I just received instant approval via internet application on the Platinum Mastercard with 40k miles.
I'm a bit surprised because I was just denied a Visa card a couple days ago. It is a long story, but I had the Citi Visa card for several years and recently cancelled in it a fit a rage over some horrible customer service over the phone. I then had remorse from cancelling the card and missing out on a bunch of future miles from purchases. I called back a couple days later to try to get the account opened again, and they denied me. I couldn't believe it.
Oh well. I'll now get 40k more miles and the little ding on my credit report doesn't matter for me at this time.