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Sometimes you just need a fair 50/50 random decision. Our coin flipper provides cryptographically-seeded randomness (not pseudorandom), supports multi-flip sequences for probability demos, lets you flip biased coins (custom probabilities), and tracks heads/tails streaks for statistics education.

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À propos de Coin Flip Simulator

Sometimes you just need a fair 50/50 random decision. Our coin flipper provides cryptographically-seeded randomness (not pseudorandom), supports multi-flip sequences for probability demos, lets you flip biased coins (custom probabilities), and tracks heads/tails streaks for statistics education.

Comment l'utiliser

  1. Click "Flip" for a single coin flip.
  2. Enter a number to flip multiple coins at once (up to 10,000).
  3. Set a custom probability for a biased coin experiment.
  4. View the running tally, longest streak, and probability distribution chart.

Formule et méthodologie

Fair coin: P(heads) = P(tails) = 0.5. Expected runs in n flips: (n+1)/2 ≈ n/2. Probability of k heads in n flips: C(n,k) × 0.5^n (binomial distribution). Expected longest streak in n flips: log₂(n) ≈ 10 heads in a row in 1,000 flips is not unusual. Law of large numbers: as n→∞, proportion→0.5.

Cas d'usage courants

  • Decision-making: tie-breaking between two equal options
  • Probability education: demonstrating the law of large numbers
  • Gamble simulations: seeing how streaks and variance play out over many flips
  • Sports: virtual coin toss for kickoff, batting order, or possession
  • Fair assignment: randomly assigning tasks, teams, or roles

Questions fréquentes

Physical coins are very close to 50/50 but not perfectly so. Stanford researchers found that coins land on the same side they started on about 51% of the time due to slight wobble during the flip. Heads/tails bias due to design weight is negligible (0.01% at most). Digital coin flippers using cryptographic random number generators are closer to true 50/50 than physical coins.
No — this is the gambler's fallacy. Each flip is independent; the coin has no memory. The probability of tails on the 11th flip is still 50%. However, the probability of 10 heads in a row occurring at all is 1/1024 ≈ 0.1% — which makes you question whether the coin is fair. If you see 10 heads in a row on a real coin, statistically suspect bias; but the next individual flip is still 50/50.

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