Raffle Odds: What More Tickets Buy, and When Draw Order Matters

The short answer

• One prize. Your chance is your tickets over all tickets sold: 10 of 300 is exactly 1 in 30 (3.33%). A ticket that makes the raffle one ticket bigger adds slightly less than a full share: at 10 of 100 it takes you from 10.0% to 10.9%, 0.89 points rather than a full point.
• Several prizes, each ticket can win once. In a sold-out 300-ticket raffle with 10 prizes, holding 20 tickets instead of 10 doubles the prizes you can expect (from 1/3 to 2/3 of a prize), but your chance of winning anything only goes from 29.1% to 50.4%.
• One prize per person. A person with 10 entries among 99 people with one entry each has 9.17% at the prize drawn first and 6.44% at the prize drawn fifth. When a buyer can win with each of their tickets, order makes no difference.
• Bonus entries. When 50 of 200 entrants earn 4 bonus entries for sharing, the sharers hold 62.5% of the entries, and everyone who did not share drops from 0.50% to 0.25% for a single prize.

The figures come from exact fractions and from 41.5 million spins simulated through random.js, the file that picks every result on Wheel Cue; compared at 97 points, all 97 agreed within four standard errors. Percentages are exact unless the sentence says "simulated". For buyers, extra tickets add less than they seem to: buy them to support the cause, not to win. To work out your own draw, use the odds calculator further down.

One prize: your chance is your share of the tickets

With a single prize and N tickets, each equally likely, a holder of t tickets wins with probability exactly t/N. The raffle wheel gives every ticket line an equal slice, so that is the whole calculation: 1 in 300 for one ticket in a 300-ticket raffle, 1 in 30 for 10.

What the next ticket adds depends on where it comes from. If the book is fixed and sells out either way, your extra ticket is one someone else would have bought, and it adds exactly 1/N. If buying it makes the raffle one ticket bigger, your chance moves from t/N to (t + 1)/(N + 1), a gain of (N − t)/(N(N + 1)): a little less than 1/N, because each new ticket also dilutes the ones you already hold. The table shows this second case.

At 1 ticket in 100, the next ticket adds 0.98 points, almost a full share; at 20 in 100 it adds 0.79 points, about 79% of one. Buying 10 more on top of 10 of 100 takes you from 10.0% to 18.2%, not 20%: 1.82 times the chance, because your new tickets join a pool of 110. In a 1,000-ticket raffle the effect almost disappears: at 20 tickets the next one still adds 0.979 of a full share.

Several prizes: twice the tickets, twice the expected prizes, not twice the chance

With several prizes, the raffle wheel retires each winning ticket (Retire each ticket once it wins is on by default). Each ticket can win once, but a person holding several tickets can win several prizes.

Take a sold-out raffle of N tickets with m prizes, t of the tickets yours. Your expected number of prizes, the average you would win over many identical raffles, is exactly m·t/N: each of your t tickets wins with chance m/N, and averages add up. Your chance of winning at least one prize is 1 − C(N − t, m)/C(N, m), one minus the chance that none of the m winning tickets is yours (C(a, b) counts the ways to choose b tickets from a).

Holding 20 tickets instead of 10 multiplies expected prizes by exactly 2 but the chance of at least one prize by only 1.73. The difference goes into multiple wins: the chance of two or more rises from 3.91% to 13.8%. A holder of 30 tickets averages exactly 1 prize, yet wins nothing 34.3% of the time.

The same holds ticket by ticket. In a fixed book of 300, where each ticket you add is one someone else would have held, every extra ticket adds the same 1/30 of a prize to what you can expect, but less and less to your chance of winning anything: 3.33 points for your first ticket, 2.44 points when you already hold 10, 1.77 points when you hold 20.

With tickets retired, draw order does not matter

Before the first spin, any ticket is as likely to be drawn 10th as 1st, so a holder of 10 of 300 tickets has exactly 1 in 30 at the first prize, the fifth and the tenth (simulated: 3.36%, 3.34% and 3.28%). When a buyer can win more than once, drawing the big prize first or last is showmanship, not odds.

