The basic rule
In a standard raffle, each ticket has an equal chance of being drawn. If the draw picks one ticket, your chance of winning is:
tickets you hold ÷ total tickets sold
Holding 5 of 500 tickets gives 5/500 = 1/100, or 1 percent. You can also say the odds are 1 in 100, or 99 to 1 against. Moving between those forms is a matter of odds conversion, and both describe the same event.
Raffles are simpler to analyse than a numbers game, because you do not need any counting of combinations. Every ticket is an item in a hat, so the total number of tickets sold is the only thing you need besides your own count.
Why the total, not the printed range, matters
Tickets may be numbered 1 to 1,000, but if only 500 are sold, only those 500 can win. Your chance depends on tickets actually in the draw. That has a practical consequence: the odds are not known until the raffle closes, and a raffle that sells fewer tickets than expected gives each ticket a better chance. A raffle that sells out gives each ticket a worse chance.
If a raffle does not state a cap, ask or check how many tickets were sold before you decide how much it is worth to you. Some organisers announce the ticket count; many do not.
Buying more tickets
If you hold 5 tickets out of 500 and add 5 more, you do not end up with 10 out of 500. The new tickets also add to the total, so you hold 10 of 505. That is 10/505, about 1.98 percent, compared with 1 percent before. The chance almost doubles here only because 5 extra tickets is small compared with 500 total.
When your holding is a larger share of the total, the effect weakens. Imagine the raffle has 500 tickets held by others and you buy more. With 100 tickets you hold 100/600, or about 16.7 percent. With 200 tickets you hold 200/700, or about 28.6 percent. Doubling your tickets raised your chance by a factor of about 1.7, not 2. Each extra ticket helps a little less than the one before.
At the same time, each ticket costs the same, so the cost grows in a straight line while the benefit grows more slowly. A bigger share of the pool is therefore not the same as a better deal.
Raffles with several prizes
Many raffles draw more than one prize, and each ticket normally can win only once: once a ticket is drawn, it is set aside and the next prize is drawn from the rest. This is sampling without replacement, the same idea explained in the context of cards under without replacement.
For a raffle with 3 prizes and 500 tickets sold, where you hold 5 tickets:
- Your expected number of prizes is 3 × 5/500 = 0.03. This is the average count of wins, not a probability.
- The chance of winning at least once is easiest to find from the complement, the chance of winning nothing, as in complement counting.
The chance that none of your tickets is drawn for the first prize is 495/500. For the second prize, given you missed the first, it is 494/499. For the third, it is 493/498. Multiplying the three fractions gives 120,553,290 ÷ 124,251,000, which is about 0.9702. So the chance of winning nothing is about 97.02 percent, and the chance of winning at least one prize is about 2.98 percent.
That is a little below 3 percent, which is what you would get by simply adding three 1 percent chances. The small gap arises because the three draws are dependent events: once a prize is drawn, the pool shrinks, and your tickets cannot win twice with the same ticket. When the number of prizes is small relative to the tickets sold, adding is a decent shortcut. The more prizes there are relative to the tickets, the less well it works.
Different prize values
If prizes differ, the draw order matters for what you win, although not for your chance of winning something. Each ticket still has the same chance of being drawn first, second or third. A simple way to see this is to imagine shuffling all the tickets and reading off the first three: every ticket is equally likely to end up in any position.
So with 500 tickets, the chance that a particular ticket takes first prize is 1/500, the same as its chance to take second or third. A raffle with prizes of different value therefore gives each ticket the same average return, and if you hold 5 tickets you are 5 times as likely as a one-ticket holder to land each prize.
A quick look at average return
You can also use the ticket count to estimate the average value of a ticket. Suppose a single prize worth 1,000 is drawn from 500 tickets sold. Each ticket is worth, on average, 1,000 ÷ 500 = 2. If tickets cost 5, the average return is below the price. That is not surprising when a raffle raises money for a cause: the difference is the contribution. The idea is the same as ticket expected value in a lottery, with a much simpler set of numbers.
Prizes that were donated or have a retail value different from the value to you change the picture, so treat any calculation like this as a rough guide.
Things worth checking
- One draw or several. Are all prizes drawn from one pool, or are there separate draws with their own tickets?
- Whether a ticket can win more than once. Most raffles remove a drawn ticket, but rules vary, so read the terms.
- Whether the draw is fair. A well-mixed drum, a numbered list with a random selection, or an independent witness all help. If the draw is not random, the equal-chance assumption fails, and so does the arithmetic above.
- Who is eligible. Tickets that are bought but not eligible do not participate.
Keeping it in proportion
The numbers above describe chances, not outcomes. A 1 percent chance does not mean you win once in 100 tries, and it does not become more likely because you lost last time. Treat raffle tickets as a donation with a small chance of a prize, set a limit on what you are willing to spend, and avoid buying more tickets to make up for earlier ones. If gambling is causing you problems, a local support service can help.