"Less is More": Lotto Pairs, Least-Pairings in Lottery, Reduction of Combinations to Play
Posted by Nik Barker on March 16, 2002.
Dear all,
You will see below the test I've just completed for the Least Pairings for lotto. This is an important test. It is almost as arduous as the test I did for Util-6 lotto 6 software. The aim of this analysis was to look at the relationship between the least pairings and the numbers drawn in 100 consecutive lottery drawings.
The headings in the table below are fairly self-explanatory, but I will clarify for lack of confusion… by the way, the way to read the table is from bottom to top…and the +/- relates whether the 'overall' figure was higher or lower than the previous draw…
“Draw No.” – that's obvious, right?!
“No. of least pairings that could have been discarded for each lotto ball” – this means that each time, I have run a frequency report and looked at the Pairs6 file, gone to each number that occurred in the relevant draw, and counted back from the END of the Pairs6 file to see how many least pairings for EACH lottery number could have been eliminated before finding another number that came up in that draw…example…in draw number 649 I looked at the Pairs6 file and found the B1 number, went to the end of the line and then counted back until I found the occurrence of either B2, B3, B4, B5, or B6 – whichever came first…then did the same for EACH lotto ball that came up in that draw.
“Overall Least pairings that could have been used” – this is the lowest 'common denominator'. I.E. B1 may have been able to have 10 of its worst lottery pairings eliminated without affecting it coming up with the other 5 lotto balls drawn, but B6 could only 'survive' 2 worst lotto pairings being eliminated without that affecting it coming up with the other 5 balls drawn. So the end result – to still be able to eliminate worst pairings and still leave the 6 winning numbers available – is the lowest value for any of the 6 balls' least pairings.
This table relates to the UK National Lottery and is for the most recent (at time of going to press – 14/03/02) 100 lotto draws. I should also say that each time I ran the frequency report I used the default of 147 draws to check against.
Conclusions
Initially I was a little perplexed. I was expecting much higher figures for the 'overall' category. After all, if we can say with some surety that 'on average' we could eliminate, say, 10 worst lotto pairings for each lotto number and still 'enable' the 6 winning numbers, then this would be a good thing…because to eliminate 10 worst pairings each draw for each number (and be right the majority of the time) would be a powerful tool in eliminating 'unlikely' lotto combinations.
However, the results are not like that at all. But that is not to say that they are not useful. Indeed, I believe they are most powerful. If we disregard the single occurrences for '8', '9', and '10' – we can say with 97%(!!!) assurance that each draw, one of the lotto numbers drawn will appear with one of its 6 worst pairings!
For a random event, this assuredness of 97% is phenomenal. For those of you that pick a pool of lotto numbers to play with each draw, I bet you that no one ever before picked their numbers that way – using some of LEAST PAIRINGS!
Also you will notice at the bottom of the table I have totted up the scores for all the occurrences for each lottery numbered ball where the individual least pairings that could have been eliminated was greater than or equal to 10. For some reason, the 3rd ball in numerical order has a figure significantly higher than any of the other balls – 42% of the time the third lotto ball in any draw is not drawn with AT LEAST 10 of its worst lottery pairings. Perhaps others can comment as to why this might be, or check it with their own lottery and post their results.
I'm not even sure right now of the whole implications of this test. Maybe others can comment. Maybe this fits into the jigsaw of others' thinking. I feel it is significant somehow, but I don't know quite how yet. I am researching further, but for now, I just wanted to let you know of my results.
I hope it helps.
Best wishes all.
