Simulate 1,000 independent coin tosses in milliseconds. Test central limit convergence, examine 10-flip streaks, and analyze statistical variance.
Simulate thousands of fair binary trials off the main thread with live Binomial Distribution analysis.
At $N = 1,000$, the discrete binomial distribution closely matches the continuous normal distribution $N(\mu = 500, \sigma^2 = 250)$:
μ = 1000 · 0.5 = 500 | σ = √(1000 · 0.5 · 0.5) ≈ 15.811388 Flips (1.58%)Historical comparison: French naturalist Comte de Buffon (1777) tossed a coin 4,040 times to record 2,048 heads (50.69%), mirroring the exact variance predicted by our 1,000-flip Gaussian model.
In 1,000 fair coin tosses, the theoretical expected mean is μ = 500 Heads (50.0%). The standard deviation is σ = √(1000 * 0.25) ≈ 15.811 flips.
In 95.45% of 1,000-flip trials, the observed heads count will land between 468 and 532 heads (46.8% to 53.2%). In 99.73% of trials, it will fall between 453 and 547 heads.
In 1,000 flips, the longest expected consecutive run of heads or tails is approximately log2(1000) ≈ 9.97 (about 9 to 11 in a row).
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