Best Lower Bounds for Lotto Covers or Wheels

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The following mathematical Cover lower bounds are given for reference purposes only and not as a recommendation to be played in Lotto.

As an example in the first table for Pick 6 Lotto games from the column heading 3if6 and for Pool 25 a match-3 prize is guaranteed when the 22 line Cover is played. In other words all the 177,100 combinations of 6 integers from a Pool of 25 are covered by the 22 lines such that at least one match-3 is guaranteed.

For the column 3if3 for the same Pool of 25 a match-3 prize is guaranteed as all the 2,300 CombThrees are covered by the 130 lines played.

Whether playing these covers for a Pick 6, Pool 25 Lotto game is the best approach is discussed for the West Virginia Cash 25 game here

The bounds in red are Steiner Systems which cannot be further compacted.
Beyond Pool 30 for a Pick 6 Lotto game see merged mathematical covers.

Covers or Wheels with Guarantee for Pick 6 Lotto with World's Lowest Bounds
Pool	3if6	3if5	3if4	3if3	4if6	4if5	4if4	5if6	5if5
7	1	1	1	4	1	1	5	1	6
8	1	1	3	4	1	3	7	4	12
9	1	2	3	7	3	3	12	7	30
10	2	2	4	10	3	7	20	14	50
11	2	2	5	11	5	10	32	22	100
12	2	2	6	15	6	14	41	38
13	2	5	9	21	10	21	66	61
14	4	5	11	25	14	31	80	98
15	4	7	14	31	19	41
16	5	8	16	38	25	54
17	6	11	20	44	34	66
18	7	12	24	48	42	81
19	9	15	30	60	54
20	10	18	35	71	66
21	13	21	40	77	80
22	15	22	46	77
23	17	26	54	104
24	20	30	61	116
25	22	34	68	130
26	25	39	76	130
27	27	45	86	167
28	31	49	97	185
29	35	55	108	217
30	39	61	119	225

Covers or Wheels with Guarantee for Pick 5 Lotto with World's Lowest Bounds
Pool	2if5	2if4	2if3	2if2	3if5	3if4	3if3	4if5	4if4
6	1	1	1	3	1	1	4	1	5
7	1	1	2	3	1	3	5	3	9
8	1	2	2	4	2	3	8	5	20
9	2	2	2	5	2	5	12	9	30
10	2	2	2	6	2	7	17	14	51
11	2	2	4	7	5	9	20	22	66
12	2	3	4	9	6	12	29	35	113
13	3	3	5	10	8	16	34	48
14	3	3	6	12	10	19	43	69
15	3	3	7	13	13	24	56	95
16	3	5	8	15	14	31	65	132
17	4	5	9	16	18	37	68
18	4	6	10	18	22	43	94
19	4	7	11	19	26	52	108
20	4	8	12	21	32	61
21	6	9	13	21	37	72
22	6	10	14	27	40	83
23	7	11	16	28	49	95
24	8	12	17	30	54	107
25	9	13	18	30	63
26	10	14	20	37	68
27	11	15	21	38	77
28	12	16	23	40	86
29	13	17	24	43	97
30	14	18	26	48	102

Colin Fairbrother

This article first published on the web 20/9/2007 and has been viewed 7214 times.
The author may be contacted at fairbros@bigpond.com. To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ^® where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster