I enjoy video games and one of the games that I play involves running simulations to test damage per second (DPS). I am wondering whether running five $10,000$-iteration simulations is equivalent to running a single $50,000$-iteration simulation. (More generally, is running $X$ $Y$-iteration simulations equivalent to running $A$ $B$-iteration simulations when $XY = AB$?) I use the word equivalent vaguely because I am not exactly sure how to compare simulations of different iterations to each other. I am very new to the statistics/math behind simulations.
This question interests me because, in my case, it is often easier to run simulations with higher numbers of iterations instead of running more simulations with fewer iterations. I picture equivalence of two simulations would mean that they tend toward the same distribution in the limiting case, but I lack the knowledge of the area to formalize that easily. Any input or resources on this question or similar questions is appreciated.
This is by no means a conclusive expert answer, but in my opinion, it should depend on your task. If your simulations are independent of each other, there should be no difference between running several instances of the same simulation and running the same instance longer. If they are not independent, then you should ask this question on stack overflow.
In my experience there is a fine balance between number of simulation instances, $S$, and number of iterations $I$, assuming $SI$ is constant.
I did a lot of simulations geared for Narrow Escape Problem. Starting several instances helps a lot to speed up the process. However, probably depending on the number of cores on your computer, there is a limit to how high $S$ can be.
My computer has 8 cores and I notice a slowing down after I tried to run more than 10 instances. However, a workstation with 48 cores had absolutely no problem running 40 of them at once. I did not time it accurately though.