One prize per person: here the draw order matters

The giveaway winner picker has Remove each winner before the next draw on by default, and with Weighted choices turned on, a person with extra entries is one line such as Sam *10. When that line wins, all of Sam's entries leave at once, so each person can win once.

We put one person with w entries among 99 people with one entry each and drew 5 prizes under two rules: one prize per person (the whole line leaves) and one prize per entry (entries retired one at a time, as on the raffle wheel).

When every rival has one entry, the chance of winning at least one prize is exactly the same under both rules: 38.8% with 10 entries, 22.2% with 5. Until your first win, each draw that misses you removes one single-entry rival under either rule, so the two wheels are identical up to that point.

What differs is when you win, and whether you can win again:

• One prize per person: with 10 entries, your chance is 9.17% at the prize drawn first, falling to 6.44% at the fifth, 1.42 times as high at the start. You cannot win twice. (Simulated: 9.17% and 6.47%.)
• One prize per entry: your chance is 9.17% at every draw (10/109), and you win two or more prizes 6.56% of the time, for 0.459 prizes on average.

The decline is not the wheel favoring anyone. A later prize can go to you only if you have not already won and left, and with 10 entries you often leave early. With 20 entries the gap is wider: 16.81% at the first prize against 8.24% at the fifth (exact math only, not simulated). So when each person can win once, the draw order is a real decision: drawing the grand prize first gives people with many entries their best shot at it, and drawing it last moves part of that chance to people with fewer entries. Either is fair if announced.

Extra entries also help less than their count suggests. Against 99 single-entry rivals, under either rule, 5 entries give 4.45 times the one-entry chance of winning something and 10 entries 7.76 times, not 5 and 10: your own entries make the wheel bigger, and once you have won, further entries cannot add a first prize.

In a mixed giveaway the draw-order effect can be much smaller. With 70 people holding 1 entry, 20 holding 3 and 10 holding 10 (230 entries, 5 prizes, one per person), a 10-entry person has 4.35% at the prize drawn first and 3.97% at the fifth, and a 1-entry person 0.43% against 0.47%. The calculator below works out any draw where you hold several entries and everyone else holds one.

Bonus entries move odds from one group to another

Online giveaways often give extra entries for sharing a post. Each entry is a slice of the wheel, and the slices have to come from somewhere.

Take 200 entrants with 1 entry each, and 4 bonus entries (5 in total) for anyone who shares. With one prize and S sharers, a sharer's chance is 5/(5S + (200 − S)) and a non-sharer's is 1/(5S + (200 − S)).

• If nobody shares, everyone has 1 in 200 (0.50%).
• If 50 share, a sharer has 1/80 (1.25%) and a non-sharer 1/400 (0.25%). Sharers are 25% of the people but hold 62.5% of the entries, and so 62.5% of the chance of a single prize.
• With the same 50 sharers, 3 prizes and one per person, a sharer's chance of a prize is 3.736% and a non-sharer's 0.755%, 4.95 times as high (simulated over 500,000 giveaways: 3.73% and 0.76%).
• If all 200 share, everyone is back to 1 in 200 (0.50%).

A bonus is worth the most when few others take it. If none of the other 199 share, sharing lifts your one-prize chance from 0.50% to 2.45%. If all of them share, sharing only keeps you at 0.50%, and not sharing leaves you at 0.10%.

None of this makes bonus entries unfair, but it changes everyone's odds, so the posted rules should say what earns a bonus, how many entries it is worth, and whether there is a cap. Give bonus entries only for free actions: if entries can be bought, or come with a purchase, the giveaway can legally become a lottery unless there is an equally good free way to enter. Platforms have rules too: Facebook, for one, does not allow "share on your timeline" or "tag a friend" as ways to enter or earn entries, so check them first.

