How this calculator works
Each complete combination is equally likely in an unordered draw. To match exactly m of k picks, choose m from your k numbers and k - m from the unselected pool. A separate independent bonus pool multiplies both the favourable counts and total outcomes. The multi-ticket output applies only to the jackpot and assumes all complete tickets are distinct. It does not combine lower-tier win probabilities, which overlap across tickets. A bonus ball drawn from the same main pool needs a different model.
Formula
P(exactly m matches) = C(k,m)C(N - k,k - m)/C(N,k). Independent bonus-pool probabilities multiply. Jackpot chance for t distinct complete tickets = t / total complete combinations.
Worked example
Choose two numbers from five. There are C(5,2) = 10 combinations. Exactly one match occurs in C(2,1)C(3,1) = 6 of them, so its probability is 60%. One distinct ticket has a 10% jackpot chance.
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Frequently asked questions
Does buying two identical tickets improve the jackpot chance?
No. They win on the same outcome. The distinct-ticket input assumes every complete combination differs.
Can an exact match count be impossible?
Yes. When many numbers are drawn, a low overlap may be impossible. The calculator returns zero probability for that event.
Does this calculate prize value or expected profit?
No. It calculates outcome probabilities. Prize sharing, rollover rules, ticket cost and prize tiers require additional information.