6/11/2012

Lotto 6/55 Distance Between Two Adjacent Numbers In Numerical Order

Imagine the lotto numbers as stars in space. From one star to another is a constant distance caused by gravity push and pull. Maybe, that's the reason why they are suspended in space. Just maybe but I don't really know :). Anyway, no two stars occupy the same space; and perhaps, no two distances from one star to another are equal.

Let's look at another example. The petals of a sunflower grow in such a way that no two petals emerge from the same point and that no two distances between one petal to another are equal. If the location of each petal is to be calculated in relation to another petal, the measure is equivalent to the golden ratio or phi (Greek symbol ΙΈ).


Let's go back to the lotto numbers. What if the lotto numbers are like stars or petals wherein their distances play a significant reason? With that imagination in mind, if we can calculate the distance between two numerically ordered jackpot numbers, maybe, we can get some significant information.


Based on actual 331 Lotto 6/55 results, the following are the results of my study.

Distance Ba Cb Dc Ed Fe Sum Overall
Highest
36
30
35
36
32
54
36
Lowest
1
1
1
1
1
15
1
Median
6
7
6
6
7
41
7
Mode
1
1
2
1
1
40
1
Assuming that the jackpot numbers are arranged numerically, “Ba” is the distance (or difference) between the first number and the second number. “Cb” is the distance between the third number and the second number; and so forth and so on. Based on the data above, the distance between two numbers range from 1 to 36 where 1 is the most common but the median plays around 6 and 7. Let's leave the sum for a moment.

Eliminating The Lower Probability

Distances ranging from 1 to 16 comprised the 53% of the sampled data. To capture a higher probability, like 89%, we can take a few exceptions. These are distances ranging from 1 to 16 with at least one distance that is between 17 and 27 inclusive. This forms 37% of the sample data. The remaining 11% ranges from 1 to 16 with at least one distance that ranges from 28 to 36. Therefore, if you're going to construct or combine your lotto numbers, the distance (i.e. difference) between two adjacent numbers should not be greater than 16. You may want to play a few exceptions. In that case, one distance can range from 17 to 27. Distances greater than 27 are rare.

Is it possible that there may be two equal distances?

Yes! But they are rare. So far no 4 or 5 distances can be equal. Three distances can be equal but the probability is only 12 out of 331 and this is only possible for distances 1 to 8. The probability of two distances to be equal occurred 136 (40%) times, and this is only possible for distances 1 to 19. Higher distances that are equal cannot occur.

So that means, most often than not, distances are not equal. To capture a higher probability, you may take exceptions by having two distances that are equal.

How to calculate the distances?


  1. Arrange the jackpot numbers numerically in ascending order.
  2. Calculate the difference between the second and the first number, between the third and second, etc.
  3. Sum the distances.


A
B
C
D
E
F
Lotto #s
9
15
17
21
52
53
Formula

B-A
C-B
D-C
E-D
F-E
Calculation

15-9
17-15
21-17
52-21
53-52
Distance

6
2
4
31
1

Eliminating Further the Lower Probability

If the distances range from 1 to36, deciding which distance is appropriate add more headache to choosing among the 55 lotto numbers. As a remedy, you need a container to control the numbers (something like the universe that contains the stars). This container acts in the form of sum of distances.


Calculating all the sums of distances of the sample data, the sums range from 15 to 54. Extracting the lower probability, the ideal sum ranges from 29 to 53 which form 89% of the sample data.

You need a spreadsheet calculator to make things easier for you rather than calculating mentally (unless you're very good in math). The formulas are simple addition and subtraction.

In A Nutshell

Sound confusing? Let me summarize the whole thing. When combining lotto numbers that you wish to play,
  1. First, arrange them in ascending numerical order.
  2. Subtract the first number from the second number (i.e. 2nd number minus 1st number), which is B - A in the example above. The difference is called the distance between those 2 numbers.
  3. Calculate the distances between the remaining numbers: 3rd minus 2nd, 4th minus 3rd, 5th minus 4th, and 6th minus 5th. All in all, you should have calculated 5 values for distances.
  4. Ideally, the values of the 5 distances should range from 1 to 16. This covers 53% of the sample data.
  5. To increase the odds, it's a good thing to cover around 90% instead of only 53%. For that reason, we need to capture other possibilities. These are distances that range from 1 to 16 with the exception of one distance which can range from 1 to 28, which covers 37%. All in all, that makes 89%.
  6. Like magnets that push and pull each other to maintain their distances, we use a container called sum of distances. If you add the values of the 5 distances, the sum should range from 29 to 53. A sum that is less than 29 is very rare.
  7. It is possible that two of the distances may be equal. More than two is already unlikely.



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