Coin Flip

Features

• Single animated flip or bulk flipping
• Custom labels instead of heads and tails
• Running tally with a visual distribution bar
• Up to 10,000 flips at once
• Cryptographically fair

How to use it

1. Press Flip for a single toss.
2. Set a count and flip many at once.
3. Rename the sides if you are deciding between two options.
4. Watch the split converge as the count rises.

Why a real coin is not quite fifty-fifty

A physical coin toss is not perfectly fair, and the deviation has been measured. Persi Diaconis and colleagues at Stanford showed that a coin caught in the hand lands the same way it started about 51% of the time, because the coin precesses about an axis rather than flipping cleanly. A 2023 study with 350,757 recorded flips confirmed the effect at almost exactly the predicted rate. A coin allowed to bounce on a surface behaves differently again, since the bounce introduces chaotic dynamics.

This simulation has no such bias. Each flip draws from the operating system's cryptographic entropy pool with rejection sampling, so the two outcomes are exactly equally likely and each flip is independent of the last.

That independence is the thing people find hardest to accept. After eight heads in a row, the ninth flip is still exactly fifty-fifty, the coin has no memory. The gambler's fallacy is the belief that a run must be corrected; the equally wrong hot-hand version is the belief that a run will continue. What actually happens is that the proportion converges toward 50% as the count grows, while the absolute difference between heads and tails typically drifts further from zero. Flip a thousand times here and you will usually see something close to 50% alongside a gap of twenty or thirty flips.