Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the worl… - Didier Sornette

Indeed, the frequency of crashes in the Monte Carlo simulations was much smaller than the frequency of crashes in the real data: if one of the most frequently used benchmarks of the industry is incapable of reproducing the observed frequency of crashes, this indeed means that there is something to explain that may require new concepts and methods.

Profiting from being in the minority leads to interesting paradoxes. Rather diabolically, if all traders use the same set of rules, they will end up doing the same thing at the same time and cannot therefore be in the minority.

The problem is not that this optimistic view is wrong. By economic accounting, the optimistic view is mostly right.