Comment by derriz
3 days ago
At a certain point a bias in the prng just has to become significant? This will be a function of the experiment. So I don’t think it’s possible to talk about a general lack of “practical impact” without specifying a particular experiment. Thinking abstractly - where an “experiment” is a deterministic function that takes the output of a prng and returns a result - an experiment that can be represented by a constant function will be immune to bias, while one which returns the nth bit of the random number will be susceptible to bias.
> At a certain point a bias in the prng just has to become significant?
Sure, at a point. I'm not disputing that. I'm asking for a concrete bound. When the state space is >= 2^64 (you're extremely unlikely to inadvertently stumble into a modern PRNG with a seed smaller than that) how large does the sample set need to be and how many experiment replications are required to reach that point?
Essentially what I'm asking is, how many independent sets of N numbers must I draw from a biased deck, where the bias takes the form of a uniformly random subset of the whole, before the bias is detectable to some threshold? I think that when N is "human" sized and the deck is 2^64 or larger that the number of required replications will be unrealistically large.