In a usual poker hand, I would like to calculate the probability that one has a straight.

Without royal straights or flushes. I am comfortable with straight forward counting such as $nCr$ and $nPr$ and stuff, but this is giving me trouble.

Can anyone help ?

P.S.

For consistency, I would like to consider any combination of 10JQKA to be a royal straight.
I will also consider QKA23 a straight as well, so that a loop is accepted.