Coin Flip

The coin needs no setup. The only setting is how many coins to flip with one press.

1. Leave Coins to flip at 1 for a single decision, or type a whole number from 1 to 1,000 to flip a batch in one go.
2. Press Flip the coin, click the coin itself, or press the Space bar. The coin spins for a second or so.
3. Read the result under the coin. One flip reads Heads or Tails. A batch reads something like 529 heads and 471 tails, and the coin comes to rest showing the last flip of the batch.
4. Check the tally: Heads, Tails, Flips and Heads share. The totals keep growing from press to press until you choose Reset tally.
5. Look at the strip of H and T dots, which shows up to the last 60 results in order, so you can see runs as they happen.

Agree what heads and tails mean before you flip, for example heads means the first option. Nothing is saved, so refreshing the page starts again from zero.

Each flip asks the browser's secure random number generator for a number, then uses rejection sampling, which discards any value that would favor one outcome. The result is exactly 50 percent heads and 50 percent tails, and every flip is independent. The coin has no memory of what came before.

Independence is why streaks are normal. For any chosen run of flips, the chance of all heads is one half multiplied by itself once per flip:

Those odds describe one particular stretch. Over a long session a run is likely somewhere: across 100 flips there is about an 81 percent chance of at least one run of five or more heads, and about a 97 percent chance of a run of five or more of the same side.

Large batches show the law of large numbers. Flip 1,000 coins and you expect 500 heads, with a standard deviation of about 16 (the square root of 1,000 x 0.5 x 0.5). About 70 percent of batches land between 484 and 516 heads, and about 96 percent between 468 and 532. Exactly 500 heads happens only about 2.5 percent of the time. A batch of 529 heads and 471 tails is 29 away from even, which turns up in roughly 7 percent of batches, so it is not evidence of a rigged coin.

The classic mistake is the gambler's fallacy: believing that after five heads, tails is due. It is not. The next flip is 50 percent, exactly as it was before. The opposite mistake is reading a short run as proof of bias. After only 10 flips, seven or more heads happens about 17 percent of the time with a perfectly fair coin, so watch the Heads share swing widely at first and settle only as the flips pile up. Even then the raw gap between heads and tails tends to grow while the share narrows toward 50 percent.

• Choose what each side means first, then flip once. Re-flipping until you like the answer defeats the purpose.
• For three or more options, use the wheel spinner or the random choice picker. For a number from 1 to 6, use the dice roller, and for any other range the random number generator.
• To turn a tally into a share of a larger total, the percentage calculator does the arithmetic.

Be honest about the limits. It is a fair coin only, with no option to bias it, and nothing is saved or shareable. It leaves no audit trail, so it is not suitable for settling a contest with real stakes or for gambling outcomes with money on a regulated platform. It suits kick-offs, turn order, tie-breaks and everyday decisions between two choices.