Reviewed by: JJ Ben-Joseph

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Raffles and prize drawings add excitement to community events, charity fundraisers, and online giveaways. Participants often buy multiple tickets to boost their chances, yet the actual probability of winning can be elusive. This calculator demystifies the odds by applying the hypergeometric distribution, the classical model for draws without replacement. Whether you are assessing how many tickets to purchase or explaining the fairness of a raffle to attendees, the computation happens instantly and entirely within your browser for privacy and convenience.

To model a raffle, imagine a population of $N$ tickets, of which you hold $k$. The organizers randomly draw $n$ winning tickets without replacement. You are interested in the probability $\mathrm{P(X\; \backslash ge\; 1)}$ that at least one of your tickets is selected. The underlying distribution is hypergeometric because each draw changes the composition of the remaining pool.

The probability of exactly $x$ of your tickets winning is

$P(X=x)=\frac{\text{kCx}\times \text{(N-k)C(n-x)}}{\text{NCn}}$

Where the notation $\text{aCb}$ denotes a binomial coefficient, often spoken as “$a$ choose $b$.” The chance of winning at least one prize is then

$P(X\backslash ge1)=1-P(X=0)$

Which evaluates to

$1-\frac{\text{(N-k)Cn}}{\text{NCn}}$

Because the formula uses combinations, your odds are determined solely by proportions. Buying 10 tickets in a pool of 100 has the same odds as buying 100 tickets in a pool of 1,000. The calculator evaluates these expressions using JavaScript’s BigInt arithmetic for accuracy even with large numbers of tickets or prizes.

Consider an example: a charity sells 2,000 tickets and will draw 3 prizes. If you buy 25 tickets, your chance of winning at least once is about 3.7 %. The probability of winning exactly one prize is 3.6 %, and the chance of winning two or three prizes drops below 0.1 %. The output table generated by the calculator lists all probabilities from zero up to the number of prizes, letting you see the full distribution.

The mathematics behind the hypergeometric distribution can be expressed in table form as well. Suppose $N=100$, $n=3$, and you hold $k=5$ tickets. The table below enumerates the probabilities:

Number of Wins (x)	Probability P(X = x)

These calculations assume each ticket has an equal chance of being drawn and that winners are not returned to the pool. If your raffle rules differ—for instance, if drawing is with replacement or if a person can only win once regardless of multiple tickets—the probabilities change. However, the hypergeometric model covers the most common format where each ticket is eligible for exactly one prize.

Understanding raffle odds is not just a curiosity; it informs rational decision‑making. If tickets cost $2 and the top prize is worth $100, buying 60 tickets in a 1,000‑ticket raffle gives you roughly a 5.8 % chance of winning. The expected value of your purchase is then 0.058 times $100 minus the $120 cost of the tickets, which is negative. This illustrates why raffles are fundraising tools—the expected return is typically lower than the ticket price. The calculator helps visualize this trade‑off so participants can support a cause without unrealistic expectations.

For organizers, presenting transparent odds can boost credibility. By embedding this calculator on a fundraising website or displaying its logic at an event, you show that the drawing is fair and mathematically grounded. The detailed explanation on this page walks through every step so non‑technical readers can follow along. Because the script runs locally, no ticket counts or user entries are transmitted to a server, preserving privacy.

To further demystify the math, consider how the combination formula works. The binomial coefficient $\text{NCn}$ counts the number of ways to choose $n$ items from $N$ without regard to order. It equals . Although factorials grow quickly, BigInt arithmetic keeps the computation exact for ticket pools into the millions. The JavaScript code leverages a custom combination function to avoid floating‑point rounding errors that could otherwise skew probabilities.

Another noteworthy feature is the ability to compute the expected number of prizes you might win. This expectation is simply , reflecting that each of your tickets has a chance of being selected. While the expected value might be fractional, it provides a sense of the average outcome over many similar raffles.

Although winning is never guaranteed, understanding the odds can add to the enjoyment. Some participants derive entertainment from optimizing their chances, pooling tickets with friends, or analyzing whether to spread purchases across multiple raffles. The calculator equips you with quantitative insight so you can make those choices with confidence.

To use the tool, simply enter the total number of tickets sold, the number of tickets you control, and the number of prizes. The results update immediately, displaying probabilities for zero through the number of prizes along with the cumulative chance of at least one win. You can copy the distribution to the clipboard for further analysis or for sharing in spreadsheets and reports.

This extensive explanation is intentionally verbose to support search engines and educational value. By blending formulas, examples, and narrative discussion, the page doubles as both a calculator and a mini‑lesson on discrete probability. Teachers can incorporate it into classroom demonstrations, while hobbyists might use it to analyze everything from school raffles to high‑stakes lotteries. Although lotteries often involve replacement and more complex rules, the underlying combinatorics are related, making the hypergeometric approach a valuable stepping stone.

Probability theory has profound historical roots. The study of combinatorics and random draws helped launch modern statistics when mathematicians like Pascal and Fermat analyzed games of chance in the 17th century. Today, these same principles undergird quality control, biological sampling, and information retrieval. The humble raffle thus serves as an accessible gateway into a rich mathematical tradition. By experimenting with different ticket counts and prize numbers in the calculator, you gain intuition that extends to many other fields.

In summary, the Raffle Odds Calculator leverages the hypergeometric distribution to deliver precise probabilities for winning prizes based on ticket ownership and draw counts. It operates entirely in the browser, preserves privacy, and accompanies the computation with a detailed primer on the underlying math. Whether you are a fundraiser seeking transparency, a participant curious about your chances, or a teacher illustrating combinatorics, this tool transforms abstract equations into an interactive learning experience.