Let the observations accumulate.
For independent tosses with the same success probability, the observed proportion becomes increasingly likely to lie near that probability as the sample grows.
Inside this model
Each seeded uniform draw is counted as heads when it is below p. The curve shows cumulative heads divided by toss count, with a horizontal reference at p. Absolute counts can drift even as proportions stabilize.
Out in the world
A practical use
Estimate a product defect rate from a larger representative sample. More data reduces sampling noise, but it cannot repair a biased sampling process.
A useful lens. Not a universal law.
- The next toss never compensates for previous tosses. The displayed path need not approach its target monotonically. Dependence and changing probabilities require different assumptions.
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.
Grinstead & Snell — Introduction to Probability, Chapter 8 ↗