About the Raffle Odds Calculator
Raffles and prize draws are a popular way to raise money for schools, charities and clubs, and a bit of fun for the people who buy tickets. Unlike a lottery, the odds are usually quite easy to understand — if there is one prize, your chance is simply your tickets divided by the tickets sold. But with several prizes, and tickets that can only win once, the calculation takes a little more care.
This raffle odds calculator works out your chance of winning at least one prize from your tickets, the total tickets sold and the number of prizes drawn. It gives the odds, the chance with one ticket, your expected prizes, how many tickets would give you a 50 percent chance, and what your tickets cost.
How to Use the Raffle Odds Calculator
Enter the number of tickets you have.
Enter the total tickets sold, including yours.
Enter the number of prizes drawn. The calculator assumes each ticket can win only once, as in most raffles.
Optionally, enter the ticket price.
How Raffle Odds Are Worked Out
chance of no prize = (sold − yours) ÷ sold × (sold − yours − 1) ÷ (sold − 1) × …
one factor for each prize drawn
chance of a prize = 1 − chance of no prize
expected prizes = your tickets × prizes ÷ tickets soldStep-by-Step Example
5 tickets out of 500, with 3 prizes.
No prize: 495/500 × 494/499 × 493/498 = 0.97024
A prize: 1 − 0.97024 = 2.98% (about 1 in 33.6)
Expected: 5 × 3 ÷ 500 = 0.03 prizes
One ticket: 3 ÷ 500 = 0.6%How More Tickets and More Prizes Help
With one prize, doubling your tickets doubles your chance. With several prizes, the chance of winning at least one grows a little more slowly than in proportion, because you cannot win the same prize twice — but more prizes raise everyone's chances. In the example, one prize would give a 1 percent chance; three prizes raise it to nearly 3 percent. To reach an even chance of winning something in that draw, you would need about 103 of the 500 tickets.
Expected Prizes
Expected prizes is the average number of prizes you would win if the same raffle were held many times. For 5 of 500 tickets with 3 prizes, it is 0.03: you would expect to win about 3 prizes in every 100 raffles. If the prizes have a known value, multiplying their average value by the expected prizes gives the average value of your tickets, which is almost always less than you paid — the difference is the donation to the cause.
Raffles and the Law
In many countries, raffles and prize draws are regulated. Small raffles at events such as school fairs are often exempt, but larger raffles, those sold over time or online, and those with valuable prizes may need a licence, published rules and a fair, witnessed draw. If you are organising a raffle, check the rules where you live and make clear how many tickets are for sale and how the draw will be made.
Running a Fair Draw
Number every ticket, keep a record of sales, and draw in public where everyone can see. A random number generator from 1 to the number of tickets sold is a simple fair method for online raffles; drawing again for each prize, and setting aside tickets that have already won, matches the calculation here. Announce the winners and the number of tickets sold so everyone can see their real odds.
Raffles With Replacement
In a few draws, a winning ticket goes back in and can win again. Then each prize is an independent draw, and the chance of winning nothing is (1 − your tickets ÷ tickets sold) raised to the power of the number of prizes. For 5 of 500 tickets and 3 prizes, that is 0.99³, about 0.9703, giving almost exactly the same 2.97 percent chance of winning something. The difference only becomes noticeable when you hold a large share of the tickets or there are many prizes.
Prize Value and Ticket Price
For a charity raffle, the point is to support the cause, and the prizes are a bonus. Still, it can be interesting to compare the value of the prizes with the money raised. If 500 tickets are sold at 2 each, the raffle raises 1,000. If the three prizes are worth 300 in total, each ticket's share of the prize value is 0.60, and the remaining 1.40 of every ticket goes to the cause, less any costs. Donated prizes mean more of the money raised goes to the good cause.
Buying Tickets as a Group
Friends or colleagues sometimes pool money to buy a block of tickets and share whatever they win. The group's chance is calculated from all its tickets together, and each member shares any prize.
Understanding Your Result
Chance to win gives the chance of winning at least one prize.
Odds expresses the chance as 1 in a number.
With one ticket gives the chance for a single ticket.
Expected prizes gives the average number of prizes won.
For a 50% chance shows the tickets needed for an even chance.
Spending shows what your tickets cost.
When Should You Use This Calculator?
Deciding how many tickets to buy.
Organising a raffle and setting ticket numbers.
Checking your chances in a prize draw.
Explaining odds to supporters or students.
Comparing raffles with different numbers of prizes.
Common Mistakes
Adding your chance for each prize instead of using the formula.
Ignoring the total sold, which changes the odds.
Assuming a ticket can win more than once.
Expecting to win back what you spend.
Forgetting local rules when organising a raffle.