Coin Flip

The Coin Flip is the simplest decision-making “game” — flip a coin, get heads or tails, each with 50% probability. Used for decisions, gambling, and statistical demonstrations for centuries. Despite its simplicity, the coin flip has been studied extensively: real coins aren’t perfectly fair, and famous “fair coin” assumptions in math and stats often hide subtle biases.

How to play

• Click “Flip Coin”, click the coin itself or press Space to flip.
• Result: Heads or Tails. Each 50% probability.
• Pick 10, 100 or 1000 flips from the menu to run a batch instantly.
• The counters show total flips, heads, tails, your current streak and your longest streak, plus the heads/tails percentages and your last 30 results. Totals are saved in your browser until you press Reset.
• Use for: decisions, statistical demonstrations, simple games. Over many flips the split should approach 50/50.

The probability

• Each flip is independent. Previous results don’t influence the next.
• Law of large numbers: over many flips, the ratio approaches 50/50.
• Short-term variance: 10 flips might give 7 heads / 3 tails. Doesn’t mean the coin is biased.
• Real coins: physical coins have slight biases. Studies of real tosses found a coin lands the same way up as it started about 51% of the time.
• Spinning vs flipping: spinning a real coin on a table has stronger biases than flipping.

The Gambler’s Fallacy

The Gambler’s Fallacy is the false belief that past outcomes influence future independent events. “I’ve flipped 5 heads in a row, so tails is due.” Probability has NO memory — the next flip is 50/50 regardless of history. This fallacy costs many gamblers their money.

FAQ

• Q: Is a coin flip truly 50/50? A: Theoretically yes for an ideal coin. Real coins have slight biases.
• Q: What’s the chance of 10 heads in a row? A: 0.5^10 = 1/1024. About 0.1%.
• Q: Can I predict the result? A: No — each flip is independent.
• Q: What’s the gambler’s fallacy? A: Believing past flips influence future ones. They don’t.

For other simple games, try Higher Lower, Rock Paper Scissors, Farkle, or Slot Machine.