Ultra Lotto 6/58 Probability of Distance


Predicting the Next Winning Number

Is it possible to figure out which numbers can probably win based on a given number? The probability of distance can give you the answer.

Highlights

  • The smaller the value of a distance, the more probable.
  • If the difference between two numbers is anything between 41 - 57, this is not probable at all.
  • Having equal distances in a combination is not probable.
  • 100% of the results studied comprise distances of 1 to 11.
  • By knowing the probability rules of distance, you can never go wrong.

Distance Between Two Numbers

Distance means the difference between two adjacent numbers, assuming that the numbers are arranged numerically from lowest to the highest number.

For example: the 8 May 2018 result was drawn as 19 • 27 • 07 • 46 • 18 • 53; but for the purpose of determining the distances between the numbers, the order of the result should be re-arranged as 07 • 18 • 19 • 27 • 46 • 53.

So, for the purpose of this study, each draw result included in this study was arranged numerically from the lowest to the highest number. Then, the difference between every 2 adjacent numbers was calculated. Let’s call the result the distance between 2 numbers; or distance for short.

Using the example result mentioned earlier, the distances of the 8 May 2018 draw result are:
  • Distance AB(7,18) = 18 - 7 = 11
  • Distance BC(18,19) = 19 - 18 = 1
  • Distance CD(19,27) = 27 - 19 = 8
  • Distance DE(27,46) = 46 - 27 = 19
  • Distance EF(46,53) = 53 - 46 = 7
  • Distance FA(53,7) = 53 - 7 = 46
We now have the distances: 11 • 1 • 8 • 19 • 7. If we sum up all these numbers we get the result:
11 + 1 + 8 + 19 + 7 = 46
Therefore, the sum of all distances is 46; which is the same as the distance between the highest and the lowest number.
Distance FA = 53 - 7 = 46 = Sum of all distances
Distance AB (or B minus A) means the difference between the first and second number. With the numbers in a combination arranged from smallest to largest, A refers to the 1st number, which is the smallest. B refers to the 2nd number; C is 3rd; D is 4th; E is 5th; and F refers to the 6th number, which is the largest.

Significance of the Distances

Imagine the lottery balls as a group of small planets which maintain their positions based on alternating fixed set of distances. By determining the distance, we can figure out the number next to a given number.

For example, if the common distance is 12, then we would know that the probable next winning number after 21 is 33 calculated as follows:
21 + 12 = 33
where 21 is the given lotto number, 12 is the probable distance, and 33 is the calculated next probable winning lotto number.

So, how do we figure out the probable distances?

Probable Distances Between Two Numbers

As mentioned earlier, the differences between two numbers of every result were calculated. Then, the results were tallied to find out what’s most probable. The table below shows the summary of the results.
Distance Prob
From To %
1 7 54.9%
8 15 31.0%
16 40 14.1%
41 57 0.0%

The Safe Zone

If the differences between two consecutive numbers are between 1 and 15 inclusive, your numbers have 85.9% chance of winning.

The most common recorded differences are 1 to 5 while the rest are also common, they have occurred with a few exceptions. For instance, the distance of 6 is more common to distances AB, CD and DE but less common to distances BC and EF.

The Risk Zone

The distances 41 to 57 have 0% probability. This means that if the difference between two consecutive numbers is 41 - 57, there’s a strong possibility that your combination is unlikely to win.

For example, in this combination 01 • 42 • 50 • 53 • 57 • 58, the difference between 42 and 1 is 41, making this combination unlikely to win. To make it a probable combination, you can change 42 to any number between 2 and 37 (refer to the probable winning range table on the previous posts).

If the difference between two consecutive numbers is between 16 and 40, consider changing your numbers with a distance between 1 and 15 to increase the probability of winning. The reason is that the distances 16 to 40 make only 14.1% of all probable chances. If you want to take a risk, choose a smaller distance value, say between 16 and 25.

Is it Advisable To combine Numbers with equal distances?

The 3rd most common of all distances is 3. With that in mind, is the following combination a probable winner: 1 • 4 • 7 • 10 • 13 • 16 wherein the differences between all numbers are all 3s? (Calculate 4-1 = 7-4 = 10-7 = 13-10 = 16-13 = 3.)

There are 3 reasons why this type of combination is not a probable winner:
  • Though the distance of 3 is third most common, it comprises only 9.1% of all occurrences. If all results have distances of 3, its probability is 100%; but such is not the case. Therefore, the distance of 3 shares popularity with other values of distance.
  • The distance or difference between 16 and 1 (6th and 1st numbers) is 15 (which is also the sum of 3+3+3+3+3). The distance of 15 between the 6th and 1st numbers is not at all common. In fact, statistically, it does not exist yet; or 0% probability.
  • The numbers 7, 10, 13 and 16 are all outside the probable winning range (check previous post).
Therefore, it is not advisable to play numbers that result to uniform distances. So, what’s ideal?

