How to calculate the probability of a repeating sequence of values from a random selection within a fixed range

Suppose you have a regular six-sided die and cast it repeatedly, in series of twelve throws. The throws return the following values:

S1 = [1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6]

S2 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]

S3 = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]

S4 = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]

S5 = [2, 4, 6, 2, 4, 6, 2, 4, 6, 2, 4, 6]

S6 = [5, 3, 5, 1, 5, 3, 5, 1, 5, 3, 5, 1]

What formula would you use to calculate the probability of each series?

Also:

How does the length of each repeating sequence affect the probability?

Are S3 and S5 equally probable?

Are S2 and S6 equally probable?