A filter changes the combinations you consider. It does not change the probability that one exact selection matches all the main numbers. Repeating a selection adds no new matching outcome; a personal preference for a pattern is separate from its probability.
Revised 2026-09-14: pattern-based advice was replaced with an explanation of filters, distinct selections and the limits of statistics. The original publication date is retained.
One selection and a category
The examples below are theoretical calculations over complete sets of combinations, not observed draw frequencies. The model assumes uniform, independent draws under fixed rules. The miniature examples do not represent real ticket conditions.
C(N,k) counts ways to choose k distinct numbers from N without regard to order. Each exact selection has probability 1/C(N,k) of matching all main numbers. For the Classic 6/49 model, based on the Loto-Québec rules, this is 1/13983816.
An exact combination inside a filter and an exact combination outside it each match one possible outcome. These calculations exclude the bonus number, Gold Ball, auxiliary draws and probabilities of winning any prize across all prize categories; the 6/49 denominator does not apply to Lotto Max.
What a range filter changes
Divide the 6/49 pool into 1–10 / 11–20 / 21–30 / 31–40 / 41–49, with sizes 10,10,10,10,9. A range is occupied when the selection contains at least one number from it. These are chosen boundaries, not official preferred zones; changing them changes the categories.
Complete theoretical distribution of occupied ranges — not historical frequencies
| Occupied ranges | Theoretical share of combinations |
|---|---|
| 1 | 924/13983816 |
| 2 | 337392/13983816 |
| 3 | 4207500/13983816 |
| 4 | 7458000/13983816 |
| 5 | 1980000/13983816 |
Read the first row as follows: 924 of the 13983816 possible combinations occupy exactly one range. Each fraction divides the number of combinations in that category by the total number of possible combinations.
To count the combinations, let s_i be a range’s size and x_i the number selected from it. Here i identifies the range being considered; the suffix _i ties s and x to that same range.
Multiply C(s_i,x_i) across the ranges, then add these products over all allocations whose x_i sum to 6 and occupy the required number of ranges. Divide by the full number of possible draws, C(49,6).
A filter requiring at least 3 occupied ranges retains 13645500/13983816 of all combinations. Requiring at least 4 retains 9438000/13983816, a smaller candidate set.
Under either filter, an exact selection still matches all main numbers with probability 1/13983816: the draw’s possible outcomes have not shrunk to the filter’s size.
Repeated selections and distinct outcomes
These are invented mathematical models, not lottery history or experiments with real tickets. List every combination in numerical order, then make a selection list containing [first combination, first combination, last combination]. Counting every possible combination gives:
| Model | Possible outcomes | Listed selections | Distinct selections | Matching outcomes |
|---|---|---|---|---|
| 3 from 8 | 56 | 3 | 2 | 2 |
| 4 from 9 | 126 | 3 | 2 | 2 |
The repeated first combination counts twice in the list but adds no new matching outcome. In this model, d distinct selections match d of the possible outcomes, giving d/C(N,k) for matching all main numbers. One exact selection still has probability 1/C(N,k).
This comparison concerns distinct outcomes, not prize amounts, all prize categories or a reason to buy additional selections.
Past results and personal preferences
An occurrence count records how often a number appeared within a specified observation window. The number of draws since its last appearance measures something different. Neither definition assigns actual numbers a label here.
In the invented models above, each possible past outcome is paired with the same full set of possible future outcomes. This is how independence is assumed in the model; it is neither an empirical study nor proof from real lottery history.
Under that assumption, a past result cannot make an exact future selection more likely. A preferred pattern remains a preference, not a probability improvement.
A short checklist before interpreting a statistic
- Which game and rules does it use?
- Does it describe an exact combination or a category?
- Is it theoretical, or an observation with a stated date?
- Does it count listed selections or distinct combinations?
For dated examples, see Lotto 6/49 Analysis: September 12, 2026 Draw and Lotto Max Analysis: September 11, 2026 Draw.