Monte Carlo: 100k iteration simulation five times vs 500k iteration simulation once

Question

I am unknowledgeable about Monte Carlos. What would be the difference in the reliability/accuracy of the final expected value in a Monte Carlo simulation under the following two methods:

1) Run a 100k-iteration Monte Carlo simulation, five times over, get the average of each of the five simulations, and then take the average of the average of those five simulations
2) Run a 500k-iteration Monte Carlo once.

Presumably the second would be more accurate and reliable, but I am not sure how?

In: Mathematics

Answer 1

The simulations have a burn-in period – it takes a number of iterations for the distribution of the list of values it outputs to “forget” the simulation’s initial state and converge to the equilibrium distribution.

If you’re not discarding some of the initial iterations in each run, both 1) and 2) will be inaccurate – therefore 1) is more wasteful of iterations than 2) when you’re doing it right, in terms of finding the true average.