The law of large numbers (LLN) states that the average of the outcomes from a large number of independent random samples converges to the expected value. For example, if we flip a fair dice 100,000 times, the result should be closer to 0.5 than if we flip the dice 10 times on average.

More formally, the LLN states that given a sample of independent and identically distributed values, the sample mean converges to the population mean. 1

Note that the LLN only applies to the sample mean. It does not claim that the sample sum gets close to the when increase.

Footnotes

  1. Law of large numbers - Wikipedia