I'm on the tww of my first IVF treatment (so hoping it works!). My clinic doesn't insist on an AMH test but I had to have one as my estradiol level was high on day 3 and they worried about that the high estradiol level was masking my FSH (my FSH was 6.4 and they were worried that if the estradiol was lower the FSH would be higher). My AMH was 20, which they said was good.
AFAIK the tests are just to establish how you'll react to the stimulating drugs. Check out this website www.advancedfertility.com/ - it's an American clinic with loads of educational pages about fertility and the various scans/tests like AFC/day 3/AMH. Checking out clinics' success rates for your age group is probably the best way to work out your chances. I've been at the Lister who have a handy pregnancy success calculator on their website - it's based on their stats only but can be a handy way of working out chances (see www.ivf.org.uk/success-rates/pregnancy-calculator)