@Bumblefish

Which one is random?
(data sets are 100 numbers 1 to 6)

listA=[2,3,5,1,2,2,4,2,4,5,2,3,3,4,5,6,4,2,6,2,2,1,3,4,5,5,6,3,3,6,1,4,2,1,4,5,2,2,3,3,3,5,6,3,2,4,5,5,1,1,1,6,1,4,3,5,5,3,1,1,1,6,1,4,6,6,3,6,6,2,4,4,4,5,1,5,6,2,6,1,1,2,4,2,2,3,4,4,5,6,1,3,3,3,5,4,6,5,1,6]

listB=[4,2,5,6,3,5,3,1,3,4,2,3,4,3,4,5,5,1,3,3,2,1,1,6,1,3,2,2,2,6,1,5,6,3,6,3,2,3,2,4,6,1,1,6,3,2,4,1,6,1,3,1,5,6,2,3,3,5,1,6,4,5,2,5,1,1,5,3,6,2,3,3,6,5,2,3,3,1,6,3,2,3,2,1,6,6,4,4,6,2,4,5,4,5,3,4,6,5,3,2]

@futurebird
just to clarify what she means is as if from random unbiased 6 sided die rolls.

@Bumblefish

@futurebird
things I would check are first the frequency of each number... they should be somewhat uniform but not TOO close to equal as all exactly equal is unlikely... next I'd look at the length of repeat sequences and compare to expected values.

the actual definition of random sequences (Per Martin-Löf) is in terms of passing tests actually
@Bumblefish

@dlakelan @futurebird @Bumblefish another thing to look for could be frequency of pairs of numbers. for an unbiased, independent dice, there should be about a 1/36 chance of each pair of numbers to appear.

unfortunately you'd quite a large number of randomly generated samples to get this chance exactly, but i guess you could do some fancy statistics to analyze these distributions and try to guess which one is "more random looking"