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Lottery Match Probability Calculator — result sheet
Calculate the chance of meeting a chosen lottery match threshold from a pool, ticket size, draw size, and number of tickets without assuming a particular country's game rules.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For one ticket, count every draw with k matches as C(ticket picks,k) × C(pool − ticket picks, draw size − k), sum k from the entered minimum through the feasible maximum, and divide by C(pool, draw size). The multiple-ticket result uses 1 − (1 − p)^tickets as an independent-ticket planning approximation.
The page is a jurisdiction-neutral combinatorics worksheet. It models equally likely draws without replacement and keeps the multiple-ticket independence approximation visible because overlapping ticket choices are not the same as guaranteed distinct combinations.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Numbers in the pool — numbers; minimum 2; maximum 500
- Numbers selected per ticket — numbers; minimum 1; maximum 500
- Numbers drawn — numbers; minimum 1; maximum 500
- Minimum matches of interest — matches; minimum 0; maximum 500
- Tickets in the scenario — tickets; minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Numbers in the pool | 49 |
| Numbers selected per ticket | 6 |
| Numbers drawn | 6 |
| Minimum matches of interest | 6 |
| Tickets in the scenario | 1 |
There are 13,983,816 possible six-number draws; one fixed ticket has a jackpot chance of about 0.00000715%, or about 1 in 13,983,816.
Assumptions and limits
- The draw is uniform and selects numbers without replacement from the entered pool.
- The order of drawn numbers does not matter for a match threshold.
- The ticket's selected numbers are treated as distinct and fixed before the draw.
- Minimum matches can be zero, but a zero-match event is mathematically certain.
- The one-ticket probability sums all feasible match counts at or above the threshold.
- The multiple-ticket percentage assumes independent tickets and is not an exact joint probability when tickets overlap.
- Bonus balls, separate pools, rollovers, payout tables, taxes, and local game rules are not modeled.
- The result is probability arithmetic, not a prediction of a future draw.
- A very small probability can be displayed as odds without implying that buying more tickets creates value.
- Use the official rules of the specific game for a real ticket or payout decision.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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