|
Question about abbreviated wheels
Dear All, hello from Portugal.
I like to post a question about abbreviated wheels and how to...
Sorry if my english is not very correct, but... I will try to explain myself...
As an example, the (8,5,4,5) wheel system of EuroMillions 5/50 (the European Lottery).
I know that the minimal abbreviated wheel has only 5 combinations:
1: 01 02 04 06 07
2: 01 03 04 05 08
3: 01 03 05 06 08
4: 02 03 05 07 08
5: 03 04 05 06 08
But as we see, the combinations 3: and 5:, are only one number different from combination 2: !!!
This means that when we are retiring the entries that are different of one number from combination 2:, even covering the 4/5, the combinations 3: and 5: are "called back" to the system.
I also know that if we don't 'call back' any entries, the final abbreviated wheel will have 7 entries.
The same thing happens with (9,5,4,5) wheel system of EuroMillions 5/50. The minimal abbreviated wheel has only 9 combinations:
1: 01 02 03 06 08
2: 01 02 04 07 09
3: 01 03 04 05 08
4: 01 03 05 08 09
5: 01 04 06 07 09
6: 02 03 05 06 07
7: 02 04 05 06 09
8: 02 05 06 07 08
9: 03 04 07 08 09
but we see that combination 2: retires number 5:, 3: retires 4: and 6: retires 8:. So combinations 5:, 4: and 8: are "called back" to the system!
I know that if we don't 'call back' any entries, the final abbreviated wheel will have 14 entries, instead of the 9 entries.
I know that with 6/49 (here in Portugal its name is Totoloto) it happens the same thing. The minimal abbreviated wheels also have situations like this.
Covermaster and other applications deals or calculate the abbreviated wheels playing with this facts.
Question:
can somebody teach me how to know about this fact?
or why it (must) happens?
it's mathmatical?
it's our feeling?
some help?
Thanks in advance & kind regards
Paulo Franco
(Portugal)
|
Linear Mode
