Coin Flip and Probability Mathematics
Coin flipping is one of the simplest ways to make a decision, and people have used it for thousands of years. Known in ancient Rome as "navia aut caput" (ship or head), it is now one of the basic examples in probability theory.
Theoretical Probability: 50/50?
For an ideal coin, the probability of heads on any flip is exactly ½, or 50%. Real coins are not perfectly symmetrical, though; Stanford University research found that physical coin flips land on the face they started on about 51% of the time. This small bias is why a digital simulator gives fairer results.
The Law of Large Numbers
Whether a single flip lands heads or tails is completely unpredictable. But as the number of flips grows, results move toward 50%; statistics calls this the law of large numbers. Getting 8 tails in 10 flips is normal, but 10,000 flips give roughly 4,900–5,100 tails. To look at this more closely, use the standard deviation calculator.
Is the Simulator Different from a Real Coin Flip?
The browser simulator uses JavaScript's Math.random() function. It is not cryptographic, but its results are unpredictable enough for everyday use. It works well for choosing between two options, deciding who goes first or learning about probability. If you need more options, use the random number generator.