army1987 comments on Worse Than Random - Less Wrong
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You don't need that much shoddiness to get very weird things in certain situations (IIRC there was a PRNG getting some value wrong by 20 standard deviations in a Monte Carlo simulation of the Ising model because of a non-zero three-way correlation between the n-th, (n + 63)-th, and (n + 126)-th outputs or something like that), and some off-the-shelf solutions are shoddier than you may think.