Sum Count of identical Rightmost digits

[johnph77]

Sammy -

The following information is valid only only for a specific rightmost number selected in the complete Thunderball 5/34+1/14 matrix, with 3,895,584 possibilities.

If the specific rightmost number selected is 1 through 4 then there will be:

60 quints, with the Thunderball.
2,610 quads, with the Thunderball.
49,590 triples, with the Thunderball.
219,240 doubles, with the Thunderball.

360 quads, without the Thunderball.
15,660 triples, without the Thunderball.
297,540 doubles, without the Thunderball.

If the specific rightmost number selected is 5 through 0 then there will be:

465 quads, with the Thunderball.
13,485 triples, with the Thunderball.
94,395 doubles, with the Thunderball.

6,045 triples, without the Thunderball.
175,345 doubles, without the Thunderball.

Please note that if a combination has been used in a combination with the Thunderball, it is not re-tallied in the combinations without the Thunderball. For instance, in the 1 through 4 derivations, there are actually 420 quads in the 5/34 matrix alone, but 60 of them were combined with the Thunderball to form the quints.

As before, the above figures do not take into consideration that there can be doubles, triples or quads of one rightmost number and doubles or triples of another in the same drawing.

gl

j

 

[Sammy]

Hi John,

Thank you so much for further input - much appreciated.

There's just one paragraph I'm not sure about -

Sammy -

When the Thunderball (1/14) is included and the rightmost number is 1 through 4 you can wind up with quints - 01-11-21-31-41-xx plus either 01 or 11.

gl
j

Is the above a typo "wind up with quints - 01-11-21-31-41-xx"

The UK 5/34 Thunderball Lotto draws 5 main numbers from a pool of 1-34. Would this not exclude number 41 from the above?

I think the relevant 5/34 Decades is 0-9, 10-19, 20-29 and 30-34 which would exclude the possibility of Rightmost / Last Digit quints from the 5 main numbers drawn?

Please advise.

Cheers
Sammy

 

[Sammy]

Hi PAB,

This additional information on Rightmost / Last Digit is great!

I'd love to see the Actual Excel Formulas for both the

Total Combinations Available for EACH Distribution Possible.
Last Digit Distribution for EACH Draw.

Your assistance is very much appreciated.

Cheers,
Sammy

 

[Sammy]

Hi PAB,

Thank you again for all the information you have provided.

Is it possible to see the Excel Formulas that calculate the Distribution Expected to be Drawn Every.

Cheers,
Sammy

Hi Sammy,

Just some Extra Information you Might Find Useful.
The Table Below Lists the Total Combinations Available for EACH Distribution Possible, the Total Percentage Available and the Number of Draws that the Distribution is Expected to be Drawn Every.

Here is the Table :-
Distribution 11111 = 111,906 Combinations = 40.22% = 1 in 2.49 Draws
Distribution 21110 = 135,420 Combinations = 48.67% = 1 in 2.05 Draws
Distribution 22100 = 21,060 Combinations = 7.57% = 1 in 13.21 Draws
Distribution 31100 = 8,940 Combinations = 3.21% = 1 in 31.12 Draws
Distribution 32000 = 810 Combinations = 0.29% = 1 in 343.53 Draws
Distribution 41000 = 120 Combinations = 0.04% = 1 in 2,318.80 Draws

NONE of the Above Information takes the Thunderball Number into Consideration. ALL the Above Information Deals ONLY with the 5 Main Numbers Drawn from 34.

Hope this Helps.
All the Best.
PAB

 

[Sammy]

Hi John,

This is brilliant!

Cheers,
Sammy

Sammy -

The following information is valid only only for a specific rightmost number selected in the base 5/34 matrix, with 278,256 possibilities.

If the specific rightmost number selected is 1 through 4 then there will be:

30 quads.
1,305 triples.
24,795 doubles.

If the specific rightmost number selected is 5 thorugh 0 then there will be:

0 quads.
465 triples.
13,485 doubles.

Note that the above figures do not take into consideration that there can be doubles or triples of one rightmost number and doubles of another in the same drawing. The program from which the above numbers have been derived have, however, eliminated the two doubles of the same number in the quads occurances.

I haven't done the programming necessary to include the Thunderball in this data yet and it may be a while before I get around to it.

 

[Sammy]

PAB & John,

Thank you both for all your help and interest in this Thread.

Greatly appreciated!

Cheers,
Sammy

 

[johnph77]

Hi John,

Thank you so much for further input - much appreciated.

There's just one paragraph I'm not sure about -

Is the above a typo "wind up with quints - 01-11-21-31-41-xx"

Sammy -

It wasn't a typo - it was a flat-out error on my part. Of course, there's no "41" in a 34-number draw. Remove the reference to that number and the rest of the statement stands as written.