Combining Numbers with Probable Distances

What is ideal is to form a combination with unique or non-repeating distances. The 8 May 2018 result is an example: 7 • 18 • 19 • 27 • 46 • 53 with distances of 11 • 1 • 8 • 19 • 7.

Let’s explore further.

The probability that a result has unique or non-repeating distances is 56.15%. In contrast, 43.85% would have 2 or more distances of equal value. The result of 1 May 2018 is an example of a result with 2 distances of equal value: 15 • 28 • 39 • 42 • 48 • 51 with distances of 13 • 11 • 3 • 6 • 3.

For that reason, it is advisable to play at least 2 combinations:
  • One combination must have unique or non-repeating distances.
  • The other combination must have 2 distances of equal value.

What about 3 distances of equal value?

Three (3) distances of equal value is already very rare. There were only 6 instances. Having 4 or 5 equal distances is no longer probable.

How do we decide which distances should we mix?

The general rules are:
  • Avoid distances of 41 - 57.
  • The smaller the value of a distance, the greater the probability.
  • Remember that the difference between the smallest and largest numbers should be between 27 and 56 (94.1% probability).
  • Using a distance of 1 - 11 has 100% probability. It means that every result that was tested had at least 1 distance whose value is between 1 - 11. The most common is having 3 - 4 distances with a value of between 1 - 11.
  • If 3 - 4 distances are between 1 and 11, the others would definitely be greater than 11 such as between 12 and 30. Remember rule#2 when picking a distance value between 12 and 30.

Probability of Occurrence of Any Distance

What is the probability that a specific value of a distance is to exist in a result? I will tackle the first 3 distances: 1, 2, and 3. The rest of the figures are presented in the table Probability of a Distance to Occur.

If Distance is 1; x - y = 1

Actual result example: 03 • 34 • 35 • 39 • 44 • 50 (5 Jun 18)

The difference between 34 and 35 is 1 (35 - 34 = 1).

The probability that a distance of 1 may exist is 44.06%. This means that there’s almost 50% chance that a winning result may contain two consecutive numbers, the difference of which is 1. Examples are: 34 - 35; 26 - 27; 13 - 14.

This probability rate is the highest one.

On the other hand, this probability rate also means, that at 55%, the distance of 1 may not exist. Perhaps, a distance of 2, 3, or 4 may exist instead.

Therefore, not at all times, that a result would give a distance equal to 1. So, to increase the odds of your numbers to win, play 2 combinations: one that contains a distance equal to 1; and the other contains a distance other than 1.

The Probability of 1 Distance To Exist Twice

It is possible that the distance of 1 may exist twice. For example: the 6 March 2018 result was 07 • 17 • 18 • 36 • 56 • 57; the difference between 17 & 18 is 1; likewise, the difference between 56 & 57 is 1. The probability of such case to occur is only 5.69%.

If Distance is 2; x - y = 2

Actual result example: 05 • 31 • 39 • 41 • 43 • 49 (8 Jun 18)

The difference between 41 and 43 is 2 (43 - 41 = 2). Also, the difference between 39 and 41 is 2.

The probability that a distance of 2 may exist is 41.09%. This means that there’s nearly a little less than 50% chance that a winning result may contain two adjacent numbers,  whose difference is 2. Examples are: 41 - 43; 18 - 19; 39 - 41.

The Probability of 2 Distance To Exist Twice

It is also possible that the distance of 2 may exist twice. For example: the 8 Jun 2018 result was 05 • 31 • 39 • 41 • 43 • 49; the difference between 39 & 41 is 2; likewise, the difference between 41 & 43 is 2. The probability of such case to occur is only 6.68%. This rate is already the highest probability compared to the rest of values occurring twice.

The Probability of Distances 1 & 2 Combined

The probability that a result may contain both distances of 1 and 2 is 14.85%. Therefore, not many times that you see distances of 1 and 2 together in one result. Most of the time, they exist independently.

If Distance is 3; x - y = 3

Actual result example: 05 • 08 • 17 • 22 • 48 • 54 (10 Jun 18)
The difference between 05 and 08 is 3.

The probability that a distance of 3 may exist is 39.36%. Nearly, there’s a 40% chance that a result may contain two numbers, the difference of which is 3. Examples are: 05 - 08; 19 - 22; 37 - 40.

The Probability of 123 Distances Combined

The probability of a result to contain distances of 1 & 3 together is 15.84%. The probability of a result to contain distances of 2 & 3 together is 13.86%. And, the probability of a result to contain distances of 1 & 2 & 3 together is 4.95%.

