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# What number is too high to play for a first ball? (mm/pb)

Topic closed. 23 replies. Last post 5 years ago by sandnan.

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Economy class
Belgium
Member #123696
February 27, 2012
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 Posted: March 21, 2014, 11:01 am - IP Logged

I'm surprised Jo one eon the prize. Ball 75 would be too high. Lol. Sorry guys had to say it

## What number is too high to play for a first ball? (mm/pb)

76 is too high too.

United States
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March 14, 2012
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 Posted: March 21, 2014, 12:02 pm - IP Logged

I'm surprised Jo one eon the prize. Ball 75 would be too high. Lol. Sorry guys had to say it

I think 74 might be too high too.

Quantum Master
West Concord, MN
United States
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 Posted: March 22, 2014, 11:07 am - IP Logged

2 last night (2014-03-21).

We ran a 10,000 draw simulation to see what kind of continuation this run of selecting in the range of 01 to 12 might look like.

A count of 1 in the left column means it selected in the range of 01 to 12 and the next draw did not; essentially the selection cycle starts again.

This last cycle makes it a count of 8 and the next cycle is 9 for 2014-03-25 draw.

 Consecutive Run or # of Selections Drawn in Range 01 to 12 Percent of 10,000 Draw Sample Observation 1 9.77% 2 5.82% 3 3.42% 4 2.08% 5 1.28% 6 0.79% 7 0.28% 8 0.22% 9 0.13% 10 0.17% 11 0.04% 12 0.02% 13 0.03% 14 0.01% 18 0.01%

.

United States
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 Posted: March 22, 2014, 3:48 pm - IP Logged

I will state most emphatically that pseudo-random number generators are absolute junk.

Quantum Master
West Concord, MN
United States
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December 7, 2001
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 Posted: March 23, 2014, 3:16 pm - IP Logged

I will state most emphatically that pseudo-random number generators are absolute junk.

It follows this thread we posted many draws ago.

Discharging Reoccurrence Distribution

To find the distribution you have to determine what it is by what it is not.

.

Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
4309 Posts
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 Posted: March 24, 2014, 3:29 pm - IP Logged

It follows this thread we posted many draws ago.

Discharging Reoccurrence Distribution

To find the distribution you have to determine what it is by what it is not.

Ok, to start we need to determine the total distribution of numbers by column.

We've also posted another topic many draws ago,

Combinatorial Distribution

In it there is a formula for determining any Pick r of n column distribution:

"

Combinatorial Distribution

Factorial - n! = n * (n -1) * (n - 2) * ... * 3 * 2 * 1 , and 0! = 1

Permutation - P(n,r) = n! / (n - r)!

Combination - C(n,r) = P(n,r) / r!

Combinatorial Distribution - D(n,r,c,z) = C(z - 1, c - 1) * C(n - z, r - c)

n - total number of items
r - number of items in a combinatorial or permutational set
c - column number of the distribution
z - item number of the distribution

"

For the Mega Millions current matrix of 5 of 75 the distribution is as follows:

 Column C Item Z 1 2 3 4 5 1 1150626 2 1088430 62196 3 1028790 119280 2556 4 971635 171465 7455 71 5 916895 218960 14490 280 1 6 864501 261970 23460 690 5 7 814385 300696 34170 1360 15 8 766480 335335 46431 2345 35 9 720720 366080 60060 3696 70 10 677040 393120 74880 5460 126 11 635376 416640 90720 7680 210 12 595665 436821 107415 10395 330 13 557845 453840 124806 13640 495 14 521855 467870 142740 17446 715 15 487635 479080 161070 21840 1001 16 455126 487635 179655 26845 1365 17 424270 493696 198360 32480 1820 18 395010 497420 217056 38760 2380 19 367290 498960 235620 45696 3060 20 341055 498465 253935 53295 3876 21 316251 496080 271890 61560 4845 22 292825 491946 289380 70490 5985 23 270725 486200 306306 80080 7315 24 249900 478975 322575 90321 8855 25 230300 470400 338100 101200 10626 26 211876 460600 352800 112700 12650 27 194580 449696 366600 124800 14950 28 178365 437805 379431 137475 17550 29 163185 425040 391230 150696 20475 30 148995 411510 401940 164430 23751 31 135751 397320 411510 178640 27405 32 123410 382571 419895 193285 31465 33 111930 367360 427056 208320 35960 34 101270 351780 432960 223696 40920 35 91390 335920 437580 239360 46376 36 82251 319865 440895 255255 52360 37 73815 303696 442890 271320 58905 38 66045 287490 443556 287490 66045 39 58905 271320 442890 303696 73815 40 52360 255255 440895 319865 82251 41 46376 239360 437580 335920 91390 42 40920 223696 432960 351780 101270 43 35960 208320 427056 367360 111930 44 31465 193285 419895 382571 123410 45 27405 178640 411510 397320 135751 46 23751 164430 401940 411510 148995 47 20475 150696 391230 425040 163185 48 17550 137475 379431 437805 178365 49 14950 124800 366600 449696 194580 50 12650 112700 352800 460600 211876 51 10626 101200 338100 470400 230300 52 8855 90321 322575 478975 249900 53 7315 80080 306306 486200 270725 54 5985 70490 289380 491946 292825 55 4845 61560 271890 496080 316251 56 3876 53295 253935 498465 341055 57 3060 45696 235620 498960 367290 58 2380 38760 217056 497420 395010 59 1820 32480 198360 493696 424270 60 1365 26845 179655 487635 455126 61 1001 21840 161070 479080 487635 62 715 17446 142740 467870 521855 63 495 13640 124806 453840 557845 64 330 10395 107415 436821 595665 65 210 7680 90720 416640 635376 66 126 5460 74880 393120 677040 67 70 3696 60060 366080 720720 68 35 2345 46431 335335 766480 69 15 1360 34170 300696 814385 70 5 690 23460 261970 864501 71 1 280 14490 218960 916895 72 71 7455 171465 971635 73 2556 119280 1028790 74 62196 1088430 75 1150626

