Oystein Schonning-Johansen wrote:
Now the interesting part: How can you construct a scientific test to
prove
(or falsify) the postulate that a software uses such scheme?
Assuming that you mean statistical proof, it depends on what you're
trying to establish. If you're just trying to establish non-randomness
then simply counting how often a roll appears twice in a row should be a
pretty strong test. In a random sequence, the probability that the next
roll will be the same as the current roll is 1/36 if it's a doublet and
1/18 if it's a non-doublet. In the system I described, I think the
probability is (1/18)*(1/36) for a doublet and (17/18)*(1/36) +
(1/18)*(1/18) for a non-doublet. I'm too lazy to work out how many
rolls it would take to reach 95% confidence but I'd guess that a few
dozen rolls would suffice.
If you're trying to establish in detail what the algorithm is doing then
it's obviously going to require more data. How much data exactly
depends on what alternative hypotheses you're willing to entertain.
Tim
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