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Do they Work? Systems, Covers, Designs and Wheels tested.
 LottoPoster Forums : LOTTO PLAYING SYSTEMS TEST RUN RESULTS : Do they Work? Systems, Covers, Designs and Wheels tested.
Message Icon Topic: 3 if 6 in 49 Abrev Wheel 51% Cover 32 L Post Reply Post New Topic
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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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Quote Colin F Replybullet Topic: 3 if 6 in 49 Abrev Wheel 51% Cover 32 L
    Posted: December 17 2004 at 7:39am

I have to admit that even in the middle of doing something more complicated I have always been attracted to the idea of using all the integers in a particular Lotto just once or twice in a random way. In a Pick 6 from 45 as played mainly in Australia you can do this in 15 Combs each integer appearing twice only.

This test is on the 6/49 Lotto Game using a partial Cover where each integer appears pretty well 4 times. There are 13,983,816 Combinations of 6 that can be obtained from the 49 integers. The full Cover of 163 Combs optimized or 322 Combs unoptimized have already been done; this is only a 51% cover.

Elaborating a little on that if we take as our first Comb 1 2 3 4 5 6 (it doesn't have to be this) then because from each 6 we can obtain 20 combinations of 3 we find when we test each 3 combination that we can cover 260,624 combinations of 6 from the 13,983,816 combinations of 6. A breakdown on each would be starting with 123 (you don't have to - you could start with 456 and get the same figure):

 
123                                                15,180 x  1 =  15,180
124, 134, 234                                      14,190 x  3 =  42,570
125, 135, 145, 235, 245, 345                       13,244 x  6 =  79,464
126, 136, 146, 156, 236, 246, 256, 346, 356, 456   12,341 x 10 = 123,410

So tagging our 260,624 Combinations of 6 that are now covered and subtracting from 13,983,816 we are left with 13,723,192 to still cover. If we pick 7 8 9 10 11 12 as our next Comb we find this can cover 260,224 Combs and so on until we have 51% coverage.

 
Regards
Colin
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