How different do random seeds need to be?

Question

Consider code like this (Python):

import random

for i in [1, 2, 3, 4]:
    random.seed(i)
    randNumbers = [random.rand() for i in range(100)] # initialize         


        

Answer 1

Short answer: Avoid the re-seeding, as it doesn't buy you anything here. Long answer below.

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That all depends on what exactly you need. In Common defects in initialization of pseudorandom number generators it is outlined that linear dependent seeds (which 1, 2, 3, 4 definitely are) are a bad choice for initializing multiple PRNGs, at least when used for simulation and desiring uncorrelated results.

If all you do is rolling a few dice, or generating some pseudo-random input for something uncritical, then it very likely doesn't matter.

Note also that using some classes of a PRNG itself for generating seeds have the same problem in generating linear dependent numbers (LCGs spring to mind).