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

Both methods 1 and 2 produce an estimate with the same mean and same variance, i.e., both estimates are equally reliable. You can see this through a simple application of the properties of the mean and variance.