You're trying to equalize the variables to control for race alone, but the odds are of two people with equal education and experience, who both want to work for as cheap as the job market will reasonably go, and are both generally cordial and easy to get along with (from the hiring manager's perspective) are slim to none.

The fact is that you're never going to be able to control for just race as the world doesn't look like that, which is why race quotas are stupid. Odds are one of them will inevitably be the better pick. Will their race have anything to do with it? Hard to say because it's impossible to control for just race in a real world scenario like hiring a good candidate.