Law of Large Numbers

The law of large numbers describes the phenomenon, that performing the same experiment for a large number of runs will let the average outcome converge to the expected outcome.

This is a fallacy for most processes in the modern world, though. Modernity is exposing us to fat-tailed distributions wherever we look. In the realm of fat-tails, the risk-reward of a distribution is heavily dependent on the singular outcome of the distribution. (See Black Swan )

The fat-tailed distribution will produce a number of non-relevant examples with every run, and the mean will not reflect the full effect of the function.

In a non-modern world, with n large, the mean will approach the average quickly. In modernity, the mean will only reflect the full effect of the outcome, after the Black Swan has happened, and thus everything before will be statistically insignificant.