See the Law of Large Numbers in action. Run 1,000 coin flips instantly and watch the result converge toward 50/50. Includes streak analysis and deviation stats — the most complete coin flip simulator for statistics class.
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One thousand flips is where the Law of Large Numbers becomes impossible to ignore. With 10 flips, a result of 70% heads might seem suspicious; with 100 flips, you're reliably within 10% of 50%; but at 1,000 flips, your result almost always settles within 3–4% of exactly 50%. The convergence is visually striking — run this tool a few times and you'll notice the percentage barely moves between runs. This is the clearest demonstration of why probability predictions grow more reliable with larger samples.
After each run, the streak panel shows the longest consecutive heads run and the longest consecutive tails run. At 1,000 flips, a streak of 10 or more is expected in over 99% of runs — it is virtually guaranteed. A streak of 13 appears in roughly half of all 1,000-flip sequences. This is one of the most counterintuitive findings in probability: the larger your sample, the longer the streaks you should expect, even though the overall percentage stays near 50%. If you see a streak of 10 or 11, that's not a sign of a biased coin — it's exactly what mathematics predicts.
With 1,000 flips, the expected deviation follows a binomial distribution with standard deviation σ = √(1000 × 0.5 × 0.5) ≈ 15.8. In practice: getting 484–516 heads is within 1 standard deviation (68% of runs), getting 468–532 heads is within 2 standard deviations (95% of runs), and landing outside the 468–532 range is statistically notable and occurs only about 5% of the time. The summary line after each run tells you whether your result was "very close to 50/50," "within normal range," or a "notable deviation."
At 1,000 flips, classroom demonstrations become powerfully convincing. For a Law of Large Numbers lesson, have each student run one trial — all results will cluster tightly around 50%, making the theorem concrete rather than abstract. For a streak analysis lesson, ask students to predict the longest streak before running and compare to the actual result — nearly everyone underestimates. For a standard deviation exercise, collect all students' heads counts and calculate the mean and spread; with 1,000-flip data, the measured SD will closely match the theoretical σ ≈ 15.8 with even a small class. The density of the chip grid also gives a vivid visual sense of how H and T interleave in a truly random sequence.