Lottery Blackbody Radiation

Reply #39

Sunglasses — Wed, 03 Aug 2016 19:03:00 GMT

MUSL, which lottery? Seed please

Reply #38

RJOh — Tue, 02 Aug 2016 19:58:06 GMT

Who knows, with a RNG anything is possible. Just ask Tipton about the MUSL RNG.

Reply #37

LiveInGreenBay — Tue, 02 Aug 2016 17:55:58 GMT

Thanks. I've been following a 6/39 RNG game for some time now. And occasionally a semi-predictable pattern seems to emerge then after a few days the pattern changes and trends in a different direction. Is this coincidence or do you think RNG numbers are predictable

Reply #36

RJOh — Tue, 02 Aug 2016 17:38:50 GMT

All computer languages have a RND function which needs a seed number. If the same seed number is used every time the same sequence of random numbers are generated every time. A programmer might use the time as a seed to get different numbers since it's unlikely a program would need a seed number the same time every day.

Reply #35

LiveInGreenBay — Tue, 02 Aug 2016 15:35:39 GMT

JADE you seem to know a lot about math and computers. I have a question regarding RNG computers. I understand the first number drawn is called a seed and is drawn using background radiation or noise? Are all the numbers picked using this method or after the seed number is drawn, the rest of the numbers are the result of a program using that seed number as a starting point. Thanks.

Reply #34

JADELottery — Sun, 31 Jul 2016 15:45:21 GMT

We're an Exohumanoid Terran Consultant at the Area 51 Starport.

Best estimated relative I.Q. would be around 105.

Reply #33

LiveInGreenBay — Sat, 30 Jul 2016 19:22:47 GMT

OMG JADE...You're posts make my head spin. What do you do for a living and what's your IQ? Do you ever win

Reply #32

CARBOB — Sat, 30 Jul 2016 14:50:30 GMT

Jade, when you get the mojo solved, keep me in mind

Reply #31

JADELottery — Sat, 30 Jul 2016 14:43:48 GMT

This would be different from the Wave Matrix for the Excel Addin.

The formula is as best a fit we could come up with for these data sets in this short a time.

The actual tie in with the picking probability is much more complex and would need a great deal of mathematical mojo manipulation to get done.

Sometimes spend long hours just staring into virtual space to see the flurry of formula flutter by in fantastic frenzy.

Reply #30

JADELottery — Sat, 30 Jul 2016 14:24:01 GMT

After a fourth rerun, we're going back to the original first posted data.

When some things don't look right, try, try, try, and try again.

Seems we were right the first time.

One Million Tracked # Selections

Draws

Mega Millions

Powerball

P5

MM

P5

PB

0

0

0

0

0

1

0

0

0

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

5

0

0... [ More ]

Reply #29

JADELottery — Sat, 30 Jul 2016 14:08:11 GMT

we may have intermixed Mega Millions with the Powerball data.

it's done in 100,000 blocks of data and have to complete the rerun and curve fitting.

should be finished in about 20 min or so.

Reply #28

JADELottery — Sat, 30 Jul 2016 13:36:03 GMT

Below is a table showing the Total Probability for each Pick 1 to Pick 5.

In the Pick 1, we see the probability reaches 100%, but that is just due to rounding.

It's actually more like 99.95% and is very close to 100%.

This shows that as more draws occur, the more likely the cycle will end.

In the Pick 1, by draw 27, it's above 50%; by draw 35, it's above 75%; by draw 44, it's just above 90%.

In Pick 3, by draw 8, it's above 50% and in Pick 4, by draw 6, it's above 50%.

If there... [ More ]

Reply #27

JADELottery — Sat, 30 Jul 2016 13:15:22 GMT

That's an observed maximum in the 29,283,008 data samples we collected.

The actual upper limit extends to .

However, the probability reaching that draw is very, very low; 0.000000396554819 or 0.0000396554819% or 1 in 2,521,719.45 .

It's much more likely the cycle will end sooner than later.

Reply #26

JADELottery — Sat, 30 Jul 2016 13:03:25 GMT

It has to do with the Mega Millions and Powerball, again.

We think the P5 columns are swapped as well.

Just need to complete a few hundred million samples to verify.

Working it now.

Reply #25

Sunglasses — Sat, 30 Jul 2016 10:48:25 GMT

You are new to mathematics and gambling. Step off this and go play classical games in casinos. Your learning curve will be higher.

Reply #24

CARBOB — Sat, 30 Jul 2016 10:41:29 GMT

Magnificent job, Jade. I knew there had to be a maximum number of draws for all of the digits to show. Now, we need a plan of the range to play, maybe median. We have some fantastic math individuals on this fantastic forum.

