Ultra Lotto 6/58 Bounds of Probability

Probable Combinations Only

All are possible but not all are probable.

The total possible 6-number combinations that you can form out of 58 numbers from 1 to 58 is 40,475,358. All these combinations are possible but not all are probable.

By arranging the results from lowest to highest number, statistics reveal that certain numbers do not win at certain positions. For example, in the first position, common winning numbers are from 1 to 16 (eliminating those with only 1% or lesser probability, and those that have not won so far.)

The following table shows the number that usually win based on ordered positions, ie if the lotto numbers are arranged from lowest to highest number. It has eliminated the numbers that have not yet won so far, and those that only have 1% or lesser probability. This data is based on 329 results.


Winning probability within bounds

The table below shows the complete standing of most probable winning numbers in the ordered positions. The left column are the lotto numbers 1 to 58. The next 6 columns show the number of times each lotto numbers have won if following the ordered positions. For a better visual presentation, view it here.



The data above serve as bounds or lower and upper limits that can guide you when forming your combinations. For example, the lowest number in your combination should be between 1 and 22, 25, 26, 29, 30 (as of this writing) – ignoring the lotto numbers that have won only once. For the second position, your next lowest number should be between 2 and 37, and so forth and so on. This is the reason why [ 01 • 02 • 03 • 04 • 05 • 06 ] or [ 53 • 54 • 55 • 56 • 57 • 58 ] is not a probable winning combination.

By eliminating what’s not probable, the bounds or lower and upper limits reduce the number of probable winning combinations to just about 1.6 million. That’s already good news compared to 40.4 million combinations.

Perfect Combinations

A perfect combination would be when all the 6 numbers in a combination are within the lower and upper limits. However, not all results are perfect. Based on 337 results, 49.9% were perfect combinations; the rest contradicted the norm with 1 to 4 numbers winning outside the lower and upper limits.

An example of a perfect combination is the 26 Dec 2017 result which is 09 • 22 • 35 • 41 • 44 • 46.

The 31 Dec 2017 result ⎯ 06 • 14 • 15 • 24 • 25 • 43 ⎯ showed 1 number, which is 25, outside the limits.

The table that follows shows the rest of the probability data.
Number Within BoundsOccurrencesProb
6 16849.9%
5 9327.6%
4 4713.7%
3 24 7.1%
2 5 1.55
1 0 0
0 0 0

Which column usually play within bounds?

Which column in ordered positions usually give a winning number within the the upper and lower limits?

The 1st to 5th positions usually play within bounds at 81% - 88% probability. The 6th position is more loyal at 92.6% probability. The 1st to 5th positions refer to the 5 lowest numbers in a combination while the 6th refers to the highest number in a combination. For example, in the 26 Dec 2017 result ⎯ 09 • 22 • 35 • 41 • 44 • 46 ⎯ the first 5 numbers are in the 1st to 5th positions; while the highest, which is 46, is in the 6th position.

Analysis

Playing your 6 numbers within bounds is already safe at ~
  • 49.9% chance of winning the jackpot;
  • 77.4% chance of winning 5 numbers; and
  • 91.4% chance of winning 4 numbers.

Tip & Strategy

Play 9 combinations as follows:
  • 5 combinations where all 6 numbers are within bounds
  • 3 combinations where all 5 numbers are within bounds
    • 1 combination where the 2nd position is outside bounds;
    • 1 combination where the 5th position is outside bounds;
    • 1 combination where the 3rd, 4th or 1st position is outside bounds;
  • 1 combination where all 4 numbers are within bounds except the 1st and 2nd position.

Combination Calculator Based on Bounds

To help you compose your combinations that are within the lower and upper limits, use or download this template on Google Sheets.