I'm Platinum, too, and have been for years. About half the time I'm upgraded. The other half, I get a nice room on a non-Concierge floor, but with Lounge privileges. I always complain about that and usually get a room on the Concierge floor.
A couple of months ago at the Metro Center Marriott in D.C., I was told that the Concierge floor (two of them!) was full, and this was at 4 p.m. I told them that I didn't believe it and ended up in a long debate with the front desk supervisor. At the end of the discussion, I got a room on the Concierge floor. They got a tiny victory by putting me in a smoking room!
Bruce