Law of Large Numbers
Version 1.0.0 · Updated 2026-07-30
CORE DEFINITION
When the number of trials is sufficiently large, the frequency of an event will approach its theoretical probability infinitely closely. -
SCAFFOLDING EFFECT
Reduce cognitive load
The mathematical guarantee of long-termism. - Why isn't the casino afraid of you winning? Because under the law of large numbers, as long as you play long enough, the casino's slight mathematical advantage (House Edge) will inevitably wash away your money. Conversely, for an individual, if you have a system with positive expected value (such as value investing, doing the right thing), all you need to do is "increase the number of attempts" to let the law of large numbers take effect and smooth out the fluctuations of luck.
Anchor fast decisions
In independent repeated trials, the sample mean converges in probability to the expected value as the number of trials increases. The mechanism is that random fluctuations are "averaged out" by a large number of repetitions, and the frequency tends to a stable probability.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Law_of_large_numbersverified
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