Coin Flip — Heads or Tails

About the Coin Flip — Heads or Tails

Press Flip and the coin spins and lands on heads or tails. The side is chosen by your browser’s cryptographically secure random number generator before the animation starts, so the animation only shows a result that is already fixed — every flip is exactly 50/50 and has nothing to do with the flips before it.

Flip one coin, many coins at once (up to 1,000, with the count of each side and the longest run), or play a best of 3, 5 or 7 match. You can name the sides (heads = Asha, tails = Ravi), call a side before the flip, and keep a running tally with your current and longest streak. A streak calculator then shows how likely a streak really is — usually much more likely than it feels.

Common uses

• Settling a decision or choosing who starts a game, match or turn.
• Classroom probability lessons: run 1,000 flips and compare the share of heads with 50%.
• Showing why streaks are normal (the gambler’s fallacy) with exact numbers.
• Quick yes/no choices — for more than two options use the random generator.

How fair is the flip?

The result comes from crypto.getRandomValues, the Web Crypto API’s cryptographically secure generator, through the same engine as the random generator: a random 32-bit number is drawn and its lowest bit decides the side, which splits the 4,294,967,296 possible numbers exactly in half. The animation starts only after the side is known and always lands on it, so a fast or slow device cannot change the outcome. With Reduce motion turned on in your system settings, the coin does not spin at all.

A real coin is very close to fair, but not perfectly: in a 2023 study of 350,757 hand flips, coins landed on the side they started on 50.8% of the time (Bartoš et al., arXiv:2310.04153). This virtual coin has no starting side.

The maths of streaks

Each flip is independent, so the chance of a specific sequence of k flips is 1 ÷ 2^k: five heads in a row from the next five flips is 1 in 32 (3.125%), and five of the same side (all heads or all tails) is 1 in 16. After four heads, the next flip is still 50/50 — believing a tail is "due" is the gambler’s fallacy.

Over many flips, a streak somewhere becomes likely. The calculator counts exactly how many sequences of n flips contain a run of at least k: for one named side it uses the recurrence s(m) = s(m−1)/2 + s(m−2)/4 + … + s(m−k)/2^k for the chance of no run, and for either side the number of ways to split n into runs shorter than k. For example:

• 10 flips: at least 3 heads in a row — 50.8%; 3 of the same side — 82.6%
• 100 flips: at least 5 heads in a row — 81.0%; 6 of the same side — 80.7%; 8 of the same side — 31.5%
• 1,000 flips: 10 of the same side in a row — 62.4%

Best of 3, 5 or 7

A best-of-N match is won by the first side to take more than half of the N flips: 2 of 3, 3 of 5 or 4 of 7. It stops as soon as that happens, so a best of 7 can be over after 4 flips. With a fair coin both sides have the same 50% chance of winning the match, however many flips it lasts.

Limitations

• This is for games and everyday decisions, not for regulated draws, gambling or legal procedures that require a certified random source.
• Many coins: up to 1,000 per flip; the first 100 are drawn, the rest are listed as H and T.
• The tally and its history (the last 200 flips) are saved in this browser only; clearing site data removes them.

Privacy

Everything happens in your browser. Your tally, side names and settings are saved in this browser only so they are still there next time; nothing is uploaded.