Coin flip guide
Is a Coin Flip Really 50/50?
A fair-coin model assigns half the probability to each side. It does not promise that every small batch balances.
Physical tossing is a different process
Diaconis, Holmes, and Montgomery studied coins flipped and caught in the hand. Their 2007 work found a tendency to return to the starting side under the studied conditions. This is not a universal claim that heads wins 51% of all tosses: starting orientation and procedure matter.
How this tool selects a side
The single flipper requests an unsigned 32-bit Web Crypto value: even values map to heads and odd values to tails. The simulator splits the 256 possible byte values into two equal groups. The animation displays the result; it does not simulate coin physics.
One unusual batch is not a verdict
For 100 fair flips, expected heads is 50 and the standard deviation is √(100 × 0.5 × 0.5) = 5. A count of 60 is two standard deviations above the mean. One unusual sample alone does not establish a biased generator.
Make a repeatable comparison
Choose the sample size in advance, record every result, and keep the method constant. Compare multiple batches rather than selecting surprising ones. Simulator exports preserve observations but do not certify a physical coin’s fairness.
Sources and further reading
- Dynamical Bias in the Coin Toss — Diaconis, Holmes and Montgomery (2007)
- Web Crypto getRandomValues — MDN
Worked examples use the independent fair-coin model unless a section explicitly discusses physical tossing.