Give Up:
Truth be told, Roy Mustang was a good chess player but he had one major weakness. And though the Flame Alchemist did his best to hide that weakness, it inevitably displayed itself the more he played with the same opponent. And Roy was all too aware of this as well, which was why he tried to avoid playing with the same people, knowing that the one flaw in his plan could be his downfall.
For you see, no matter how dire the situation or how high the potential of winning by doing so, Roy Mustang never, ever sacrificed his queen.