How to Decide at Random: Coin, Dice or Wheel
Last updated: November 2, 2026
Deciding at random is a legitimate tool, not a way of avoiding thought: it works for breaking ties, handing out turns without argument and getting unstuck when the options are truly equivalent. But doing it right has details few people pay attention to, above all how many options you have and whether the mechanism treats them equally. This guide explains what to use in each case, a classic bias mistake, and what is (and is not) known about deciding with a coin.
When it makes sense to let chance decide
Chance is appropriate when the options are practically equivalent to you and what matters is that the result is accepted: who starts a game, who picks the movie, whose turn it is to wash dishes, which of several restaurants you do not mind. In those cases thinking harder rarely improves the decision and does use up time; and a neutral mechanism avoids the suspicion that someone got their way.
It is not a good idea when one option is clearly better, when the decision affects third parties who did not agree to the rules, or when you need to be able to justify the why (a hire, a resource allocation). In those cases it is better to decide using explicit criteria and, at most, use chance only to break ties between candidates who already tied on those criteria.
Which tool to use by number of options
The rule is simple: use the mechanism whose number of possible outcomes matches your number of options, or is a multiple of it. That way each option has exactly the same probability with no tricks.
| Options | Tool | Probability of each | Note |
|---|---|---|---|
| 2 | Coin | 50% | A physical coin has a tiny bias toward its starting side; a virtual one does not. |
| 3, 4 or 6 | Die (d6, d4 or d12) | 33.3% / 25% / 16.7% | Use the die whose number of faces is your number of options or a multiple of it. |
| 5, 7, 9 or more | Random number or wheel | 1/n for each | Number the options and ask for a number between 1 and n, or load the options into the wheel. |
The classic mistake: forcing a die onto a number of options it does not divide
Say you have 4 options and only a regular 6-sided die. It is tempting to assign each result by "the remainder after dividing by 4": 1 and 5 go to option 1, 2 and 6 to option 2, 3 to option 3 and 4 to option 4. The result: options 1 and 2 each have a 2/6 probability (33.3%) and options 3 and 4 only 1/6 (16.7%). The first two come up twice as often. It is a real bias, and it appears whenever the number of faces is not a multiple of the number of options.
The correct fix is called rejection sampling: if a result comes up that does not fit evenly (here, 5 or 6), you discard it and roll again. That way only results 1 to 4 count and each option has exactly 25%. The generators on this site apply the same idea when they generate a number within a range, so no value is more likely than another.
When the options should not have equal weight
Sometimes you do not want every option to be equally likely: for example, you want the pizzeria you like most to come up more often. The most transparent method is to repeat options according to their weight. If you want one option to be twice as likely as two others, write it twice on the wheel: with 4 entries in total it will have 50% and each of the others 25%.
What matters is fixing the weights before spinning and having everyone involved see them. Changing the weights after seeing a result you did not like turns chance into a formality.
What the evidence says about deciding with a coin
There is a study by economist Steven Levitt (first an NBER working paper in 2016, then in the Review of Economic Studies in 2020) in which more than 20,000 people torn over an important life decision let a coin on a website tell them what to do. According to the NBER summary, those who got "change" were more likely to make the change than those who got "don't change", and those who changed reported greater well-being six months later; the effect was smaller for less important decisions.
It should be read carefully. Participants chose to enter the study with a real doubt, and those who decided by the coin could still ignore it. The authors read it as a sign that many people are too cautious about major changes, not as proof that deciding at random is better in general. It is an interesting finding about status-quo bias, not an invitation to leave your career to a coin.
A popular trick, which does not come from that study but from many people's experience, is to use the coin as a mirror: flip it, and notice whether after seeing the result you feel relief or disappointment. If you are disappointed, you probably already preferred the other option. It is a way to discover your preference, not to delegate the decision.
How to make the result accepted by everyone
If the decision involves more than one person, three habits avoid fights. First, define the options and the weights before flipping. Second, use a mechanism everyone can see or verify: a flip in plain view, or a tool whose result is generated on the spot and visible on a shared screen. Third, agree beforehand that the result is final; chance only works as a referee if the parties commit to respecting it.
For prize draws or platform rules, the guide on how to run a fair social media giveaway covers the extra requirements worth meeting.
Frequently asked questions
- What do I use to decide between three options?
- A six-sided die works with no bias: 1 and 2 for option A, 3 and 4 for B, 5 and 6 for C, at 33.3% each. A random number between 1 and 3 or the wheel with the three options also works.
- Why not use a 6-sided die for 4 options with the remainder?
- Because 6 is not a multiple of 4: two of the options would come up twice as often (33.3% versus 16.7%). The right way is to discard the leftover results and roll again, or to use a 4-sided die.
- Is it a good idea to decide important matters with a coin?
- For decisions where the options are truly equivalent to you, yes. For important decisions with one clearly better option, no: a study of more than 20,000 participants suggests the coin pushes some people into a change they later value, but it does not prove that deciding at random is better in general.
- How do I make one option more likely than another?
- Repeat options according to the weight you want: if A should be twice as likely as B and C, write A twice on the wheel. Fix the weights before spinning.
- Is the virtual wheel really fair?
- This site uses the browser's crypto.getRandomValues() with rejection sampling, so each option has exactly the same probability and does not depend on force or angle like a physical wheel.