Running a draw people can check

The numbers above come down to a few decisions to announce before the first spin. Selling raffle tickets is regulated almost everywhere and is usually limited to licensed charities and non-profits, so check with your local regulator before you sell any; see the raffle guide.

Decide: one prize per ticket, or one per person

• Ticket raffle. On the raffle wheel, Retire each ticket once it wins is on by default, so a buyer of 20 tickets can win several prizes. If you want one prize per buyer, announce that when an earlier winner's ticket comes up again, you spin again: that gives exactly the same odds as taking all of the buyer's tickets off the wheel, so the one-prize-per-person results above apply, draw order included.
• Giveaway of people. On the giveaway winner picker, write each person once with their entries, such as Sam *3, and turn on Weighted choices before you draw; with it off, that line is one entry named "Sam *3". With Remove each winner before the next draw left on, Sam's whole line leaves when Sam wins.
• Never paste a person several times when the rule is one prize per person. If Sam is on three plain lines, a win removes only one of them and Sam can win again. See weighted picking.

Big books: a block first, then the ticket

One wheel takes up to 500 tickets, but above about 200 the slices are too thin to read, so the raffle wheel page suggests drawing a block first, then the ticket within it. With equal blocks that is exactly fair for the first prize: 10 blocks of 100 give each ticket 1/10 × 1/100 = 1/1,000.

Later prizes need care. With Retire each ticket once it wins on, the winning block leaves the block wheel, so its other 99 tickets cannot win and every other ticket gets 1/900 instead of a fair 1/999. The exact fix is a weighted block wheel: retirement off, Weighted choices on, each block written with its number of tickets (Block 1 *100), that number lowered by one whenever one of its tickets wins, and past winners left out when a block's tickets go back on the ticket wheel. The raffle wheel page shows the setup. In 500,000 simulated second prizes drawn this way, the first winner's block won again 9.84% of the time, against an exact 11/111 (9.91%).

Announce the order, draw live, publish the log

• Say whether the grand prize is drawn first or last. It changes nothing when a buyer can win with each ticket; with one prize per person, including a ticket raffle that redraws past winners, it changes who is most likely to get it.
• Read out the odds. For example: "300 tickets, 10 prizes, each ticket can win once. Holding 10 tickets gives you 1 in 30 at each prize and a 29.1% chance of at least one."
• Draw where everyone can see it, and re-spin only under a rule you announced in advance, such as an absent winner.
• Publish the whole log. Copy in the Winning tickets panel (raffle wheel) or Winners drawn panel (giveaway picker) exports every draw with its probability and spin ID. The raffle guide and the giveaway guide cover absent winners and more.

If someone still calls a fair result rigged, why random feels rigged explains why fair draws repeat more often than people expect.

How to check these numbers

Every exact value here is a fraction computed with whole-number arithmetic: the hypergeometric formula (the standard count for drawing without putting tickets back) for retired tickets, and a step-by-step calculation over the draw sequence for one prize per person. The simulation is separate: one CueRandom.pickWeighted() call per spin over the weights still on the wheel, removing each winner the way each tool does (one ticket line on the raffle wheel, the whole weighted line on the giveaway picker).

• Checks. A check passes when the simulated and exact values differ by less than four standard errors. All 97 passed; the largest gap was 2.58 standard errors.
• Even spread. In the 100-ticket raffle, over 1,000,000 simulated draws, the least-drawn ticket won 9,728 times and the most-drawn 10,239, against an average of 10,000, a normal spread for fair draws. The 1,000-ticket raffle, drawn as a block and then a ticket, came up as evenly over 1,000,000 draws.
• Re-run it. The script and raw results are linked at the top of the page. Save the script and random.js in one folder and run node raffle-odds-what-more-tickets-buy.mjs random.js results.json with Node.js. The simulated values will differ in the last decimals; the exact ones will not.
• The code itself. The fairness report tests random.js at scale, and how randomness works explains the method.