My very limited experience, with a 500 and an 870. Diff chokes for both. Would have to look what I have for the 500. My approach was a little different.
My son's 870 patterns better with a 2 3/4" particular turkey load. My 500 wouldn't pattern any 2 3/4" loads, and favored a 3". We used 3-4 diff loads/shells to see what the gun/choke combo liked.
