Two outcomes, decided by one bit
For each coin the tool draws a 32-bit unsigned integer and reads its parity: even means Heads, odd means Tails. Because 232 is even, exactly half of the possible values fall on each side, so there is no modulo bias at all. A single flip shows a gold disc with the result. When you ask for 2 to 1,000 coins, the page switches to a summary of Heads, Tails and a Heads % figure that is rounded to a whole number. The individual order of the flips is not listed, only the counts.
What 100 or 1,000 flips should look like
Fair coins do not split exactly 50/50. The spread of the head count has a standard deviation of sqrt(n) / 2. Roughly 95% of the time the count lands within two standard deviations of half.
| Flips | Std. deviation (heads) | Typical 95% range |
|---|---|---|
| 10 | 1.6 | 2 to 8 heads |
| 100 | 5 | 40 to 60 heads (40% to 60%) |
| 1,000 | 15.8 | about 468 to 532 heads (47% to 53%) |
A result of 54% heads from 100 flips is therefore unremarkable, while 54% from 1,000 flips happens only about once in a hundred tries. The percentage converges toward 50 as the count grows, but the raw difference between heads and tails actually tends to grow, which is a frequent source of confusion in classroom demonstrations.
Streaks are normal
People expect a fair sequence to alternate, and genuinely random runs look suspiciously streaky. The chance that a specific set of 10 flips is all heads is 1 in 1,024. But the chance that 100 flips contain a run of 6 or more of the same face (either side) is about 81%, a run of 7 or more is about 54%, and a run of 8 or more is about 31%. The expected longest run in 100 flips is close to 7. In 1,000 flips it is about 10, and a run of 10 or longer shows up around 62% of the time.
Common mistakes
- The gambler's fallacy: after five heads the next flip is still 50/50.
- Flipping until you like the answer. If a decision matters, agree on the rule first, such as "heads means yes", then flip once.
- Using a coin for three or more options. Use a dice roller for up to 20 outcomes, or the random picker to choose among named entries.