# New or same seed for each Monte Carlo simulation run

I'm running a Monte Carlo simulation with 200+ input variables which I'm varying with a zero mean normal distribution via a random number generator. Does it matter if I set the seed once and then perform 1,000 runs, or do I need to reset the seed on the random number generator before each of the 1,000 runs?

As a quick test, I wrote up a test in Matlab to answer this question -- Are 10,000 random numbers pulled from the same seed nearly statistically equivalent to 10,000 random numbers pulled from 10,000 different seeds?

numCases = 10000;
% Same seed
rng(42056)
Xsame = randn(numCases,1);

% Different Seeds
Xdifferent = zeros(numCases,1);
for ii = 1:10000
rng('shuffle');
Xdifferent(ii) = randn();
end


This produced means on the same order of magnitude, but I wasn't sure if that was good enough, or if I was missing some understanding of random number generators and Monte Carlo simulations.