Raffle Odds Calculator

How the calculator finds your odds

A raffle is a jar of $N$ tickets. You hold $k$ of them, and the organizer reaches in and pulls $n$ winning stubs, one after another, never putting a drawn ticket back. Because each pull shrinks what is left in the jar, the chance of the next pull depends on the ones before it. That "draw without replacement from a finite pool" setup is exactly what the hypergeometric distribution was built to describe, and it is what this page uses. Enter your three numbers below, press Compute Odds, and the results appear instantly — nothing leaves your browser.

If $X$ counts how many of your tickets get drawn, the probability of winning exactly $x$ prizes is the number of ways to pick $x$ winners from your $k$ tickets and the remaining $\mathrm{n}-x$ winners from everyone else's tickets, divided by all the ways to choose $n$ winners from the whole jar:

Formula: P(X = x) = (kCx × (N-k)C(n-x)) / NCn

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

The headline number most people want — the chance of winning anything at all — is quickest to get by turning the question around: instead of adding up every winning outcome, subtract the single losing outcome (none of your tickets drawn) from 1.

Formula: P(X ≥ 1) = 1 - P(X = 0) = 1 - (N-k)Cn / NCn

$P(X\ge 1)=1-P(X=0)=1-\frac{\text{(N-k)Cn}}{\text{NCn}}$

Here $\text{aCb}$ is "$a$ choose $b$," the count of ways to pick $b$ items from $a$ without caring about order. Those counts explode fast — a 2,000-ticket raffle produces numbers with hundreds of digits — so the calculator does the combinatorics in exact BigInt integer arithmetic and only rounds to a percentage at the very end. It also reports the expected number of prizes you'd win, which for this model is simply your share of the jar times the number of draws:

Formula: E[X] = k / N n

$E\left[X\right]=\frac{k}{N}n$

That figure is an average over many repeats of the same raffle, not a promise. An expected value of 0.48 doesn't mean half a trophy; it means that if you ran this exact drawing thousands of times, your wins would average out to about 0.48 per drawing.

Filling in the three inputs

Three whole numbers drive everything. Total Tickets Sold ($N$) is the size of the whole pool once sales close. Your Tickets ($k$) is how many stubs carry your name — enter 0 if you're just curious. Number of Prizes ($n$) is how many winning tickets get pulled. The calculator returns a row-by-row table of the chance of winning 0, 1, 2, … prizes, your chance of at least one win, and your expected haul. A handy way to explore is to change one field at a time — bump your tickets from 5 to 10 and watch how much (or how little) the "at least one" number moves.

A worked example you can check by hand

Say a school fundraiser sells 2,000 tickets and will draw 3 prizes, and you bought 25. Plug those in and the chance of winning at least once comes out to about 3.7%. Almost all of that is the chance of winning a single prize; landing two or three is a rounding footnote at these numbers. Now scale everything down so you can follow the arithmetic: a tiny raffle with $N$ = 50 tickets, $k$ = 6 of them yours, and $n$ = 4 prizes drawn. The table lists 0 through 4 wins. P(X = 0) is the chance none of your six stubs surface among the four winners; P(X ≥ 1) is one minus that, the number you'll quote to friends. Expected prizes work out to (6 / 50) × 4 = 0.48 — just under half a win on average. Buy two more tickets and it climbs to (8 / 50) × 4 = 0.64, a concrete way to price what those extra stubs actually buy you.

Where this model fits — and where it doesn't

Everything here rests on one clean picture: every ticket has an equal chance, a drawn ticket never goes back in the jar, and owning several tickets means you can win several prizes — one per stub. Two smaller notes: displayed percentages are rounded, so a genuinely tiny chance shows as "<0.01%" rather than a misleading 0.00%, and the tool weighs probability only, never whether the ticket price is a good deal. Most fundraising raffles are designed to return less than you pay, because the point is the cause.

Real raffles bend those rules in a few predictable ways, and it's worth matching the fine print before you trust a number. If the event caps each person at one prize no matter how many tickets they hold, your chance of two-or-more wins collapses to zero, and a redraw rule changes the math entirely because the pool of "still eligible" tickets shrinks with every winner. If prizes are handed out in separate drawings by tier — a grand prize, then several runner-ups — and tickets go back between rounds, each round behaves like its own fresh raffle; compute them one at a time. And if organizers set aside house or sponsor tickets, or guarantee winners from a subgroup, some stubs no longer share the same odds; shrink the effective pool for that prize or treat the result as a ballpark.

The intuition worth carrying away is coverage. Own 10 of 1,000 tickets and you cover 1% of the jar. With a single prize your chance is exactly that 1%. With ten prizes drawn it climbs toward, but never quite reaches, 10% — every losing ticket the organizer pulls is one that can't be pulled again, which nudges the odds down a hair. The calculator tracks that subtlety so you don't have to.

Questions people ask about raffle odds

Is "chance of at least one win" the same as "my odds of winning"? In casual conversation, yes — that's the number most people mean. When several prizes are on the line you might also care about the split between winning exactly one and winning several, which is what the full table shows.

What if prizes are drawn on different days? As long as the same pool is used and winning tickets are set aside each time, drawing three prizes across three evenings gives identical odds to drawing all three at once. Only if tickets are returned between draws does each night become a separate raffle.

Does buying tickets early or late change anything? No. In a fair drawing everything is mixed before the pull, so timing is irrelevant — only the final counts of total tickets and your tickets matter.

Privacy

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