.

Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
4309 Posts
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 Posted: March 24, 2014, 4:08 pm - IP Logged

Ok, to start we need to determine the total distribution of numbers by column.

We've also posted another topic many draws ago,

Combinatorial Distribution

In it there is a formula for determining any Pick r of n column distribution:

"

Combinatorial Distribution

Factorial - n! = n * (n -1) * (n - 2) * ... * 3 * 2 * 1 , and 0! = 1

Permutation - P(n,r) = n! / (n - r)!

Combination - C(n,r) = P(n,r) / r!

Combinatorial Distribution - D(n,r,c,z) = C(z - 1, c - 1) * C(n - z, r - c)

n - total number of items
r - number of items in a combinatorial or permutational set
c - column number of the distribution
z - item number of the distribution

"

For the Mega Millions current matrix of 5 of 75 the distribution is as follows:

 Column C Item Z 1 2 3 4 5 1 1150626 2 1088430 62196 3 1028790 119280 2556 4 971635 171465 7455 71 5 916895 218960 14490 280 1 6 864501 261970 23460 690 5 7 814385 300696 34170 1360 15 8 766480 335335 46431 2345 35 9 720720 366080 60060 3696 70 10 677040 393120 74880 5460 126 11 635376 416640 90720 7680 210 12 595665 436821 107415 10395 330 13 557845 453840 124806 13640 495 14 521855 467870 142740 17446 715 15 487635 479080 161070 21840 1001 16 455126 487635 179655 26845 1365 17 424270 493696 198360 32480 1820 18 395010 497420 217056 38760 2380 19 367290 498960 235620 45696 3060 20 341055 498465 253935 53295 3876 21 316251 496080 271890 61560 4845 22 292825 491946 289380 70490 5985 23 270725 486200 306306 80080 7315 24 249900 478975 322575 90321 8855 25 230300 470400 338100 101200 10626 26 211876 460600 352800 112700 12650 27 194580 449696 366600 124800 14950 28 178365 437805 379431 137475 17550 29 163185 425040 391230 150696 20475 30 148995 411510 401940 164430 23751 31 135751 397320 411510 178640 27405 32 123410 382571 419895 193285 31465 33 111930 367360 427056 208320 35960 34 101270 351780 432960 223696 40920 35 91390 335920 437580 239360 46376 36 82251 319865 440895 255255 52360 37 73815 303696 442890 271320 58905 38 66045 287490 443556 287490 66045 39 58905 271320 442890 303696 73815 40 52360 255255 440895 319865 82251 41 46376 239360 437580 335920 91390 42 40920 223696 432960 351780 101270 43 35960 208320 427056 367360 111930 44 31465 193285 419895 382571 123410 45 27405 178640 411510 397320 135751 46 23751 164430 401940 411510 148995 47 20475 150696 391230 425040 163185 48 17550 137475 379431 437805 178365 49 14950 124800 366600 449696 194580 50 12650 112700 352800 460600 211876 51 10626 101200 338100 470400 230300 52 8855 90321 322575 478975 249900 53 7315 80080 306306 486200 270725 54 5985 70490 289380 491946 292825 55 4845 61560 271890 496080 316251 56 3876 53295 253935 498465 341055 57 3060 45696 235620 498960 367290 58 2380 38760 217056 497420 395010 59 1820 32480 198360 493696 424270 60 1365 26845 179655 487635 455126 61 1001 21840 161070 479080 487635 62 715 17446 142740 467870 521855 63 495 13640 124806 453840 557845 64 330 10395 107415 436821 595665 65 210 7680 90720 416640 635376 66 126 5460 74880 393120 677040 67 70 3696 60060 366080 720720 68 35 2345 46431 335335 766480 69 15 1360 34170 300696 814385 70 5 690 23460 261970 864501 71 1 280 14490 218960 916895 72 71 7455 171465 971635 73 2556 119280 1028790 74 62196 1088430 75 1150626

Next, if we sum the frequencies in the first column for the range 01 to 12 we get:

1150626 + 1088430 + 1028790 + 971635 + 916895 + 864501 + 814385 + 766480 + 720720 + 677040 + 635376 + 595665

or

10230543

Now, this tells the frequency when that range hits, however, it's when it does not hit when the consecutive run ends.

