[elif]

111111 is just as likely as any other *SEQUENCE* of numbers. This is a little confusing because the "sequential" requirement is somewhat masked by the repeating sequence used by the example. however, the odds of rolling six 1's is 0.00002143347.

considering the non-sequential set of rolls 625631 you have the odds of exactly two 6's at 0.201 and also one 2 5 3 and 1 each at 0.402

0.402^4 * 0.201 = 0.00524928641, or ~244 x more likely.

[prolyx]

There are many ways of slicing and dicing things so that you group different sequences, e.g. group permutations as the same as you have done. But by "number" I was referring to a sequence of symbols drawn from a uniform distribution, so order matters. (On the website, you also choose options sequentially, anyways.)