Bare minimum tread depth
 

What would you guys say is the bare minimum tread depth for tires when going to a race? 8/10, 7/10, 6/10???

depends on the race.

If you're running appropriate slicks, none.

A race? Zero is best. Tread is for dealing with water and dirt, which shouldn't be on a track. The only exceptions would be off-road racing or rain tires.