# What property must a RNG have to be used in Monte Carlo simulations?

For example, every cryptographically secure pseudo-random number generator (CSPRNG) is required to satisfy the next-bit test and withstand "state compromise extensions". This makes me wonder what properties must a RNG have to be used in a Monte Carlo simulation.

It appears that most people just use runif or sample.int in R, but are they really good enough? Please note that I expect the answer to be language-agnostic, as I might switch to C, Clojure or even SQL at some time.

I find this question interesting because such a RNG must be random enough to produce quality result, and at the same time not as CPU-expensive as CSPRNGs due to performance concerns.

• In addition to Xi'an's observations, you might have a glance at section 4.2 of this paper. – pjs Mar 10 at 23:54

$$\qquad\qquad$$