Probability of a Distance To Occur

Distance Freq Prob
1 178 44.1%
2 166 41.1%
3 159 39.4%
4 137 33.9%
5 121 30.0%
6 102 25.2%
7 97 24.0%
8 92 22.8%
9 94 23.3%
10 76 18.8%
11 85 21.0%
1 - 11 404 100%
12-15 204 50.5%
16-20 127 31.4%
21-30 116 28.7%
31-57 26 6.4%

Probability of Every Distance to Occur in a Result

The table Probability of a Distance To Occur presents all the possible distances ⎯ which are 1 to 57 ⎯ and their probability to occur in a winning result. Following are some interesting findings to note:
  • Notice that as the value of distance gets higher, its corresponding probability goes lower.
  • Note further, that the distances 1 to 11 comprise 100% probability (100% of the results). This means that every result drawn contain a combination of the distances 1 to 11.
  • 50% of the results studied contain a distance value ranging from 12 to 15. This means that, aside from values 1 to 11, two of your numbers may have any distance from 12 to 15.
  • In some cases, include two numbers whose difference is any value from 16 - 20 or 21 - 30. Just remember, the lower the value of the distance, the better odds.
It is safe to avoid the distance values of 31 to 57 as these distances almost do not exist.

The Case of Repeating Distance Values

Mentioned earlier in this section that for a distance of 1, 2 or 3 to exist twice in a result is rare because the probability for these distances to occur twice is only 5.7%, 6.7%, and 5.9% respectively. The probability of 6.7% is already the highest; therefore, all other values have lesser probability ranging from 0.05% to 5% (for distance values of 4 to 11). For distance values greater than 11, the probability to occur twice is from 0% to 0.05%.

Based on these data, it is advisable not to have repeating distance values. However, we cannot disregard the statistical fact that a distance can occur twice. Though each distance value from 1 to 40 can appear twice at a low probability of 0.05% to 6.7%, collectively, they comprise 37.4% of all the results tested.

As a remedy, to increase more the probability of your numbers to win, play at least 2 combinations ⎯
  • One combination should have unique distance values (non-repeating). For example: 05 • 08 • 17 • 22 • 48 • 54 (10 Jun 18 result) consists of distances 3 • 9 • 5 • 26 • 6
  • The other combination should have a repeating distance values but only up to 2 occurrences. For example: 05 • 31 • 39 • 41 • 43 • 49 (8 Jun 18 result) consists distances of 26 • 8 • 2 • 2 • 6.

Which Distance Goes Well With Another?

All possible pairing of distances were gathered and calculated. The purpose of this is to find out which distance value commonly mix with another distance value. Is it more probable to have a distance of 1 and 2 together versus 1 and 3? What about 2 and 4, are they common? Is having a mix of 1, 2 and 3 distances in any order a good idea? Let’s find out.

Based on calculated statistics, any distance paired with any other distance value has the probability to win from 2.7% to 15.8%. This is a low probability. This only means that any distance value mixed with another is a good mix; but preferably, choose the distances with lower values.

Most Probable Distance Factors

Here’s what you have to remember when formulating your lotto number combinations based on distance factors.
  • For every result, there are 5 distance values.
  • Three to four (3 - 4) of them should have values of 1 to 11 (87% probability).
  • One distance may have a value of 12 to 15 (probability of 37%).
  • Optionally, one distance may have a value of 20 to 30 (probability of 31%).
  • Another option is one distance may have a value of 16 to 19 (probability of 21%).
  • But don’t forget that the distance between your lowest and highest numbers should be 27 to 56 (probability of 94.1%).

In A Nutshell

  • The lower the value of a distance, the more probable.
  • Your combination should contain any distance value from 1 to 11. This is 100% probable. Commonly, 4 distances have values of 1 to 11.
  • The sum of the distances should be between 27 and 56.
  • No distance should be greater than 40.
  • One distance would usually be greater than 11 by default.

Further note.

The beauty of the distance probability is that your choice of numbers are controlled or delimited by distance factors. Just by knowing that the sum of the distances should be between 27 and 56; and that no distance should be greater than 40, you can never go wrong.

For instance. If your combination has calculated distances of 1 • 2 • 3 • 4 (in any order), your 5th distance can only be between 17 and 40 because 1 + 2 + 3 + 4 + 17 = 27 (minimum sum is 27). On the other hand, 1 + 2 + 3 + 4 + 40 = 50 (maximum distance is 40).

Here’s another example. If your combination has calculated distances of 3 • 4 • 5 • 6 (in any order), your 5th distance can only be between 9 and 38 because 3 + 4 + 5 + 6 + 9 = 27 (minimum sum is 27). On the other hand, 3 + 4 + 5 + 6 + 38 = 56 (maximum sum is 56).

The only element that can go against the distance factors is that any good probable combination is competing against more than 24 million likewise good probable combinations.

Combining Probable Numbers Tool

Download this tool Lotto 6/58 Combining Probable Numbers on Google Drive. This tool will make it easier for you to combine your numbers based on the probable winning range and distances.

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