Reply #23

JADELottery — Sat, 30 Jul 2016 03:38:07 GMT

Need to quad check some numbers again.

Trying to do too many at once.

Reply #22

JADELottery — Sat, 30 Jul 2016 03:08:59 GMT

Get back to this later.

Data Data Data.

Reply #21

JADELottery — Sat, 30 Jul 2016 02:02:59 GMT

The following is the Instantaneous Probability, meaning, at any given draw there is a probability the tracked selection will complete the cycle at that draw.

However, as more draws occur and more numbers are tracked, there is a Total Probability the tracked selection will complete due to the decreasing numbers left to select from.

This results in a different Probability and is show in the next graph in blue.

.

Reply #20

JADELottery — Sat, 30 Jul 2016 01:02:21 GMT

Have to repost these.

Got the Powerball columns swapped and a quirk in Excel counting.

One Million Tracked # Selections

Draws

Mega Millions

Powerball

P5

MM

P5

PB

0

0

0

0

0

1

0

0

0

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

5

0

0

0

0

6

0

0

0

0

7

0

0

0

0

Reply #19

lottologix — Sat, 30 Jul 2016 00:46:43 GMT

Thank you for the clarification on this. I could still be framing this idea all wrong but this is still pointing to a given amount of game history? For example when I try to figure out how many games of history to use in Mega Millions I divide the number of numbers picked in the first pool which is 5 digits by the largest number found in the first pool which is 75. Then multiply that by 2 which... 75/5=15x2=30 this gives each number the opportunity to appear twice. This new formula seems to me t... [ More ]

Reply #18

Sunglasses — Sat, 30 Jul 2016 00:27:04 GMT

No, maximum is between 10 and number of drawings when there were 10 or more drawings. A number can set out for all drawings. 140 is mathematical average.

If the game stops after 100 games, 140 is not reached. If the game lasts 200 drawings and 1 wasn't drawn, it is not 200.

Reply #17

lottologix — Sat, 30 Jul 2016 00:22:44 GMT

I could be wrong here but it looks like this data is pointing out the ideal number of games to look back on.

Reply #16

JADELottery — Sat, 30 Jul 2016 00:22:00 GMT

Some draw points of interest for Mega Millions and Powerball.

Mega Millions

Powerball

P5

MM

P5

PB

Minimum

32

15

27

35

Peak

63.06752387

40.15977315

56.95323841

83.21506128

Mode

64

40

55

86

Median

69

46

62

94

Mean

71.89412

49.77080

64.98075

100.02987

Maximum

215

193

200

378

Keep in mind these are... [ More ]

Reply #15

JADELottery — Sat, 30 Jul 2016 00:16:00 GMT

The Mega Millions and Powerball coefficients worked out as follows.

One Million Tracked # Selections

Coefficients

Mega Millions

Powerball

P5

MM

P5

PB

-25071.1661813529

-3222.36292582329

-16462.2594409085

-17530.109547895

561.935259517947

44.842980648871

348.902303712761

130.283721952551

-2.55343571484057

0.19511648743907

-0.609658887158907

0.289651365681885

Reply #14

JADELottery — Sat, 30 Jul 2016 00:14:32 GMT

This formula is not restricted to just Daily Pick games.

We applied it to Mega Millions and Powerball.

Below is a tracked # selection data sample run for both.

One Million Tracked # Selections

Draws

Mega Millions

Powerball

P5

MM

P5

PB

0

0

0

0

0

1

0

0

0

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

5

0

0

0

0

Reply #13

JADELottery — Sat, 30 Jul 2016 00:03:01 GMT

Here are the points of interest for Pick 1 to Pick 5.

Draws

Pick 1

Pick 2

Pick 3

Pick 4

Pick 5

Minimum

10

5

4

3

2

Peak

22.732498

11.031043

7.202824

5.261479

4.031870

Mode

24

11

7

5

4

Median

27

13

8

6

5

Mean

29.283008

14.131397

9.047672

6.483503

4.933889

Maximum

140

73

51

34

24

Reply #12

JADELottery — Fri, 29 Jul 2016 23:59:16 GMT

The coefficients worked out to the following.

