Flip a coin

Every flip on this page is decided by the browser's cryptographic random number generator before the coin starts turning. There is no account, no advertising, and nothing to install — and the result is one of exactly two things, at exactly even odds.

Which, as it turns out, is more than can be said for a real coin.

Is a coin flip really 50/50?

A real one is not, quite. A physics model published by Persi Diaconis, Susan Holmes and Richard Montgomery in 2007 predicted that a coin flipped by a human tends to land on the side it started on, because the coin wobbles about an axis that is not its axis of symmetry and so spends a little longer with its starting face upwards. In 2023 a team led by František Bartoš tested that prediction across 350,757 flips and found the same side came up 50.8% of the time, with a 95% credible interval of 50.6% to 50.9%. Note what is and is not biased: the pull is towards the side the coin started on, not towards heads. If you do not look at which way up the coin began, heads and tails are as even as makes no practical difference.

Sources: Persi Diaconis, Susan Holmes and Richard Montgomery, “Dynamical Bias in the Coin Toss”, SIAM Review 49(2), 2007, 211–235 (full text). František Bartoš and colleagues, “Fair coins tend to land on the same side they started: Evidence from 350,757 flips”, 2023, since peer-reviewed and published.

How does this coin decide?

The browser's cryptographic random number generator picks the face, with rejection sampling so that no outcome is favoured by rounding. That happens before anything moves: the flight is then solved backwards from the answer, so that the number of half-turns is whatever leaves the winning face upwards. Nothing is read off the end of a simulation, which means no dropped frame and no slow phone can change the result. It also means this coin has no starting-side bias to inherit, because it has no starting side.

Can I change what is on the coin?

Yes. The editor below takes any list, and the moment the two faces stop being Heads and Tails the page draws a wheel instead of a coin. That is deliberate rather than a limitation: a coin is an honest picture of one even choice between two things and of nothing else, so a third option, or odds that are not even, has to be drawn as slices where the geometry can show the real proportions.

Whatever you build travels in the link, so a coin renamed to Yes and No, or turned into a list of six names, can be shared by copying the address. The full wheel is at truewedge.app.