Covering Designs - MM and PB

Reply #23

tokecap — Sun, 19 Jul 2026 15:20:41 GMT

You've hit precisely on the core mathematical tension that separates academic covering designs from practical play. When you scale up to a massive matrix like Powerball ( $69 \choose 5$ ) or Mega Millions ( $70 \choose 5$ ), the covering numbers ( $C(v, k, t, m)$ ) explode. The combinatorial explosion outpaces the lower-tier prize payouts so severely that you are essentially paying premium rates for guaranteed micro-returns, even before factoring in the independent $1/26$ or $1/25$ Powerball mod... [ More ]

Reply #22

NumberCruncher2 — Sat, 18 Jul 2026 15:19:51 GMT

This is one of the few genuinely rigorous angles on the whole thing, so glad to see someone working it seriously. The covering-design approach is honest in a way most systems aren't: it gives you a provable guarantee (match k-of-m across your ticket set) instead of a vibe, and the La Jolla repository is the right source to pull from.

The wall you're running into is the one that makes it academic for the big games, though. A (69,5,5,3) type covering to guarantee a 3-match on Powerball's white... [ More ]

Reply #21

tokecap — Wed, 15 Jul 2026 16:09:34 GMT

MM 7, 14, 2026

2 - 4 - 10 - 48 - 56

1 2 10 14 18 47 48 52 56 61 68 70 - 4

2 4 5 9 26 27 31 35 38 46 48 64 - 3

2 4 7 19 25 36 40 50 56 60 63 68 - 3

2 4 8 10 11 28 32 44 49 53 61 66 - 3

2 6 11 16 17 22 25 32 39 45 48 56 - 3

4 7 10 13 16 33 43 48 49 54 57 66 - 3

4 8 15 17 24 41 48 56 61 62 68 69 - 3

4 10 20 34 38 39 42 51 56 59 65 66 -3

Mother

2 4 10 14 25 47 48 51 56 61 65 68 - 5

Reply #20

tokecap — Wed, 15 Jul 2026 16:01:49 GMT

PW - 7, 13, 2026

5 - 25 - 36 - 40 - 48

2 5 8 13 18 21 36 47 48 55 59 68 - 3

2 6 10 24 27 29 30 31 36 40 48 54 - 3

3 5 8 14 25 27 44 45 48 59 60 69 - 3

4 7 11 25 27 29 30 31 33 36 40 54 - 3

5 6 7 10 11 13 23 24 25 33 39 48 - 3

5 8 13 21 22 23 40 42 48 50 63 66 - 3

5 13 17 25 33 40 41 49 52 56 58 59 -3

5 13 25 33 36 37 38 45 50 52 53 65 -3

6 9 15 17 22 24 25 26 36 44 48 62 -3

6 9 18 19 24 25 28 35 40 45 48 64 - 3

Mother

5 9 25 33 36 37 40 41 44 48 57 68

Reply #19

Player649 — Fri, 03 Jul 2026 23:41:54 GMT

If you want to get involved in wheeling with PB or MM you can do the following. I will start from MM as it is easier to implement.

MM has 70 numbers and draws 5 of them at a time. To cover all the numbers you need 14 tickets (70 / 5 = 14). This gives you the maximum hit rate no matter what numbers are drawn.

This is the base wheel to start from.

1, 15, 29, 43, 57

2, 16, 30, 44, 58

3, 17, 31, 45, 59

4, 18, 32, 46, 60

5, 19, 33, 47, 61

6, 20, 34, 48, 62

7, 21, 35, 49,... [ More ]

Reply #18

Player649 — Sun, 28 Jun 2026 00:16:03 GMT

Curious where the practical line is.

Such practical line does exist. It's called the wheel hit rate.

For the examples demonstrated above, for 12 numbers the average (expected) hit rates for PB MM are 0.87 and 0.86 respectively.

You can get the same rates with only 3 tickets in each lottery, not hundreds.

To have an expected hit rate of 3 (as required by the above wheels) you need 42 numbers for each lottery. This would require 9 tickets in each, again not hundreds.

The true v... [ More ]

Reply #17

NumberCruncher2 — Tue, 23 Jun 2026 16:49:00 GMT

Covering designs are one of the few areas where the math gives you something concrete - a real guarantee on minimum matches for a given ticket count, not just a feeling. The catch is the ticket counts balloon fast on a 1-69 pool. Have you found a coverage level that's actually affordable to play, or is it more of a theoretical exercise for the big games? Curious where the practical line is.

