Well, HDR really doesn't give the capability of displaying bright brights and dark darks. Not only is the display hardware just not designed for those levels of high dynamic range, but we really wouldn't want to do that sort of thing. For example, if things get really dark in the game, well, you just won't be able to see them at all if there's any other source of light in the room.
No, a better use of HDR would be to simulate our own human reaction to bright and dark, but keep the average brightness roughly constant (there should be some time delay, of course). Our eyes attempt to compensate for bright/dark environments by limiting the amount of light that enters our eyes. In dark environments, we see more monochrome, and more color in bright environments. Using tone mapping, one can map the high range of brightness in the framebuffer to the monitor's possible display range, such that, for example, a bright light shining in one's eyes dims the rest of the image (not immediately: at first it would just bleed over the rest of the image, simulating the temporary blindness suddenly turning on a bright light would cause).