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Guides, answers and useful information for every lottery player.
Choose a lottery format and a precise matching event. This calculator separates main balls, special balls and assigned digits, then shows the mathematical probability under a fair-draw model. It does not predict a result, recommend a purchase or calculate prize returns.
One six-number selection in one UK Lotto round. The current game has two rounds per draw night.
Exactly six main numbers match.
1 in 45,057,474A mathematical full-main match, not the chance of any prize.
Choose the number of independent rounds explicitly.
Exact single-round probability: 1 / 45,057,474
C(6, 6) × C(53, 0) ÷ C(59, 6)
C(n, k) counts unordered ways to choose k different items from n. The complement formula for at least one event in r independent rounds is 1 − (1 − p)r. Percentages are rounded for display.
The calculator needs JavaScript. The worked explanations below are available without it.
A five-main-plus-special match is a particular event. Smaller main matches, supplementary conditions and ticket-specific benefits are separate events. Without a complete, verified prize table, adding them up would risk counting overlapping categories or omitting a condition. This tool therefore labels numerical events rather than promising overall prize odds.
A current LOTTO MAX play contains four selections, while the base combination count describes one seven-number line. Repeating the same line does not create a new combination in the same result. Distinct full combinations can cover different outcomes, but more selections also require their own valid entries. This page does not model ticket purchases.
The same fixed line can be compared with future independent rounds using the complement formula. The number of independent rounds must be explicit. MillionDAY’s main and linked EXTRA results are dependent because EXTRA excludes the main balls; the simple repetition model must not be used to combine that pair.
Three sets of six main balls and optional bonus balls do not create a single uniform draw of 21 different numbers. Repeats can occur between results. Irish Lotto 21 is therefore intentionally excluded from this single-draw calculator. Its studio shows combined appearances without presenting invented single-draw odds.
These rows describe main-number matches only. They add to 100% before rounding and do not include the selected special-ball or assigned-digit condition. “Exactly three” differs from “at least three”; the calculator’s main event is always exact.
| Main matches | Probability | Reciprocal chance |
|---|---|---|
| Enable JavaScript to explore all match counts. | ||
A group of many combinations can be common even when no individual combination is more likely than another.
For six picks from 1–59, the three-odd/three-even group contains C(30, 3) × C(29, 3) = 14,835,240 combinations. The all-odd group contains C(30, 6) = 593,775. Each particular valid six-number line still has the same one-round chance of matching all six main balls. A larger group contains more equally likely lines; it does not make one chosen line better.
C(59, 6) = 45,057,474. That is the number of possible six-main results for one round. A fixed six-number line matches one of them. The current two-round game compares that same line with two distinct results; using r = 2 makes the repeated-round assumption visible rather than quietly relabelling the one-round number as a whole-ticket probability.
Five main numbers create C(50, 5) = 2,118,760 possibilities. Two Lucky Stars create C(12, 2) = 66 possibilities. Multiplying the independent selection spaces gives 139,838,160 full selections. The main-only event is different from matching both groups, even if a main number and a Lucky Star happen to share the same numeral.
Sorting a line, giving it a memorable pattern or noticing a number’s recent frequency does not change a fair independent draw. A secure generator helps choose a line without a predictable software pattern; it cannot make the lottery outcome predictable. Restricting generation to odd numbers changes which lines the tool offers, not which lines the lottery can draw.
Format references: Allwyn’s two-round announcement; Irish National Lottery EuroMillions rules; OLG’s current LOTTO MAX format. Mathematical examples are calculated by LottoLuma from the stated selection spaces.
Search all 28 number studios. Press Escape to close.
