4 Heads in a Row on a Fair Coin
The chance of 4 heads in a row on a fair coin is 6.25%, or 1 in 16. Tails is exactly the same, and so is a run of any one side you pick in advance: each flip is a 50% chance, so 4 in a row is 0.5 multiplied by itself 4 times.
The odds of 4 in a row
| Measure | Value |
|---|---|
| Chance of 4 heads from a given flip | 6.25% |
| Odds | 1 in 16 |
| Flips to wait for it, on average | 30 |
| Chance of 4 heads OR 4 tails starting on a given flip | 12.5% |
| Chance a run of 4 appears at least once in 100 flips | 97.27% |
| Chance a run of 4 appears at least once in 1,000 flips | 99.9%+ |
| Chance a run of 4 appears at least once in 10,000 flips | 99.9%+ |
| Chance a run of 4 appears at least once in 100,000 flips | 99.9%+ |
Why it is likelier than it feels
A run of 4 on one chosen flip is 1 in 16, yet across 1,000 flips there is a 99.9%+ chance one turns up somewhere. People judge a streak against a single starting point, but a long sequence gives it thousands of starting points. That is also why streaks in a real record of flips look suspicious to anyone who does not expect them, and why a sequence with no streaks at all looks more made-up than one that has them.
Does a streak change the next flip?
No. After 4 heads the next flip is still 50% heads and 50% tails. A fair coin has no memory, and on Cryptoflip every game's result comes from a provably fair roll that was committed to before anyone joined. Expecting the streak to "break" is the gambler's fallacy, and expecting it to continue is the hot-hand fallacy.
In Original, our player-versus-player coin flip, a game is a straight 50/50 and the winner takes the pot minus a 5% fee. See how a result is verified.