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Covers or Wheels with Guarantees and Unique 3's
 LottoPoster Forums : NUMBER SETS TO PLAY FROM DIFFERENT METHODS : Covers or Wheels with Guarantees and Unique 3's
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
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To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
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Posts: 678
Quote Colin F Replybullet Topic: Covers for Pool 7
    Posted: June 12 2005 at 3:02am

COVERS FOR POOL 7

In considering these covers you should bear in mind they are extremely hypothetical as there is no Pick 6 Lotto game with just 7 integers - more like 45 or 49. So, to get 3 or more right from a 6/45 or 6/49 Lotto game in just a 7 integer pool that you nominate is a very rare occurrence. Some including me do say that to predicate something happening from just 7 Combinations when there are some 8 or 14 million other possible combinations is nothing less than farcical!
 
Here are the tables of Combinations that we need. In the covered column for doing this manually you would cross out the "No" when covered or if you were doing this programatically it would be changed to true. 

C(7,6,6,6) = 7
6 win if 6 of the integers from a pool of 7 are in the winning 6.

This is a System 7 or Full Wheel which is all the combinations of 6 from a pool of 7 numbers as shown in table Sixes from Pool 7.

Now, if you manage to get 6 right not only do you get the winning six but also the other 6 combinations each have a five in them - so you do quite well on the night for an outlay of say, $3.50 or so.

If you only get 5 correct in the winning six you get 2 fives and 5 fours. If only 4 correct you get 3 fours and 4 threes. If only 3 correct you still get 4 threes.

C(7,6,5,6) = 1
5 win if 6 of the integers from a pool of 7 are in the winning 6.

Any one of the 7 Combinations of Six from the pool of 7 numbers will fulfill this cover by having at least one five in the other 6 combinations.

This cover highlights the drawbacks of covers that are other than System or Full Wheels. If on the night you see you have 6 integers correct from your pool of 7 integers then your jumping up and down and whooping should be restrained to that appropriate for a 5 win until you confirm that your one and only 6 is the winning six - then you can do cartwheels on the ceiling.

From 6 numbers we can obtain 6 combinations of 5. Let's say the winning 6 is:
01 02 03 04 05 06
and the combination we played was:
01 02 03 04 05 07
then of the 6 fives we can form from our play -
01 02 03 04 05
01 02 03 04 07
01 02 03 05 07
01 02 04 05 07
01 03 04 05 07
02 03 04 05 07
we see there is a match with 01 02 03 04 05 in the fives formed from the winning six -
Fives in our Six   ID for Six Covered
01 02 03 04 05             1
01 02 03 04 06             3
01 02 03 05 06             4
01 02 04 05 06             5
01 03 04 05 06             6
02 03 04 05 06             7

(A simple way I use in forming these sets is to drop a number from right to left for each line.)

C(7,6,4,4) = 5
4 win if 4 of the integers from a pool of 7 are in the winning 6.

I deliberately started with ID 7 Six because any one of them has 15 fours and it's better to be flexible and experimental in ones thinking rather than regimented. You can learn by making mistakes. With the small pool of 7 numbers we don't have a lot of choices and I simply formed the sixes progressively as required.

You're forgiven if you are starting to think - is that all it is! All those Guru Guru people poncing about and making out they're ever so clever and a 9 year old can understand it. (Is that right Sash? Yes, Dad! There I told you!)

C(7,6,3,4) = 1
3 win if 4 of the integers from a pool of 7 are in the winning 6.
 

Each Six contains 15 fours. Check out for yourself and you will see any of our 7 sixes from a pool of 7 integers will cover the 35 distinct fours that can be formed from the same pool. eg The Six in which the Four 01 02 03 07 appears is covered by 01 02 03 04 05 06 because the other two integers in that six must be 04 05 or 04 06 or 04 07 or 05 06 or 05 07 or 06 07 in any case providing the other required integer.  

C(7,6,3,3) = 4
3 win if 3 of the integers from a pool of 7 are in the winning 6.

There are 20 combinations of three that can be formed from any six and looking at the color coded Covering Six you see that 4 are required. Now you should be getting the hang of this. Eezy Peezy! 

Regards
Colin

ps They do get harder.

Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.
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