I created a ".csv" file for all possible Thunderball draws from the program output and text file editing. With line numbers, it's quite large - just over 100 Mb - but it'll load into Excel easily if you do it in sections and are willing to work with multiple-page worksheets. Without line numbers it goes about 75Mb. If you want it let me know.

 

[PAB]

Hi Sammy,

Here are the Excel Formulas for EACH Last Digit Distribution in a 534 Lotto.
You can Copy & Paste the Formulas from here into your Spreadsheet to Create a Table with the Total Combinations for ALL the Distributions.
You could Enter the Distribution Titles in Cells "A1:A6", and the Formulas in Cells "B1:B6" for Example.

Distribution 11111 :-
=COMBIN(6,5)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)+COMBIN(6,4)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,3)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,2)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,2)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,3)*COMBIN(4,1)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,1)*COMBIN(4,4)*COMBIN(4,1)*COMBIN(4,1)*COMBIN(4,1)*COMBIN(4,1)

Distribution 21110 :-
=COMBIN(6,1)*COMBIN(3,2)*COMBIN(5,3)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(5,2)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(5,1)*COMBIN(3,1)*COMBIN(4,2)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(4,3)*COMBIN(4,1)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,3)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,2)+COMBIN(6,2)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,2)*COMBIN(3,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,2)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(4,1)*COMBIN(4,2)*COMBIN(3,3)*COMBIN(4,1)*COMBIN(4,1)*COMBIN(4,1)

Distribution 22100 :-
=COMBIN(6,2)*COMBIN(3,2)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(3,1)+COMBIN(6,2)*COMBIN(3,2)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(5,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,2)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(4,2)*COMBIN(3,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,1)*COMBIN(4,2)*COMBIN(4,2)*COMBIN(4,2)+COMBIN(4,2)*COMBIN(4,2)*COMBIN(4,2)*COMBIN(2,1)*COMBIN(4,1)

Distribution 31100 :-
=COMBIN(6,1)*COMBIN(3,3)*COMBIN(5,2)*COMBIN(3,1)*COMBIN(3,1)+COMBIN(6,1)*COMBIN(3,3)*COMBIN(5,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,1)*COMBIN(3,3)*COMBIN(4,2)*COMBIN(4,1)*COMBIN(4,1)+COMBIN(6,2)*COMBIN(3,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,3)+COMBIN(6,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,3)*COMBIN(3,1)*COMBIN(4,1)+COMBIN(4,1)*COMBIN(4,3)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(4,1)

Distribution 32000 :-
=COMBIN(6,1)*COMBIN(3,3)*COMBIN(5,1)*COMBIN(3,2)+COMBIN(6,1)*COMBIN(3,3)*COMBIN(4,1)*COMBIN(4,2)+COMBIN(6,1)*COMBIN(3,2)*COMBIN(4,1)*COMBIN(4,3)+COMBIN(4,1)*COMBIN(4,3)*COMBIN(3,1)*COMBIN(4,2)

Distribution 41000 :-
=COMBIN(6,1)*COMBIN(3,1)*COMBIN(4,1)*COMBIN(4,4)+COMBIN(4,1)*COMBIN(4,4)*COMBIN(3,1)*COMBIN(4,1)

NONE of the Above Information takes the Thunderball Number into Consideration. ALL the Above Information Deals ONLY with the 5 Main Numbers Drawn from 34.

To Calculate the Number of Draws that EACH Distribution is Expected to be Drawn Every, if the Total Combinations Available for EACH Last Digit Distribution ( as Per the Formulas Listed Above ) were in Cells "B1:B6" for Example, then Enter the Formula …
=SUM(COMBIN(34,5)/B1)
… in Cell "C1". Then Copy this Formula Down to Cell "C6".

The Formulas for the Last Digit Distribution for EACH Draw Follows in the Next Post.

Hope this Helps.
All the Best.
PAB

 

[PAB]

Hi Sammy,

Here are the Excel Formulas to give you the Last Digit Distribution for EACH Draw in a 534 Lotto.
Assuming that the First Five Drawn Numbers are in Cells "C3:G3" ( Columns as Per your Original Post ) for Example, you could Put the Following Formulas in Cells "I3:R3" and Copy Down as Far as Needed. These will give you the TOTAL for EACH of the LAST DIGITS for EACH Draw.

Here are the Formulas :-
In Cell I3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="0"))
In Cell J3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="1"))
In Cell K3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="2"))
In Cell L3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="3"))
In Cell M3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="4"))
In Cell N3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="5"))
In Cell O3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="6"))
In Cell P3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="7"))
In Cell Q3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="8"))
In Cell R3 Enter the Formula :-
=SUMPRODUCT(--(RIGHT($C3:$G3,1)="9"))

Now in Cell "T3" Enter the Formula …
=LARGE(C6:G6,1)*10000+LARGE(C6:G6,2)*1000+LARGE(C6:G6,3)*100+LARGE(C6:G6,4)*10+LARGE(C6:G6,5)
… and Copy Down as Far as Needed.
You can Copy & Paste the Formula from here into your Spreadsheet.

