6/49 sorted out

[johnph77]

Interesting observation about the combination 1-10-20-30-40-49, johnph77. Besides having the numbers with the highest probability in each position (P1 to P6), it also shows a very nice and regular pattern with both the lowest and the highest numbers but also all 4 numbers ending with a 0 (10-20-30-40).

Looking for this combination in Canadian Lotto 6/49, Quebec 49 and UK 49 lotteries (5,215 draws altogether), it has yet to show up, the best result being in draw #2109 for Lotto 6/49 with 5 of the 6 numbers (1-10-18-20-30-40). But it is quite possible that it has come out in a 6/49 lottery somewhere.

I never had thought at looking at this characteristics on the whole set of combinations but I have a spreadsheet that calculates the minimal range covering a given percentage of results for each position, based on past draws. For Lotto 6/49, in P2 all results range from 02 to 43 with slightly over 90% in the range 03-26.

So using the table already posted for each position, I calculated the minimal range that covers at least 90% of the possibilities (or 12,585,434 combinations). For each position, the range obtained is:
- for P1, from 01 to 15;
- for P2, from 03 to 25;
- for P3, from 08 to 34;
- for P4, from 16 to 42;
- for P5, from 25 to 47;
- for P6, from 35 to 49.

Going through all combinations of a 6/49 lottery, I found 8,892,704 combinations (or 63.6%) with each number within the given range for each position.

I had done a version of this years ago and have no idea what I've done with the results, but it appears as if you're pretty well spot on.

Although the four numbers ending in zero may seem pretty, it wasn't intentional. Different matrices have different results. For instance, the same query from a 6/44 matrix would yield 01-09-18-28-36-44, those from a 6/59 matrix would yield 01-12-24-36-48-59. The query from a 5/39 matrix, though, would yield 01-10-20-30-39 - same pattern.

gl

j

 

[GillesD]

General information on lexographic values

Hopefull, yoy are somewhat lucky. In a file, I had the lexographic values for each combination starting with numbers 1 to 44. From this, you can most likely calculate most statistics you asked for.

01 - 02 - 03 - 04 - 05 - 06: LV = 1
02 - 03 - 04 - 05 - 06 - 07: LV = 1,712,305
03 - 04 - 05 - 06 - 07 - 08: LV = 3,246,244
04 - 05 - 06 - 07 - 08 - 09: LV = 4,616,998
05 - 06 - 07 - 08 - 09 - 10: LV = 5,838,757
06 - 07 - 08 - 09 - 10 - 11: LV = 6,924,765
07 - 08 - 09 - 10 - 11 - 12: LV = 7,887,363
08 - 09 - 10 - 11 - 12 - 13: LV = 8,738,031
09 - 10 - 11 - 12 - 13 - 14: LV = 9,487,429
10 - 11 - 12 - 13 - 14 - 15: LV = 10,145,437
11 - 12 - 13 - 14 - 15 - 16: LV = 10,721,194
12 - 13 - 14 - 15 - 16 - 17: LV = 11,223,136
13 - 14 - 15 - 16 - 17 - 18: LV = 11,659,033
14 - 15 - 16 - 17 - 18 - 19: LV = 12,036,025
15 - 16 - 17 - 18 - 19 - 20: LV = 12,360,657
16 - 17 - 18 - 19 - 20 - 21: LV = 12,638,913
17 - 18 - 19 - 20 - 21 - 22: LV = 12,876,249
18 - 19 - 20 - 21 - 22 - 23: LV = 13,077,625
19 - 20 - 21 - 22 - 23 - 24: LV = 13,247,536
20 - 21 - 22 - 23 - 24 - 25: LV = 13,390,042
21 - 22 - 23 - 24 - 25 - 26: LV = 13,508,797
22 - 23 - 24 - 25 - 26 - 27: LV = 13,607,077
23 - 24 - 25 - 26 - 27 - 28: LV = 13,687,807
24 - 25 - 26 - 27 - 28 - 29: LV = 13,753,587
25 - 26 - 27 - 28 - 29 - 30: LV = 13,806,717
26 - 27 - 28 - 29 - 30 - 31: LV = 13,849,221
27 - 28 - 29 - 30 - 31 - 32: LV = 13,882,870
28 - 29 - 30 - 31 - 32 - 33: LV = 13,909,204
29 - 30 - 31 - 32 - 33 - 34: LV = 13,929,553
30 - 31 - 32 - 33 - 34 - 35: LV = 13,945,057
31 - 32 - 33 - 34 - 35 - 36: LV = 13,956,685
32 - 33 - 34 - 35 - 36 - 37: LV = 13,965,253
33 - 34 - 35 - 36 - 37 - 38: LV = 13,971,441
34 - 35 - 36 - 37 - 38 - 39: LV = 13,975,809
35 - 36 - 37 - 38 - 39 - 40: LV = 13,978,812
36 - 37 - 38 - 39 - 40 - 41: LV = 13,980,814
37 - 38 - 39 - 40 - 41 - 42: LV = 13,982,101
38 - 39 - 40 - 41 - 42 - 43: LV = 13,982,893
39 - 40 - 41 - 42 - 43 - 44: LV = 13,983,355
40 - 41 - 42 - 43 - 44 - 45: LV = 13,983,607
41 - 42 - 43 - 44 - 45 - 46: LV = 13,983,733
42 - 43 - 44 - 45 - 46 - 47: LV = 13,983,789
43 - 44 - 45 - 46 - 47 - 48: LV = 13,983,810
44 - 45 - 46 - 47 - 48 - 49: LV = 13,983,816

