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The law of large numbers says the observed relative frequency converges to the true probability as trials accumulate. The standard error √(p(1−p)/n) quantifies how fast: precision improves only as √n.
Standard error of a proportion
SE = √(p(1 − p)/n)
Trials for a tolerance
n = z²·p(1 − p) / tolerance²
The standard error is 0.0158, so the observed rate lands within 2 percentage points about 79.3% of the time.
No. The proportion converges but the absolute difference in counts typically grows — the gambler's fallacy confuses the two.