πͺ Coin Flip
Flip a fair digital coin
Statistics
The Science of Coin Flips
Understand the gambler's fallacy, law of large numbers, and why streaks don't predict future outcomes.
Learn MoreAbout Coin Flips
A coin flip is one of the simplest forms of randomization with exactly two equally likely outcomes. Each flip is independent, meaning previous results don't affect future flips.
Probability
Every flip has a 50% chance of landing on heads and a 50% chance of landing on tails, regardless of previous results. The probability remains constant:
- P(Heads) = 1/2 = 0.5 = 50%
- P(Tails) = 1/2 = 0.5 = 50%
- P(Same result twice) = 1/4 = 0.25 = 25%
- P(Same result 10 times) = (1/2)^10 β 0.098%
The Gambler's Fallacy
Many people incorrectly believe that after several heads in a row, tails is "due" to appear. This is false! Each flip is independent, and the coin has no memory of previous results. A streak of 10 heads doesn't make tails any more likely on flip #11.
Law of Large Numbers
While each individual flip is unpredictable, over many flips the ratio of heads to tails will approach 50/50. Try flipping 100 times to see this principle in action!