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SergeM

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Mar 21, 2014, 11:01 am

Quote: Originally posted by SkyLine69 on Mar 20, 2014
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.
LottoBoner

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Mar 21, 2014, 12:02 pm

Quote: Originally posted by SkyLine69 on Mar 20, 2014
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.

JADELottery

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Mar 22, 2014, 11:07 am

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%

The One Over None
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GoogilyMoogily

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Mar 22, 2014, 3:48 pm

Formula please:)

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

Native American Eagle Sun

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Mar 23, 2014, 3:16 pm

Quote: Originally posted by GoogilyMoogily on Mar 22, 2014
Formula please:)

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.

The One Over None
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JADELottery

Native American Eagle Sun

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Mar 24, 2014, 3:29 pm

Quote: Originally posted by JADELottery on Mar 23, 2014

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

The One Over None
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JADELottery

Native American Eagle Sun

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Mar 24, 2014, 4:08 pm

Quote: Originally posted by JADELottery on Mar 24, 2014

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

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.

The One Over None
I Know...

JADELottery

Native American Eagle Sun

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Mar 25, 2014, 11:56 am

Quote: Originally posted by JADELottery on Mar 24, 2014

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

10230543

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

The frequency is 17259390 - 10230543 = 7028847

From Discharging Reoccurrence Distribution

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

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%.

The One Over None
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sandnan

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Apr 4, 2014, 8:39 am

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