And as far as the highest lexographic values to have come out, here they are:
- L. V. =13,958,134 for 31 - 32 - 36 - 38 - 39 - 44 (draw # 191)
- L. V. =13,963,819 for 31 - 36 - 40 - 43 - 48 - 49 (draw # 803)
- L. V. =13,970,120 for 32 - 36 - 43 - 44 - 45 - 47 (draw # 962)
- L. V. =13,983,334 for 38 - 43 - 44 - 45 - 46 - 47 (draw # 1,748)

 

[johnph77]

And as far as the highest lexographic values to have come out, here they are:
- L. V. =13,958,134 for 31 - 32 - 36 - 38 - 39 - 44 (draw # 191)
- L. V. =13,963,819 for 31 - 36 - 40 - 43 - 48 - 49 (draw # 803)
- L. V. =13,970,120 for 32 - 36 - 43 - 44 - 45 - 47 (draw # 962)
- L. V. =13,983,334 for 38 - 43 - 44 - 45 - 46 - 47 (draw # 1,748)

And this might illustrate a point we were discussing earlier. If you can assume a lexographic range of 15,180 and a selected range of 13,958,000 through 13,973,180 you have three hits within that range in this lottery's history, certainly far more than expected. Would that indicate a trend or prove a point, or could one shrug it off as a statistical anomaly?

In order to prove one's point, one must choose one's facts carefully.

 

[GillesD]

Positional anakysis

Looking at various statistics for Lotto 6/49 (sum of numbers, numbers per decade, etc.), it appears the number drawn are slightly skewed toward the high side.

And to continue on positional analysis, here is some data respectively for 100%, 90% and 80% of the results:

A - Using actual results (2,630 draws), we get the following ranges:
P1: 100% in 01–38 with 91.7% in 01–16 and 80.6% in 01–11
P2: 100% in 02–43 with 91.4% in 03–26 and 81.1% in 03–21
P3: 100% in 03–45 with 90.1% in 08–34 and 81.3% in 11–32
P4: 100% in 04–47 with 91.3% in 16–42 and 80.5% in 20–40
P5: 100% in 11–48 with 90.6% in 26–47 and 80.5% in 28–45
P6: 100% in 13–49 with 92.2% in 35–49 and 82.9% in 39–49

B - Calculating the ranges for the same percentages with every combinations, we get:
P1: 100% in 01–44 with 90.4% in 01–15 and 80.3% in 01–11
P2: 100% in 02–45 with 91.7% in 03–26 and 81.2% in 04–22
P3: 100% in 03–46 with 90.7% in 08–34 and 81.1% in 10–31
P4: 100% in 04–47 with 90.7% in 16–42 and 81.1% in 20–40
P5: 100% in 05–48 with 90.2% in 25–47 and 81.6% in 28–47
P6: 100% in 06–49 with 90.4% in 35–49 and 80.3% in 39–49

 

[hopefull]

If you can assume a lexographic range of 15,180 and a selected range of 13,958,000 through 13,973,180 you have three hits within that range in this lottery's history, certainly far more than expected. Would that indicate a trend or prove a point, or could one shrug it off as a statistical anomaly?

In order to prove one's point, one must choose one's facts carefully.
Reply With Quote

I would throw them out my self and not expect to see like them in a very long time from now.

 

[johnph77]

I would throw them out my self and not expect to see like them in a very long time from now.

OK, let's do that. But, there are so many different ways of selecting 15,180 combinations that the mind boggles. If you're using lexographics, there are 13,968,637 different 15,180-number ranges to choose from. We've mentioned the extreme low range using 01-02-03, with 15,180 combinations. But the same number of combinations can and will be achieved by selecting any three numbers, including, for instance, 47-48-49 - and there are 18,428 different 3-number combinations.

Once your preferred method has been determined, how does one bet them? You indicated in your previous post that you would eliminate those combinations within the selected range. Would you have done so when the first two combinations first appeared, thereby missing out on the chance of hitting it when it appeared the third time? Who knows when the fourth combination within the selected range will appear?

Food for thought.....

 

[hopefull]

I had mentioned the extreme low range using 01-02-03, with 15,180 combination because I was going numerical order.
I simply want to find where the bulk of the game is.
the 2nd thought is to bring both extreme ends as close to each other as possibly can.
meaning to start from the first page that has the most hits on it towards the last page that has the most hits on it.
my main aim is condensing the number of lines to pick from.

 

[johnph77]

I can understand your reasoning of eliminating the 15,180 lexographic lines. However, that number of lines is only a little over 1/10 of a percent of all possible combinations. If I were building a system, that would be only a very minor filter within that system.

Something else you might want to consider - in any 6-number draw there are 20 three-number combinations. If the draw came out 01-02-03-04-05-06 the 20 three-number combinations would be:

01-02-03
01-02-04
01-02-05
01-02-06
01-03-04
01-03-05
01-03-06
01-04-05
01-04-06
01-05-06
02-03-04
02-03-05
02-03-06
02-04-05
02-04-06
02-05-06
03-04-05
03-04-06
03-05-06
04-05-06

If one assumes that no number(s) will repeat, that lessens the number of possibilities to 6,096,454, therefore the chance that one or more numbers will repeat in the next drawing is better than even.

Just a little food for thought.

gl

j

 

[hopefull]

hands up in the air,I give up