Law of large numbers simulator
Choose an experiment, trial count and seed. The chart tracks the running mean from the first to final observation.
Running mean
The line shows the mean after successive trials; the reference level is the expected value.
Convergence checkpoints
| Trials n | Running mean | Absolute error |
|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||
How to use this page
- Choose Bernoulli trials or a die.
- Set the number of trials and optionally change the seed.
- Compare the running mean with the expected value.
What this page does not do: The simulator uses a deterministic pseudo-random generator for learning. It is not a lottery number source or a cryptographic tool.
Further reading
The law of large numbers says that for independent identically distributed trials, the sample mean approaches the expected value as n grows. The path need not be smooth or monotone.
The seed reproduces the exact simulation. Change it to see natural variation among runs.
Frequently asked questions
Does the mean always move closer?
Not at every step. The law describes limiting behaviour, so deviation may temporarily increase.
What is the seed for?
It initializes the generator. The same seed and settings produce the same sequence.
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.