Nik Kulai Barker
No. of Least Pairings that could have Overall Least
been discarded for each ball pairings that could
Draw No B1 B2 B3 B4 B5 B6 have been used +/-
649 10 5 3 12 9 2 2 +
648 9 8 0 1 1 3 0
647 0 0 3 4 6 1 0 -
646 8 2 14 24 2 2 2 -
645 8 11 13 9 10 8 8 +
644 4 11 10 6 17 29 4 +
643 0 0 1 9 0 0 0
642 19 9 22 5 12 0 0 -
641 13 10 9 9 3 4 3 -
640 24 16 13 9 18 28 9 +
639 2 6 3 2 4 18 2
638 2 3 20 11 14 10 2 +
637 2 0 13 7 11 8 0
636 10 5 6 0 14 12 0
635 9 20 10 0 5 7 0 -
634 12 3 23 3 5 10 3 -
633 13 5 23 14 4 7 4 +
632 4 3 2 7 11 1 1
631 2 1 24 13 5 8 1
630 1 8 7 16 9 6 1 +
629 2 4 9 0 0 1 0 -
628 13 1 7 15 23 1 1 +
627 0 12 4 18 2 1 0 -
626 2 15 3 5 9 1 1
625 6 1 5 1 9 3 1 +
624 8 10 0 3 0 4 0 -
623 4 7 3 12 24 17 3 +
622 0 4 4 4 1 2 0
621 1 12 3 1 0 6 0 -
620 8 6 5 1 1 1 1 +
619 7 4 11 2 4 0 0 -
618 10 4 7 2 1 10 1 +
617 13 0 29 4 12 10 0 -
616 10 10 23 23 22 32 1110 1 1+
615 3 4 9 12 4 23 3 +
614 5 0 3 7 8 0 0
613 4 0 4 0 0 2 0 -
612 16 6 5 17 5 12 5 +
611 5 4 6 5 0 4 0 -
610 15 14 1 9 9 14 1 +
609 6 2 4 0 0 5 0
608 0 3 7 0 11 3 0 -
607 6 11 5 8 4 2 2 +
606 17 5 3 4 0 0 0 -
605 3 2 8 7 5 4 2 -
604 6 11 10 5 13 12 6 +
603 16 10 10 6 10 5 5 +
602 3 6 17 3 4 8 3 +
601 2 4 11 15 17 8 2 -
600 5 12 11 3 8 11 3 +
599 18 4 14 0 19 3 0
598 1 0 15 1 1 1 0 -
597 13 27 11 6 12 3 3 +
596 5 0 0 2 3 0 0 -
595 16 4 12 9 8 8 4 +
594 0 0 4 2 5 0 0
593 0 1 1 1 2 1 0 -
592 6 25 27 3 3 3 3 +
591 0 3 1 3 4 3 0
590 29 25 1 0 21 6 0
589 0 8 3 23 10 15 0
588 4 0 18 16 11 3 0 -
587 6 3 16 3 17 1 1 -
586 22 11 15 7 6 15 6 +
585 8 5 7 4 5 11 4 +
584 2 4 1 4 29 6 1
583 4 10 23 21 1 10 1 -
582 3 12 5 6 12 10 3 +
581 15 0 28 2 4 10 0 -
580 8 9 5 6 1 3 1 -
579 27 20 5 6 21 22 5 +
578 2 6 1 2 2 18 1 -
577 25 4 14 2 11 23 2
576 3 5 11 3 2 6 2 +
575 1 6 2 1 0 3 0 -
574 5 14 8 5 3 3 3 +
573 0 3 0 3 0 2 0 -
572 4 11 11 20 17 3 3 +
571 2 16 4 1 1 7 1 +
570 0 3 1 0 9 5 0 -
569 2 7 3 18 6 17 2 +
568 28 28 5 2 0 3 0 -
567 2 7 12 14 9 22 2 +
566 2 0 0 0 0 5 0 -
565 2 9 10 10 4 9 2 +
564 4 0 7 7 3 1 0 -
563 4 4 4 3 3 3 3 +
562 2 12 22 6 3 8 2 +
561 10 1 7 10 6 0 0 -
560 27 7 5 22 7 3 3 +
559 9 2 17 8 1 8 1 -
558 22 13 9 21 5 7 5 -
557 16 11 18 14 6 24 6 +
556 8 3 16 2 10 0 0 -
555 22 8 24 4 7 16 4 -
554 6 12 20 7 7 8 6 +
553 0 6 6 1 0 1 0 -
552 3 15 9 16 20 26 3 +
551 5 2 16 1 5 8 1 -
550 5 6 14 7 5 4 4
>=10 29 27 42 25 29 29
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 = 39
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 = 17
2,2,2,2,2,2,2,2,2,2,2,2,2 = 13
3,3,3,3,3,3,3,3,3,3,3,3,3,3 = 14
4,4,4,4,4,4 = 6
5,5,5,5 = 4
6,6,6,6 = 4
8 = 1
9 = 1
10 = 1
Total = 100
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