Coin Flipper
A coin flipper simulates a fair coin toss with 50% probability of heads or tails. Despite the simplicity, coin flipping is the foundation of binary decisions, probability theory, and cryptographic key generation.
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Tip: The Law of Large Numbers guarantees heads and tails even out over many flips — but NOT that they "must" even out soon. After 10 heads in a row, the next flip is still exactly 50/50.
- 1Each flip is independent — previous results do not affect future flips
- 2P(heads) = P(tails) = 0.5 (50%) for a fair coin
- 3Expected number of heads in n flips: n/2
- 4The longest known streak of heads on record: 10 consecutive heads occurs on average every 1,024 flips
| Streak length | Probability | Expected frequency |
|---|---|---|
| 2 heads | 25% | Every 4 flips |
| 5 heads | 3.125% | Every 32 flips |
| 10 heads | 0.098% | Every 1,024 flips |
| 20 heads | 0.000095% | Every ~1 million flips |
| 30 heads | 9.3 × 10⁻¹⁰% | Every ~1 billion flips |
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Fun Fact
A real coin flip is not perfectly fair — the side facing up before the toss lands face-up slightly more than 50% of the time (~50.8%) due to the physics of angular momentum. Professional statisticians use this when it matters.
References
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