Flip a Coin 10,000 Times

Simulate 10,000 coin tosses in under 10 milliseconds. Re-create the historic 1940 John Kerrich probability experiment and observe tight Bernoulli convergence.

10,000 Flips Monte Carlo Engine

Simulate thousands of fair binary trials off the main thread with live Binomial Distribution analysis.

Trial Count:

👑Observed Heads

52.00% (Expected: 50.0%)

⚡Observed Tails

48.00% (Expected: 50.0%)

🔥Longest Streak

Consecutive Heads

⏱️Execution Latency

4ms

WebCrypto CSPRNG

Observed vs Theoretical Gaussian Bell Curve

Law of Large Numbers: As N → ∞, Observed Ratio → 0.500

The Historic 1940 John Kerrich 10,000-Flip Experiment

During World War II, South African mathematician John Edmund Kerrich was interned in a camp in Nazi-occupied Denmark. To demonstrate the Law of Large Numbers to fellow internees, Kerrich flipped a single coin 10,000 times by hand, manually recording the cumulative running totals:

Trial Milestone (N)	Observed Heads	Observed Heads %	Deviation from 50.0%
100 Flips	44	44.00%	-6.00%
500 Flips	255	51.00%	+1.00%
1,000 Flips	502	50.20%	+0.20%
2,000 Flips	1,013	50.65%	+0.65%
10,000 Flips (Final)	5,067	50.67%	+0.67% (1.34σ)

Kerrich's final result of 5,067 heads falls well within the expected 95% confidence interval ($\mu \pm 2\sigma = [4,900, 5,100]$), representing an empirical variance of $z = (5067 - 5000) / 50 = +1.34\sigma$.

Related Empirical Simulation Silos

100 Coin Toss Generator (Pillar) →Flip 1 Million Times →Is Coin Flip Actually 50/50? Research →

Frequently Asked Questions

What is John Kerrich's 10,000 coin toss experiment?

In 1940, while interned in Nazi-occupied Denmark during World War II, South African mathematician John Edmund Kerrich flipped a coin 10,000 times, meticulously recording 5,067 heads (50.67%) to prove the Law of Large Numbers empirically.

What is the expected standard deviation in 10,000 coin flips?

For 10,000 coin flips, the expected mean is μ = 5,000 Heads and the standard deviation is σ = √(10000 * 0.25) = 50 flips (0.50%). Approximately 99.73% of trials land between 4,850 and 5,150 heads.

What is the longest expected streak in 10,000 flips?

In 10,000 tosses, the longest consecutive run of identical outcomes (all Heads or all Tails) is expected to be approximately log2(10000) ≈ 13 to 15 consecutive flips.