40 Heads in a Row on a Fair Coin
The chance of 40 heads in a row on a fair coin is 9.09 × 10-11%, or 1 in 1.1 trillion. 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 40 in a row is 0.5 multiplied by itself 40 times.
The odds of 40 in a row
| Measure | Value |
|---|---|
| Chance of 40 heads from a given flip | 9.09 × 10-11% |
| Odds | 1 in 1.1 trillion |
| Flips to wait for it, on average | 2.2 trillion |
| Chance of 40 heads OR 40 tails starting on a given flip | 1.82 × 10-10% |
| Chance a run of 40 appears at least once in 100 flips | 2.82 × 10-9% |
| Chance a run of 40 appears at least once in 1,000 flips | 4.37 × 10-8% |
| Chance a run of 40 appears at least once in 10,000 flips | 4.53 × 10-7% |
| Chance a run of 40 appears at least once in 100,000 flips | 4.55 × 10-6% |
Why it is likelier than it feels
A run of 40 on one chosen flip is 1 in 1.1 trillion, yet across 1,000 flips there is a 4.37 × 10-8% 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 40 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.