using a real-drawing data file in Pennsylvania lottery, the 6-49 lotto game. The first frequency report is in sequential order, from
1-2-3-4 to 46-47-48-49.

```
Data file analyzed: C:\LOTTERY\PA-6
Total drawings analyzed:  464

1  2  3  4                0
1  2  3  5                0
1  2  3  6                0
1  2  3  7                0
....
45  46  47  48            0
45  46  47  49            0
45  46  48  49            0
45  47  48  49            0
46  47  48  49            0

```

The second report is sorted on frequency, in descending order, from the most frequent quadruplets to the least frequent 4-number groups.

```
Data file analyzed: C:\LOTTERY\PA-6
Total drawings analyzed:  464

5  19  29  36             3
7  8  10  32              3
1  7  19  33              2
1  7  23  26              2
1  8  9  40               2
1  8  26  37              2
....
44  47  48  49            0
45  46  47  48            0
45  46  47  49            0
45  46  48  49            0
45  47  48  49            0

```

Again, the standard deviation plays an important role. If the lotto data file is very large, the bias towards quadruplets with a normal standard deviation is accented. That normal standard deviation can be calculated only by the Fundamental Formula of Gambling (FFG). The parameter can be approximated as well.

The triplet rundown can be performed in less than a minute even on slow PCs. The quadruplets, however, can take more than an hour on a slower PC. So that you know and be patient. I strongly recommend running this program at the command prompt, in full screen mode. The performance is superior, since lotto processes are highly CPU-intensive.

But, hey, how do you know that the stats (frequencies, hits) are accurate? It just occurred to me the Trust, but verify! proverb. It was a saying at the Summit, spoken in two languages by two of the most influential politicians in history: Mihail Gorbachov and Ronald Reagan. They might have had the highest impact in change for the better, since they had the means to put an end to human history.

You trust me...and I thank you. But you should always verify anyone, for Truth is above anything and anybody. You can verify the accuracy of the lotto triplets/quadruplets frequencies by adding up all the hits. You can use a spreadsheet as well (much more accurate than a calculator or... sheesh...pencil-and-paper!) You get a total. If your addition operation is correct, I can tell you how many drawings you analyzed, if you tell me the sum-total! It sounds like one of those Las Vegas mentalist shows on TV, but ain't! It is pure mathematics! I know how many lotto drawings you analyzed, no matter where in the world you travel! BRRRRRRRRAHAHAHAHA!!1!! Wanna bet? BRRRRRRRRAHAHAHAHA......

Read also the article presenting the lotto-5 software tools:
ToolsLotto5: Special upgrade to the lottery utility software for 5-number lotto games.

This piece of lotto 6 software has been greatly enhanced for registered members only: SoftwareLotto6. It is part of the best 6-number lotto software package ever: Bright6. Read: Lotto Software for Singles, Pairs, Triplets, Quadruplets, Quintets, Sextets.

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