No. 39 · Risk · Statistics and Probability
Law of Large Numbers
Luck is wild in small samples and predictable in large ones.
In the Almanac
“Bernoulli’s golden theorem”, 1713 · “bet365”, 2000s
Both stories in full, three ways to use it and where it misleads.
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Questions
What is Law of Large Numbers?
The law of large numbers says that as a random process is repeated many times, the average result settles toward its true expected value. Small samples are noisy and can mislead, while large samples are reliable. It is why casinos and bookmakers profit steadily from small margins.
How do you use Law of Large Numbers?
To use it, be patient with early results, skeptical of single stories, and trust patterns built from many observations. But remember it does not mean a losing streak is due to end, and it cannot fix biased data.
When does Law of Large Numbers matter?
Law of Large Numbers is one of the 32 mental models for risk, the situations where you ask: What could go wrong, and what will I do if it does? Within that, it belongs to “Thinking in odds”, alongside Expected Value, Fat-Tailed Distributions and Foxes vs Hedgehogs.
What is an example of Law of Large Numbers?
Two stories show it at work: Bernoulli’s golden theorem (1713) and bet365 (2000s). Both are told in full in The Mental Models Daily Almanac, which has two stories for each of its 365 models.
Which mental models are related to Law of Large Numbers?
Loyalists vs Mercenaries, Regression to the Mean and Expected Value. Law of Large Numbers itself comes from statistics and probability.