Coin Flip Streaks: Odds of Heads in a Row
A fair coin lands heads half the time, so a run of N heads has a chance of 0.5 to the power of N. Here is every length.
| Streak | Chance | Odds |
|---|---|---|
| 2 in a row | 25% | 1 in 4 |
| 3 in a row | 12.5% | 1 in 8 |
| 4 in a row | 6.25% | 1 in 16 |
| 5 in a row | 3.125% | 1 in 32 |
| 6 in a row | 1.563% | 1 in 64 |
| 7 in a row | 0.7813% | 1 in 128 |
| 8 in a row | 0.3906% | 1 in 256 |
| 9 in a row | 0.1953% | 1 in 512 |
| 10 in a row | 0.0977% | 1 in 1,024 |
| 11 in a row | 0.0488% | 1 in 2,048 |
| 12 in a row | 0.0244% | 1 in 4,096 |
| 13 in a row | 0.0122% | 1 in 8,192 |
| 14 in a row | 6.1 × 10-3% | 1 in 16,384 |
| 15 in a row | 3.05 × 10-3% | 1 in 32,768 |
| 16 in a row | 1.53 × 10-3% | 1 in 65,536 |
| 17 in a row | 7.63 × 10-4% | 1 in 131,072 |
| 18 in a row | 3.81 × 10-4% | 1 in 262,144 |
| 19 in a row | 1.91 × 10-4% | 1 in 524,288 |
| 20 in a row | 9.54 × 10-5% | 1 in 1.05 million |
| 21 in a row | 4.77 × 10-5% | 1 in 2.1 million |
| 22 in a row | 2.38 × 10-5% | 1 in 4.19 million |
| 23 in a row | 1.19 × 10-5% | 1 in 8.39 million |
| 24 in a row | 5.96 × 10-6% | 1 in 16.78 million |
| 25 in a row | 2.98 × 10-6% | 1 in 33.55 million |
| 26 in a row | 1.49 × 10-6% | 1 in 67.11 million |
| 27 in a row | 7.45 × 10-7% | 1 in 134.22 million |
| 28 in a row | 3.73 × 10-7% | 1 in 268.44 million |
| 29 in a row | 1.86 × 10-7% | 1 in 536.87 million |
| 30 in a row | 9.31 × 10-8% | 1 in 1.07 billion |
| 31 in a row | 4.66 × 10-8% | 1 in 2.15 billion |
| 32 in a row | 2.33 × 10-8% | 1 in 4.29 billion |
| 33 in a row | 1.16 × 10-8% | 1 in 8.59 billion |
| 34 in a row | 5.82 × 10-9% | 1 in 17.18 billion |
| 35 in a row | 2.91 × 10-9% | 1 in 34.36 billion |
| 36 in a row | 1.46 × 10-9% | 1 in 68.72 billion |
| 37 in a row | 7.28 × 10-10% | 1 in 137.44 billion |
| 38 in a row | 3.64 × 10-10% | 1 in 274.88 billion |
| 39 in a row | 1.82 × 10-10% | 1 in 549.76 billion |
| 40 in a row | 9.09 × 10-11% | 1 in 1.1 trillion |
| 41 in a row | 4.55 × 10-11% | 1 in 2.2 trillion |
| 42 in a row | 2.27 × 10-11% | 1 in 4.4 trillion |
| 43 in a row | 1.14 × 10-11% | 1 in 8.8 trillion |
| 44 in a row | 5.68 × 10-12% | 1 in 17.59 trillion |
| 45 in a row | 2.84 × 10-12% | 1 in 35.18 trillion |
| 46 in a row | 1.42 × 10-12% | 1 in 70.37 trillion |
| 47 in a row | 7.11 × 10-13% | 1 in 140.74 trillion |
| 48 in a row | 3.55 × 10-13% | 1 in 281.47 trillion |
| 49 in a row | 1.78 × 10-13% | 1 in 562.95 trillion |
| 50 in a row | 8.88 × 10-14% | 1 in 1.13 × 1015 |
| 51 in a row | 4.44 × 10-14% | 1 in 2.25 × 1015 |
| 52 in a row | 2.22 × 10-14% | 1 in 4.5 × 1015 |
| 53 in a row | 1.11 × 10-14% | 1 in 9.01 × 1015 |
| 54 in a row | 5.55 × 10-15% | 1 in 1.8 × 1016 |
| 55 in a row | 2.78 × 10-15% | 1 in 3.6 × 1016 |
| 56 in a row | 1.39 × 10-15% | 1 in 7.21 × 1016 |
| 57 in a row | 6.94 × 10-16% | 1 in 1.44 × 1017 |
| 58 in a row | 3.47 × 10-16% | 1 in 2.88 × 1017 |
| 59 in a row | 1.73 × 10-16% | 1 in 5.76 × 1017 |
| 60 in a row | 8.67 × 10-17% | 1 in 1.15 × 1018 |
Every spin can be checked. The roll for each Wheel spin comes from an HMAC of a server seed committed in advance, your client seed and a nonce, so the result cannot be chosen after you bet. How to check one is on the provably fair page.