NONE of the Above Information takes the Thunderball Number into Consideration. ALL the Above Information Deals ONLY with the 5 Main Numbers Drawn from 34.

Hope this Helps.
All the Best.
PAB

 

[Sammy]

Hi John,

Thanks for clarification.

Would appreciate having a look at the file version with line numbers.

Cheers,
Sammy

Sammy -

I created a ".csv" file for all possible Thunderball draws from the program output and text file editing. With line numbers, it's quite large - just over 100 Mb - but it'll load into Excel easily if you do it in sections and are willing to work with multiple-page worksheets. Without line numbers it goes about 75Mb. If you want it let me know.

 

[Sammy]

Hi PAB,

Thank you very much for

the Excel Formulas for EACH Last Digit Distribution in a 534 Lotto.

Hope this Helps.
All the Best.
PAB

Cheers,
Sammy

 

[Sammy]

Hi PAB,

Thank you very much for

the Excel Formulas to give you the Last Digit Distribution for EACH Draw in a 534 Lotto.
Hope this Helps.
All the Best.
PAB

Cheers,
Sammy

 

[johnph77]

Hi John,

Thanks for clarification.

Would appreciate having a look at the file version with line numbers.

Cheers,
Sammy

Sammy -

Due to the size of the file(s) it's best sent on a CD R/W. Will need an address - contact me via Yahoo Messenger - this ID.

But I may fool with it a little more before sending - if I divide it up into a 5/34 results sheet and add the Thunderball and line numbers later I may be able to send an Excel file - 14 pages, a page for each Thunderball - complete with drawing numbers. When time permits.....

gl

j

 

[PAB]

Hi johnph77,

Great Statistical Information on the Doubles, Triples, Quadruples & Quintuples, Most Informative.
Out of Interest, ...

I created a ".csv" file for all possible Thunderball draws from the program output and text file editing. With line numbers, it's quite large - just over 100 Mb - but it'll load into Excel easily if you do it in sections and are willing to work with multiple-page worksheets. Without line numbers it goes about 75Mb.

... what Language ( or Program ) is your Code Written in, is it VBA?.
If Not, I could Probably Write a Macro in VBA that will Produce ALL the Combinations ( Including the Thunderball ) in a Single Excel Sheet if that will be of Use.

All the Best.
PAB

 

[johnph77]

PAB -

I wrote this program code in QBasic - I still keep my finger in the pie there. I print the results to a text file then edit that with UltraEdit. Unfortunately, no one Excel sheet will hold all of the possible drawings for the full 5/34+1/14 matrix, so I'm in the process of creating an Excel spreadsheet with 14 pages, each with a different Thunderball. When that's complete I'll convert everything from formulas to numeric entries to conserve space.

gl

j

 

[PAB]

Thanks for the Reply johnph77,

Unfortunately, no one Excel sheet will hold all of the possible drawings for the full 5/34+1/14 matrix, so I'm in the process of creating an Excel spreadsheet with 14 pages, each with a different Thunderball.

One Way to get Around this is to Output One Combination Per Cell in the Format 01-02-03-04-05-Thunderball. You could then Just Cut & Paste to Separate Sheets. You can Convert the Combinatiion String so that EACH Number has its Own Cell by Clicking Data, Text to Columns, Delimited, and in Other: Enter a "-" ( without the Speachmarks ).
If you are Interested, Please Let me Know.

All the Best.
PAB

 

[johnph77]

PAB -

Concur. And it could also have been done by converting all the output to strings and inserting the results in the Excel spreadsheet as labels. But then all the nice neat macros you wrote would have had to have been rewritten.

In any case, the spreadsheet is finished, awaiting contact from Sammy. It's smaller (at 219Mb) than I thought it would be. And I more or less took it on just to see if it could be done. It can.

gl

j

 

[PAB]

Hi johnph77,

In any case, the spreadsheet is finished, awaiting contact from Sammy. It's smaller (at 219Mb) than I thought it would be. And I more or less took it on just to see if it could be done. It can.

Nice One!. I LOVE it when a Plan comes Together.

All the Best.
PAB

 

[bloubul]

johnph77

Please put me on your mailing list too.


BlouBul

 

[Sammy]

Hi John,

Problem trying to contact you: tried to install Yahoo Messenger but received error message.

Sammy

Sammy -

Due to the size of the file(s) it's best sent on a CD R/W. Will need an address - contact me via Yahoo Messenger - this ID.

But I may fool with it a little more before sending - if I divide it up into a 5/34 results sheet and add the Thunderball and line numbers later I may be able to send an Excel file - 14 pages, a page for each Thunderball - complete with drawing numbers. When time permits.....

gl

j