Precisely compute combinatorial odds for any lottery. Full support for partial bonus matching (e.g., 2/12 EuroMillions stars). Visualize log-scale probabilities and estimate expected value for jackpots. Academic-grade arithmetic using BigInt.
Lottery odds are fundamentally based on combinations without repetition. For a standard format where you pick k distinct numbers from a set of n main numbers, the number of ways is C(n, k) = n! / (k!(n−k)!). When additional bonus balls are drawn from a separate pool of size m (selecting b numbers), the total number of equally likely outcomes multiplies: Total = C(n, k) × C(m, b). This product defines the jackpot denominator.
Example (Powerball): C(69,5) = 11,238,513; multiply by C(26,1)=26 → 292,201,338 → Jackpot odds = 1 in 292 million.
Secondary prizes arise from partial matching: matching exactly j of the k main numbers, and exactly s of the b bonus numbers. The number of winning combinations for a given (j, s) is: C(k, j) × C(n−k, k−j) × C(b, s) × C(m−b, b−s). This tool implements the full hypergeometric distribution for all combinations, providing a complete prize tier breakdown. BigInt arithmetic guarantees exact results even for astronomically large numbers (1 in 300M+).
Understanding the true scale of lottery odds demystifies the "dream of millions". For context, the chance of being struck by lightning in a given year is roughly 1 in 1,222,000 — orders of magnitude higher than most jackpots. The odds of winning a Powerball jackpot (≈ 1 in 292M) compare to flipping a coin and getting heads 28 times in a row. By presenting exact odds, we encourage informed decision-making and responsible participation.
With 2 bonus stars (from 12), our calculator now produces tiers for matching 0, 1, or 2 stars combined with main number matches. This matches the official prize table (e.g., Match 5 main + 1 star, Match 4 main + 2 stars, etc.). Use the EuroMillions preset to see the complete breakdown.
| Lottery Type | Total Combos | Jackpot Odds | Any Prize Odds (approx) |
|---|---|---|---|
| Powerball | 292,201,338 | 1 in 292M | 1 in 24.9 |
| Mega Millions | 302,575,350 | 1 in 302.6M | 1 in 24 |
| EuroMillions (5/50+2/12) | 139,838,160 | 1 in 139.8M | 1 in 13 |
| UK Lotto (6/59) | 45,057,474 | 1 in 45M | 1 in 9.3 |