Congratulations for your July 4th, personally, as a US National, as well.

I felt a bit of disheartenment when you tell performing random simulation experiments in matters you know the result beforehand. Or am I wrong? As I had myself this sensation many times, I hope it will work as some relieve:
___a) the known results are fine to check if *the number factory* is working properly, (or my mind, text–books, papers, algorithms interpretation):
___b) the *reward* of something new is censed to be found out on matters such are asymptotic convergence or approximate models, as well. (Risk is our pepper, isn't?)
OMU, have a nice Birthday.
__c) besides *deterministic* calculations, computers, in what concerns MC, is limited to Sample Statistics. This is the area that conventional Statisticians cannot fight us. (They joke, of course, millions of simulations! They said, whereas I answer in a second: the favorite argument they use, SNIFF).

Yours sincerely