Is a coin flip 50/50?
A fair coin has two equally likely sides, so heads and tails each have a 1 in 2 chance. Flip it many times and the share of heads gets closer and closer to half: Karl Pearson once tossed a coin 24,000 times and got 12,012 heads. Short runs can still look lopsided: flip 10 coins a few times and watch the tally.
Real coins flipped by hand have a small quirk: in a study of 350,757 flips, they landed on the side that started face up 50.8% of the time. The coin here has no starting side, so it stays exactly 50/50.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗OpenStax · Introductory Statistics 2e, 4.2 Mean or Expected Value ↗arXiv · Bartoš et al., Fair coins tend to land on the same side they started (2023) ↗
How to calculate the odds of a coin flip
Each flip is independent: one coin doesn’t change another. So the chance of all heads is 1/2 multiplied once for every coin.
Here it is with your numbers:
- P = 1 ÷ 2
- P = 50%
It means one coin lands heads half the time: a 1 in 2 chance.
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
Coin flip odds: heads in a row
| Heads in a row | Chance | 1 in |
|---|---|---|
| 1 | 50% | 2 |
| 2 | 25% | 4 |
| 3 | 12.5% | 8 |
| 4 | 6.25% | 16 |
| 5 | 3.125% | 32 |
| 6 | 1.5625% | 64 |
| 7 | 0.7813% | 128 |
| 8 | 0.3906% | 256 |
| 9 | 0.1953% | 512 |
| 10 | 0.0977% | 1,024 |
| 20 | 9.5367 × 10⁻⁵% | 1,048,576 |
How this coin flip works
Your browser has a built-in random number generator for security: a cryptographically strong generator seeded with truly random values. Each coin takes one random bit from it: 0 is heads, 1 is tails. Nothing is decided in advance or on our server, and nothing is sent anywhere.
Source W3C · Web Cryptography Level 2, the Crypto interface ↗
FAQs
Is a coin flip actually 51/49?
For a real coin flipped by hand, slightly. In a 2023 study of 350,757 flips, coins landed on the same side they started 50.8% of the time. Heads and tails still came up equally often (50.0% heads), because which side started up was random. The coin on this page has no starting side: it is exactly 50/50.
Source arXiv · Bartoš et al., Fair coins tend to land on the same side they started (2023) ↗
Is a coin flip actually fair?
This one is. Each coin is one random bit from your browser’s cryptographically strong random number generator, the same kind used for security: 0 is heads and 1 is tails, so each side has exactly a 1 in 2 chance.
Source W3C · Web Cryptography Level 2, the Crypto interface ↗
What is the probability of getting 3 heads in 3 tosses?
1 in 8, which is 12.5%. Each toss is heads half the time and the tosses don’t affect each other, so multiply: 1/2 × 1/2 × 1/2 = 1/8.
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
What’s the chance of flipping heads 5 times in a row?
1 in 32, which is 3.125%. And after 5 heads in a row, the next flip is still 50/50: the coin doesn’t remember.
How rare is it to get heads 1000 times in a row?
The chance is 1 in 2¹⁰⁰⁰, a number 302 digits long: 9.3326 × 10⁻³⁰⁰%. Type 1,000 coins into the box above to see the steps.
Sources
- arXiv: Bartoš et al., Fair coins tend to land on the same side they started (2023)
- OpenStax: Introductory Statistics 2e, 3.1 Terminology
- OpenStax: Introductory Statistics 2e, 3.3 Two Basic Rules of Probability
- OpenStax: Introductory Statistics 2e, 4.2 Mean or Expected Value
- W3C: Web Cryptography Level 2, the Crypto interface