So, we need the frequency of when that range does not hit; we simply subtract it from the total possible outcomes of 17259390 to get the correct frequency we need to figure out the reoccurrence distribution.

The frequency is 17259390 - 10230543 = 7028847

From Discharging Reoccurrence Distribution

"    Discharge Reoccurrence - y = (d / m2 ) e -(x / m )

d - total number of draws
m - average rate of reoccurrence
x - draw difference or Dd between two draw occurrences of the same number
y - the approximate frequency of reoccurrence for a given draw difference or Dd for a given draw count d

"

m = 17259390 / 7028847 and reduces to 1917710 / 780983 which is approximately 2.45550799441

We can now use the Discharge Reoccurrence formula to see approximately what kind of distribution we might see for the current 44 draws in the mega millions pick 5 of 75.

y = (44 / (2.45550799441)2 ) e -(x / 2.45550799441 )

 x - Consecutive Run of 01 to 12 Drawn y - Rounded Approximation Actual Observation Percent Probability 1 5 3 11.04% 2 3 4 7.34% 3 2 0 4.89% 4 1 2 3.25% 5 1 0 2.16% 6 1 0 1.44% 7 0 0 0.96% 8 0 1 0.64% 9 0 0 0.42% 10 0 0 0.28% 11 0 0 0.19% 12 0 0 0.13% 13 0 0 0.08% 14 0 0 0.06% 15 0 0 0.04% 16 0 0 0.02% 17 0 0 0.02% 18 0 0 0.01%

The percent probability is just the e -(x / m )  portion of the formula.

To get other draw distributions, just change d to some other value.

Based on what we can determine from this, the selection from 01 to 12 is very likely to end for this consecutive run.

.

Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
4309 Posts
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 Posted: March 25, 2014, 11:56 am - IP Logged

Next, if we sum the frequencies in the first column for the range 01 to 12 we get:

1150626 + 1088430 + 1028790 + 971635 + 916895 + 864501 + 814385 + 766480 + 720720 + 677040 + 635376 + 595665

or

10230543

Now, this tells the frequency when that range hits, however, it's when it does not hit when the consecutive run ends.

So, we need the frequency of when that range does not hit; we simply subtract it from the total possible outcomes of 17259390 to get the correct frequency we need to figure out the reoccurrence distribution.

The frequency is 17259390 - 10230543 = 7028847

From Discharging Reoccurrence Distribution

"    Discharge Reoccurrence - y = (d / m2 ) e -(x / m )

d - total number of draws
m - average rate of reoccurrence
x - draw difference or Dd between two draw occurrences of the same number
y - the approximate frequency of reoccurrence for a given draw difference or Dd for a given draw count d

"

m = 17259390 / 7028847 and reduces to 1917710 / 780983 which is approximately 2.45550799441

We can now use the Discharge Reoccurrence formula to see approximately what kind of distribution we might see for the current 44 draws in the mega millions pick 5 of 75.

y = (44 / (2.45550799441)2 ) e -(x / 2.45550799441 )

 x - Consecutive Run of 01 to 12 Drawn y - Rounded Approximation Actual Observation Percent Probability 1 5 3 11.04% 2 3 4 7.34% 3 2 0 4.89% 4 1 2 3.25% 5 1 0 2.16% 6 1 0 1.44% 7 0 0 0.96% 8 0 1 0.64% 9 0 0 0.42% 10 0 0 0.28% 11 0 0 0.19% 12 0 0 0.13% 13 0 0 0.08% 14 0 0 0.06% 15 0 0 0.04% 16 0 0 0.02% 17 0 0 0.02% 18 0 0 0.01%

The percent probability is just the e -(x / m )  portion of the formula.

To get other draw distributions, just change d to some other value.

Based on what we can determine from this, the selection from 01 to 12 is very likely to end for this consecutive run.

- Correction -

We said, "The percent probability is just the e -(x / m )  portion of the formula."

The correct probability is (1 / (2.45550799441)2 ) e -(x / 2.45550799441 ).

The (1 / (2.45550799441)2 ) propotion is required.

The proportion can also be expressed as (1917710 / 780983)2.

To get percentge, multiply by 100%.

.

Rio de Janeiro
Brazil
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December 9, 2012
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 Posted: April 4, 2014, 8:39 am - IP Logged

Jade where you're going? won the lottery?

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