The above options allow me to use shuf to efficiently simulate a dice roll, but there is a clear bias when I do so, for example:

$ for i in {1..10000}; do shuf --input-range=1-6 --head-count=1; done | sort | uniq --count
   1730 1
   1411 2
   1882 3
   1809 4
   1520 5
   1648 6

Using seq instead of input-range does not appear biased:

$ for i in {1..10000}; do seq 6 |  shuf --head-count=1; done | sort | uniq --count
   1652 1
   1696 2
   1674 3
   1638 4
   1713 5
   1627 6

Same for head:

$ for i in {1..10000}; do shuf --input-range=1-6 | head --lines=1; done | sort | uniq --count
   1639 1
   1674 2
   1655 3
   1669 4
   1688 5
   1675 6

It seems that somehow combining both options affects the distribution. I assume there's some performance optimization in that case since shuf doesn't need to permute the entire input range.