Sixteen die rolls forming a multiple of 8

A fair die is rolled $16$ times and the results are written next to each other, in order, to form a $16$-digit number. What is the probability that this number is divisible by $8$?

$\tfrac18$. Divisibility by $8$ depends only on the last three digits. Checking the $6^3=216$ equally likely endings built from digits $1$–$6$, exactly $27$ are multiples of $8$ (nine ending in each of $2$, $4$, $6$), giving $\tfrac{27}{216}$.