The Law of Large Numbers
beginner 2 Min. LesezeitAktualisiert 21.6.2026
Why long simulations stabilize while short sessions stay noisy.
Why long simulations stabilize while short sessions stay noisy.
Averages need repetition
Expected percentages describe repeated trials. The gap between observation and expectation is often large at first and usually narrows as trials accumulate.
Convergence is not compensation
A long-run average does not force the next outcome to repair an earlier streak. New independent trials retain their original probability.
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Key takeaways
- Large samples reveal underlying averages more clearly.
- Convergence does not make an outcome due.
- Short sessions can remain far from the expected value.
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