Genius hasn't risen to a genius level IMO. I have a large database of music as you can imagine from my forum name. The Genius results I've received have been underwhelming to say the least. It skews the results toward commercial music, smooth jazz, and rock. My collection is made up of about 20% of those styles of music, maximum. The rest is modern and avant jazz, most all of which is identified by the database (forget the name of it) that matches metadata from CDs when importing music into iTunes. The Genius mixes ignores the majority of my music collection, creating mixes largely made from this 20% of commercial oriented music.
There is no avant/free jazz mix. I can't generate one using the select a song method - Genius tells me to pick a new song and try again. I have to say, from a jazz perspective my collection is not so far out of the ordinary to have it not recognize some of these song selections.