An unbiased sample generator would be sufficient. That would be just pulling from the population. That’s not practically possible here, so let’s consider a gene

An unbiased sample generator would be sufficient. That would be just pulling from the population. That’s not practically possible here, so let’s consider a generator that was indistinguishable from that one to also be unbiased. On the other hand, a generator that gives the mode plus some tiny deviations is extremely biased. It’s very easy to distinguish it from the population.