One Million Tracked # Selections 0-9

Coefficients

Pick 1

Pick 2

Pick 3

Pick 4

Pick 5

-966.93367803712

-288.229657414759

-112.848634704551

-60.9196072763659

-45.5856415845385

30.6458275075256

26.4269626065139

12.9474585211997

8.68322021541142

11.5743576972091

-0.165505462399517

-0.00183622361668888

1.05332367290803

1.76921742869347

Reply #11

JADELottery — Fri, 29 Jul 2016 23:56:41 GMT

Knowing this formula works for Pick 3, we completed it for Pick 1 to Pick 5.

Below is a table of the frequency data we sampled.

One Million Tracked # Selections 0-9

Draws

Pick 1

Pick 2

Pick 3

Pick 4

Pick 5

0

0

0

0

0

0

1

0

0

0

0

0

2

0

0

0

0

3995

3

0

0

0

24378

173281

4

0

0

14907

148658

301168

5

0

6... [ More ]

Reply #10

JADELottery — Fri, 29 Jul 2016 23:52:46 GMT

We expanded this tracking to all the Pick 3 numbers and were excited to find the same formula worked for the Pick 3 overall tracking.

Below is an example of the tracking.

In this example, we can see all the numbers are picked by draw 8.

Then the cycle starts over and the next complete selection is at draw 18 or 10 draws to select all numbers.

Draw

Pick 3

Tracked # Selection

A

B

C

0

1

2

3

4

5

6

7

8

9

1

2

Reply #9

Sunglasses — Fri, 29 Jul 2016 23:51:49 GMT

I'd suggest to set the maximum to 140 to lifetime of the game.

Reply #8

lottologix — Fri, 29 Jul 2016 23:50:09 GMT

I have been trying to follow your research. So far it has led me to test skip ranges for single digits. this does tell when to best play the number. working with the 2007 add in I found that groups of 5 worked best. I was not having much luck with straight number runs but it did work better with box digit tracking. Are you going to make a new add in for this method? I find this very interesting and appreciate your work on this. I wonder how this formula in this thread would look when applied to

Reply #7

JADELottery — Fri, 29 Jul 2016 23:36:42 GMT

This is something new.

Reply #6

JADELottery — Fri, 29 Jul 2016 23:35:16 GMT

Using the coefficients and probability function we can now calculate the maximum frequency draws that it takes to draw all the numbers in a single column.

This works out to be about 22.732498 draws.

In addition, here are other points of interest in the data we sampled.

Draws

Minimum

10

Peak

22.732498

Mode

24

Median

27

Mean

29.283008

Maximum

140

Continues ...

Reply #5

lottologix — Fri, 29 Jul 2016 23:32:03 GMT

Is this the same or similar as the wave add in you made for excel 2007

Reply #4

JADELottery — Fri, 29 Jul 2016 23:26:12 GMT

The coefficients for the Pick 1 probability are:

Coefficients

Pick 1

-966.93367803712

30.6458275075256

-0.165505462399517

-0.105317939314043

These plugged in the probability function gives the following graph.

Continues ...

Reply #3

JADELottery — Fri, 29 Jul 2016 23:20:29 GMT

The formula expression we had to used is as follows.

This expression fit the data far better.

Using the expression we curve fit it and found the values for , , and .

The graph next shows the bar graph and the curve fit probability function.

Continues ...

Reply #2

JADELottery — Fri, 29 Jul 2016 22:48:57 GMT

In the graph of the Tracked # Selections, we can see the frequency is skewed to the low end and tapers off to the high end.

This graph looks very similar to a natural phenomenon know as Blackbody Radiation.

Below is a graph of the Planck Radiation Formula.

We tried to curve fit this formula to the data, but it did not fit very well.

We had to come up with a different variation that looks nearly the same as the Planck Formula.

Continues ...

Reply #1

JADELottery — Fri, 29 Jul 2016 22:39:52 GMT

The next step was to gather a frequency of draws when the cycle ends.

In the previous example, it was the 24th draw.

We ran a simulation for Millions of draws to obtain a Million data set of end draw cycles.

Below is a table of our obtained data for this run.

The table shows there is a minimum of 10 draws; which is to be expected since there are only 10 numbers 0 to 9 that can be selected.

The Peak appears to be at 24 draws.

Next we will look at the graph of the data.

Lottery Blackbody Radiation

JADELottery — Fri, 29 Jul 2016 22:27:01 GMT

As we stated in our blog, we were asked a question by CARBOB about how long does it take for all numbers in a Pick 3 type lottery to be picked; both in a single column and overall.

It led to an interesting formula that is very similar to Blackbody Radiation.

We'll start with a simple Pick 1 example.

This can apply to any individual Pick 3 column.

In the Pick 1 selection, we keep track of the number selected at each drawing.

Below is a table showing the Draw, Picked number and the... [ More ]