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Say I have a sequence that starts with:

H, H, H, H, H, H, H, H

Now each time I get another element one of two things can happen:

  1. it exhibits the same amount of randomness as the previous element T, T, T, T, T, T, T, T
  2. it exhibits more randomness than the previous element H, H, T, H, H, H, H, T

Assuming randomness is something that can be quantified, how do you analyze the sequence to determine the point (best approximation) at which it switches to completely random?

Note: in case this came out sounding like a homework problem (not sure it did) the context of this is using a pseudo random generator that seeds based on the current time in quick succession (very close time values) - they seem to generate sequences that are similar to each other and I wanted to test my theory (may very be wrong) that there's a minimum amount of time (greater than the smallest quantum in the target system) which must elapse from one run to the next in order to produce independently random results.

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Not an answer to your question, but: seed your random number generator only once. Re-seeding won't make your samples any more random; it can actually make them less random, as you are observing. –  mjqxxxx Feb 26 '13 at 21:54
    
Yeah, that's a good point for me to remember. I sometimes get caught up writing the most to succinct code I can and skip over a detail like that... –  Aaron Anodide Feb 26 '13 at 21:56
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