34 Heads in a Row on a Fair Coin
The chance of 34 heads in a row on a fair coin is 5.82 × 10-9%, or 1 in 17.18 billion. 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 34 in a row is 0.5 multiplied by itself 34 times.
The odds of 34 in a row
| Measure | Value |
|---|---|
| Chance of 34 heads from a given flip | 5.82 × 10-9% |
| Odds | 1 in 17.18 billion |
| Flips to wait for it, on average | 34.36 billion |
| Chance of 34 heads OR 34 tails starting on a given flip | 1.16 × 10-8% |
| Chance a run of 34 appears at least once in 100 flips | 1.98 × 10-7% |
| Chance a run of 34 appears at least once in 1,000 flips | 2.82 × 10-6% |
| Chance a run of 34 appears at least once in 10,000 flips | 2.9 × 10-5% |
| Chance a run of 34 appears at least once in 100,000 flips | 2.91 × 10-4% |
Why it is likelier than it feels
A run of 34 on one chosen flip is 1 in 17.18 billion, yet across 1,000 flips there is a 2.82 × 10-6% 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 34 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.