Reply #16

tokecap — Tue, 16 Jun 2026 13:06:09 GMT

06/15/2026

25 - 55 - 57 - 60 - 62 23

Reply #15

IAmABadOne — Tue, 09 Jun 2026 00:16:34 GMT

Ok, after reading the explanation again while paying more attention I completely understand what it really says.

Anyway, I do wish to thank you for posting anything about covering designs/wheels even if no one else is interested.

Best wishes.

Reply #14

tokecap — Fri, 05 Jun 2026 08:47:04 GMT

12 lines

12,5,3,4

01 02 05 06 09

01 03 08 10 11

01 04 06 10 12

01 04 07 09 11

01 05 07 08 12

02 03 04 09 12

02 03 06 07 10

02 04 05 08 10

02 07 08 11 12

03 04 05 06 11

03 06 07 08 09

05 09 10 11 12

Reply #13

tokecap — Fri, 05 Jun 2026 08:44:51 GMT

29 lines

12,5,3,3

01 02 03 09 12

01 02 04 06 08

01 02 05 07 08

01 02 06 10 11

01 03 04 05 07

01 03 05 09 10

01 03 06 07 09

01 03 08 09 11

01 04 05 09 12

01 04 07 10 11

01 05 06 11 12

01 07 08 10 12

02 03 04 09 11

02 03 05 06 12

02 03 07 10 12

02 03 08 11 12

02 04 05 08 10

02 04 06 07 12

02 05 07 09 11

02 06 08 09 10

03 04 06 10 12

03 04 08 11 12

03 05 08 10 11

03 06 07 08 11

04 05 06 09 11

Reply #12

IAmABadOne — Fri, 05 Jun 2026 00:34:24 GMT

I get that there are 350 12 number sets that guarantee a 100% coverage for a 3 number hit as described above.

The question I have is what are we to do with 12 number sets when PB or MM only use 5 number sets?

I hope that makes my question more clear.

Thanks for any info you can provide on that issue and Best Wishes for your plays.

Reply #11

tokecap — Thu, 04 Jun 2026 16:51:09 GMT

This is a mathematical covering design (or lottery wheel) that reduces the total number pool of Powerball/Mega Millions into just 350 combinations of 12-number sets . This specific optimization guarantees a 100% catch-rate for a 3-match and a 50% probability of hitting a 4-match , significantly lowering the cost while maintaining high efficiency.

Reply #10

IAmABadOne — Thu, 04 Jun 2026 02:14:12 GMT

Tokecap,

The way I am reading these covering designs, they are not for PB or MM.

I read them as games that are:

1) 69 or 70 balls covered in the design

2) 12 Balls are drawn each drawing

3) Coverage of at least one 3 ball hit guaranteed (assumed 100% coverage)

4) If 3 balls are in the 69 or 70 balls covered.

CoverMaster says it takes about 30 lines of 5 numbers to reach a 100% 12,5,3,3 cover (12 numbers in each one of your lines).

How are you planning to put these... [ More ]

Reply #9

tokecap — Mon, 01 Jun 2026 12:18:29 GMT

PW 1 - 27 - 35 - 44 - 52

Reply #8

tokecap — Thu, 28 May 2026 14:13:41 GMT

PB - 5 14 21 31 5 1

4 5 9 14 21 26 28 31 33 38 39 49 - 4

1 2 4 5 16 31 51 52 59 65 66 67 - 3

1 6 7 13 14 21 24 26 28 31 38 49 - 3

2 3 8 14 21 23 25 26 28 31 38 49 - 3

5 6 11 15 21 23 24 29 34 45 51 58 - 3

5 13 14 19 22 25 30 33 51 52 57 68 - 3

10 11 12 14 21 26 28 31 38 48 49 52 - 3

14 21 22 29 30 31 36 40 45 53 55 61 - 3

14 21 26 29 37 38 46 49 50 51 63 66 - 3

15 17 18 21 31 37 41 51 53 56 60 69 - 3

Reply #7

tokecap — Wed, 27 May 2026 12:57:40 GMT

MEGA Millions results 5/26

1-5-49-51-59

Reply #6

tokecap — Tue, 26 May 2026 16:44:40 GMT

Mathematical conference test of the latest Powerball result

POWERBALL results 5/25;

