Amen to the professional. After nearly a year of trying to get the red out of my hair after I had dyed it dark auburn, I finally broke down and got it done professionally (Saturday in fact.) I'll post pictures of the good, bad and ugly...and then good again later.
Ash does cancel out red, but it's just not that simple as SmartStyle knows. For example, you can't go from a brown with red undertones to an ash blonde and have your problems instantly disappear. Trust me....I've tried it. I think I KNEW it wouldn't work, but I was so tired of the upkeep of the auburn that I thought I might get lucky. When coloring your hair yourself you should stay within two shades of your current color. However, when dealing with red....I opt for a professional. If you're hesitant about chain hair salons such as Hair Cuttery or Great Clips, I would say if you're going for an all over color not to worry. I went to the in-store salon at Walmart and I'm EXTREMELY satisfied with my results.
I hope this helps!!