Home › Math & Conversions › Core Math & Algebra › Lottery Odds Calculator Lottery Odds Calculator Compute exact lottery odds for standard number-drawing games. Define the game rules and this calculator will return the probability of matching 0, 1, 2, … up to all numbers, plus the familiar “1 in X” jackpot odds . The engine uses hypergeometric probability behind the scenes and can handle both single-drum lotteries (classic 6-from-49 style) and two-drum lotteries with bonus balls (Powerball-style games). 1. Choose lottery type Lottery structure Single-drum (one number pool) Two-drum (main pool + bonus ball) Single-drum: all numbers are drawn from the same pool. Two-drum: main numbers + separate bonus/Powerball pool. 2A. Single-drum lottery parameters Example: “Choose 6 numbers out of 49; draw 6 winning numbers out of the same 49”. Numbers in pool (N) Total distinct numbers in the game (e.g. 49). Numbers on your ticket (T) How many distinct numbers you choose. Numbers drawn (K) How many numbers the lottery draws. Min. matches for a win (r min ) Used for “P(matches ≥ r min )” in the summary. Decimals in output 2B. Two-drum lottery parameters Example: “Pick 5 main numbers from 1–69 and 1 bonus ball from 1–26; draw 5 main + 1 bonus”. Main number pool Numbers in main pool (N₁) Numbers on ticket (T₁) Main numbers drawn (K₁) Bonus

Powerball pool Numbers in bonus pool (N₂) Bonus numbers on ticket (T₂) Bonus numbers drawn (K₂) Decimals in output Calculate odds Clear results Exact combinatorial odds – no approximations Single-drum lottery odds Summary Pool size (N) Ticket numbers (T) Numbers drawn (K) Total combinations C(N, K) Jackpot matches Jackpot probability Jackpot odds (“1 in X”) P(matches ≥ r min ) Interpretation All calculations assume a perfectly random draw without replacement. Odds refer to one ticket in a single drawing. Probability of exactly r matches Copy table as CSV Matches r P(exactly r) “1 in X” odds For a given r, the probability is \( \mathbb{P}(R = r) = \dfrac{\binom{T}{r}\,\binom{N - T}{K - r}}{\binom{N}{K}} \), where R is the number of matches between your ticket and the drawn K numbers. Two-drum lottery odds Summary Main pool (N₁) Main ticket (T₁) Main drawn (K₁) Bonus pool (N₂) Bonus ticket (T₂) Bonus drawn (K₂) Jackpot probability Jackpot odds (“1 in X”) Interpretation The calculator assumes that the main and bonus pools are drawn independently. Overall odds are the product of the odds in each drum. Joint probability table – main matches vs bonus matches Copy table as CSV Each cell corresponds to \( \mathbb{P}(R_1 = r_1, R_2 = r_2) = \mathbb{P}(R_1 = r_1)\,\mathbb{P}(R_2 = r_2) \), where \( R_1 \) and \( R_2 \) are the numbers of matches in the main and bonus pools respectively. The jackpot is the cell with all main and all bonus numbers matched. Lottery odds and hypergeometric probability Most number-drawing lotteries can be modelled using the hypergeometric distribution . Consider a single-drum game: there are N possible numbers, you choose T of them on your ticket, and K numbers are drawn for the winning combination. The number of matches between your ticket and the draw, R, follows a hypergeometric law. The probability of matching exactly r numbers is: \[ \mathbb{P}(R = r) = \frac{\binom{T}{r}\,\binom{N - T}{K - r}}{\binom{N}{K}}, \] where \( \binom{n}{k} \) is the binomial coefficient “n choose k”. The denominator \( \binom{N}{K} \) counts all possible K-number draws from N, while the numerator counts favourable draws with exactly r matches. Jackpot odds as “1 in X” For the jackpot, r is typically equal to all numbers on your ticket (e.g. r = 6 in a 6-from-49 game). Once the jackpot probability \( p_{\text{jackpot}} \) is known, the usual way to present odds is \[ \text{Odds} = \frac{1}{p_{\text{jackpot}}}. \] If \( p_{\text{jackpot}} \approx 7.15 \times 10^{-8} \), the odds are approximately \( 1