17-32-48-60-64 + 10

2 4 11 13 17 21 27 32 48 57 64 65 - 4

16 17 26 28 32 37 51 60 64 67 68 69 - 4

1 12 17 21 23 25 27 32 33 57 64 65 - 3

3 5 7 9 10 17 21 27 32 57 64 65 - 3

5 8 12 13 17 28 42 47 48 51 53 60 - 3

6 8 17 21 24 27 32 39 52 57 64 65 - 3

10 11 12 19 32 34 36 48 52 56 60 66 - 3

14 16 17 21 29 32 42 54 56 57 64 65 - 3

14 17 22 28 38 45 51 55 58 60 64 68 - 3

17 20 2... [ More ]

Reply #5

tokecap — Mon, 25 May 2026 14:08:27 GMT

PB

69,12,3,5 = 76

01 02 03 04 05 06 09 14 15 23 30 36

01 02 03 04 07 12 13 26 27 28 31 34

01 02 03 04 08 10 11 16 18 19 25 35

01 02 03 04 17 20 21 22 24 29 32 33

01 04 08 13 16 21 22 24 26 30 35 36

01 05 06 07 10 18 20 24 26 28 30 32

01 05 06 08 12 19 22 27 29 30 33 35

01 05 06 11 13 16 17 21 25 30 31 34

01 07 08 14 17 19 21 23 26 28 35 36

01 07 09 11 15 16 22 25 26 28 29 33

01 08 09 13 15 19 20 24 31 32 34 35

01 09 10 12 15 17 18 21 27 30 32 3... [ More ]

Reply #4

tokecap — Mon, 25 May 2026 14:06:43 GMT

MM

70,12,3,5 = 79

01 02 03 04 05 06 09 14 15 23 30 36

01 02 03 04 07 12 13 26 27 28 31 34

01 02 03 04 08 10 11 16 18 19 25 35

01 02 03 04 17 20 21 22 24 29 32 33

01 04 08 13 16 21 22 24 26 30 35 36

01 05 06 07 10 18 20 24 26 28 30 32

01 05 06 08 12 19 22 27 29 30 33 35

01 05 06 11 13 16 17 21 25 30 31 34

01 07 08 14 17 19 21 23 26 28 35 36

01 07 09 11 15 16 22 25 26 28 29 33

01 08 09 13 15 19 20 24 31 32 34 35

01 09 10 12 15 17 18 21 27 30 32 3... [ More ]

Reply #3

tokecap — Sat, 23 May 2026 13:10:51 GMT

Covering Design for PB

69,12,4,4 = 3276

Jan de Heer and Steve Muir

https://ljcr.dmgordon.org/show_cover.php?v=69 k=12 t=4

Covering Design for MM

70,12,4,4 = 3338

Jan de Heer and Steve Muir

https://ljcr.dmgordon.org/show_cover.php?v=70 k=12 t=4

Reply #2

tokecap — Sat, 23 May 2026 13:07:14 GMT

Covering Design for PB

69,12,3,3 = 348

Franco Atzeni

https://ljcr.dmgordon.org/show_cover.php?v=69 k=12 t=3

Covering Design for MM

70,12,3,3 = 352

Franco Atzeni

https://ljcr.dmgordon.org/show_cover.php?v=70 k=12 t=3

Reply #1

tokecap — Thu, 21 May 2026 18:31:10 GMT

PB

69,12,3,3 = 348

https://ljcr.dmgordon.org/show_cover.php?v=69 k=12 t=3

MM

70,12,3,3 = 352

https://ljcr.dmgordon.org/show_cover.php?v=70 k=12 t=3

Covering Designs - MM and PB

tokecap — Thu, 21 May 2026 18:25:39 GMT

Covering Design for MM

70,19,5,5 = 3397

Creator: Jan de Heer and Steve Muir - Method: Private Tools

https://www.coveringrepository.com/download_system.aspx?id=160692

Covering Design for PB

69,18,5,5 = 2739

Jan de Heer and Steve Muir - Method: Private Tools

https://ljcr.dmgordon.org/show_cover.php?v=69 k=18 t=5