I haven't had enough coffee yet to write an algorithm "that solve[s] this problem and that provide[s] for the necessary statistical analysis."

But in response to McDarren's comment about British rules, I found this site which specifies a more minimal set of American rules. (You have to love American sports organizations: that webpage's title is World Standardized Rules. Compare the saner "English Pool Association" from McDarren's link.)

However, in my experience, the standard in the US is one of two things: either it's utterly random, or it's very similar to the J-pattern McDarren mentions - except that you don't hook the J so perfectly by doubling inside the bottom row. Instead, you leave two of something (pretty much at random) adjacent in a bottom corner. Examples ('S' for solid and 's' for stripe):

    S            s
   s S          s S
  S 8 s        S 8 s  
 s S s S      s S s S
S s S s s    S s S s S
[download]

Most folks I know don't care if the 1-ball is uppermost, but the BCA website does include that specification. I'm not really sure why (other than "because it's the 1") since it has no significance in the game (unlike in 9-ball, where sequence matters and the 1-ball always goes at the top of the diamond).

A photo in the Wikipedia entry for eight-ball shows what I have in mind (without the 1-ball placed up top, though the image is supposed to show the World Standard rules).

Edit: thanks to ysth for pointing out that I had the wrong number of stripes and solids in my sad little examples. I'm going to blame that on the coffee deprivation.