How to Pick a Winner Fairly: Random Draws Explained
Choosing a raffle winner, deciding who goes first, or settling who does the dishes all come down to the same thing: picking one or more items from a list so that nobody can complain about how it was done. The good news is that fairness is simple to define, and it is easy to get right once you know the few ways it goes wrong.
This article covers what "fair" means, how the odds work when you draw one winner or several, a subtle bias that creeps in with dice, and a short process you can reuse for any draw.
What "fair" actually means
A draw is fair when every eligible entry has the same chance of winning, the rules were fixed before the draw, and nobody can influence the outcome after seeing it. For a list of n equal entries, each entry's chance of being the single winner is 1 ÷ n.
chance of winning one draw = 1 ÷ number of entriesWith 40 entries each has a 1 in 40 chance, which is 2.5%.
Random does not mean "looks even". A fair coin can land heads five times in a row, which happens with probability 0.5⁵ = 1/32, about 3.1%. The next flip is still 50-50, because the coin has no memory. Streaks and clusters are normal in random results, so do not redraw just because the winners look suspicious.
One winner or several
When several winners are drawn and nobody can win twice, each entry's chance of being among the winners is the number of prizes divided by the number of entries.
Worked example: 3 prizes, 40 entries. Each person has a 3 ÷ 40 = 7.5% chance of being one of the winners. The number of different groups of 3 winners is 40 × 39 × 38 ÷ (3 × 2 × 1) = 9,880, and a fair draw makes every one of those groups equally likely.
If the three prizes are different, say first, second and third, then order matters. There are 40 × 39 × 38 = 59,280 possible ordered outcomes, and each person has a 1 in 40 chance of winning first prize.
Extra entries tilt the odds in proportion. Suppose one person holds 5 of 100 tickets. In a single draw their chance is 5%. If three tickets are drawn, the chance that at least one of their tickets is among them is 1 − (95 × 94 × 93) ÷ (100 × 99 × 98) = about 14.4%, slightly under three times 5%, because the person could hold more than one of the drawn tickets and the simple sum counts those cases twice.
The dice trap: unequal remainders
Say you want to choose among 4 people using a six-sided die. A tempting shortcut is to divide the roll by 4 and use the remainder: 1 and 5 pick person 1, 2 and 6 pick person 2, 3 picks person 3, 4 picks person 4. That gives persons 1 and 2 a chance of 2/6 (33.3%) each, and persons 3 and 4 only 1/6 (16.7%). It looks random but it is not fair.
The problem appears whenever the number of outcomes is not a multiple of the number of choices. The fix is to throw away the extra outcomes and roll again: here, re-roll any 5 or 6 so that each of 1 to 4 has a chance of 1/4.
- For two, three or six choices a single die divides evenly: for example 1 to 3 against 4 to 6, or 1-2, 3-4 and 5-6.
- For other sizes, re-roll the outcomes that do not fit, as above.
- For longer lists, number the entries and use a tool that chooses uniformly from the whole range rather than improvising with dice.
A repeatable process for raffles and giveaways
- Write down the rules first: who is eligible, how many entries each person may have, and how many winners there will be.
- Build one list of valid entries and remove anything that breaks the rules. Check for accidental duplicates.
- Decide what happens if a winner cannot be reached, for example by drawing one or two runners-up in advance.
- Draw with a method that gives each entry an equal chance. A random picker draws one or several items from your list, and the random name picker is built for lists of names.
- Record the date, the list and the result so you can show how the draw was made.
If several winners are chosen one at a time, remove each winner from the list before drawing the next, otherwise the same person can come up twice. To check the odds for a bigger draw, the combination calculator counts how many different groups of winners are possible.
Raffles, lotteries and prize promotions are regulated in many places and the rules vary. This article covers the arithmetic of a fair draw, not legal requirements, so check the rules that apply where you are before running a draw for money or prizes.
- Random Picker: Enter your options one per line, choose how many to draw and press Pick Randomly. It works for names, prizes, tasks, restaurants or anything else you can type.
- Random Name Picker: Paste one name per line, say how many names you want and press the button. Each name has the same chance of being drawn, and nobody is drawn twice in a single pick.
- Combination Calculator: Enter how many items you can choose from and how many you will pick, and the calculator returns the number of different selections. Tick the repetition box when the same kind of item may be picked more than once.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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