Heads or Tails: Settling a Decision With a Coin
A coin flip is the oldest tie-breaker there is. The Coin Flip tool flips one and keeps a running tally of heads against tails.
A real coin is not quite fair
Two findings from people who have studied this properly, and both are more interesting than the folklore.
A flipped coin has a slight bias toward the side that was facing up when it left your hand - because it spends a little more time on that side as it tumbles. Work by Persi Diaconis and colleagues put the effect at roughly 51 to 49, and a very large recent study of hundreds of thousands of real flips found a bias of about the same size.
A spun coin is much worse. Spinning one on a table can be substantially biased, because the rim is not symmetrical - the weight distribution around the edge favours one side settling down.
None of which matters for deciding who washes up. It matters enormously if someone is betting on it, which is why a proper flip is called in the air and caught rather than spun.
A digital flip has neither problem, and also has no thrill.
Why handing a decision to chance works
The useful insight is not about fairness. It is that most coin flips are for decisions where the options are close to equal, and in that situation the cost of deliberating exceeds the difference between the outcomes.
If you genuinely cannot choose between two restaurants, the choice barely matters - what is costing you is the ten minutes of discussion. The coin ends that, and the ending is the value.
There is a second effect worth knowing: how you feel about the result tells you what you wanted. If the coin says one thing and you feel a flicker of disappointment, you had a preference after all, and now you know it. The Magic 8-Ball works on exactly the same mechanism.
Where a flip is the wrong tool
When the options are not close. A coin flip between a decision that matters and one that does not is not neutrality; it is avoidance.
And when more than two people are affected, a flip looks like one person's choice unless everyone watches it. The Wheel of Names is the better instrument when a group has to accept the outcome.
Streaks, and why the tally is interesting
Flip a coin twenty times and a run of four or five the same way is entirely normal - the chance of at least one run of five in twenty flips is around a quarter.
This is the gambler's fallacy in its purest form: after four heads, the fifth flip is still 50-50. The coin has no memory. Watching a running tally is a good way to feel how unevenly randomness actually distributes itself.
Common questions
Is the online flip truly random?
It uses the browser's random number generator - fair enough for any decision, not suitable for anything with money on it.
Who calls first?
Convention is that the person not flipping calls, which removes the only part either could influence.
Best of three?
Only if you decide so beforehand. Switching to best-of-three after losing is the oldest move in the book.
Got something to settle?