Lottery Odds Calculator — Jackpot & Prize Tier Probabilities

Формула

How this is calculated

A standard lottery draws K numbers from a pool of N without replacement, and you win the jackpot by matching all K. The total number of equally likely outcomes is the combination C(N, K) = N! / (K! × (N − K)!). Your probability of holding the jackpot ticket is exactly 1 / C(N, K). For the classic 6/49 lottery, C(49, 6) = 13,983,816, so the jackpot chance is about 1 in 14 million.

For partial-match prizes (matching m of the K drawn numbers), the calculation uses the hypergeometric distribution: P(match m) = C(K, m) × C(N − K, K − m) / C(N, K). Here C(K, m) counts ways to choose m correct numbers from the K drawn, and C(N − K, K − m) counts ways to fill the remaining picks from the non-drawn numbers. The prize-tier bar chart shows these probabilities relative to each other — the jackpot bar is nearly invisible compared to lower tiers, which captures the actual difficulty visually.

All combinations are computed using logarithms of factorials to avoid arithmetic overflow, allowing pool sizes up to 99 without precision loss. This calculator models a simple draw with no bonus ball; formats like Powerball or EuroMillions with a separate bonus-ball draw have different jackpot odds.