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What resolutions will game developers be required to support?
Game developers are only required to support 720p.
Does this mean I need an HDTV that supports 720p to play all of the Xbox360 games?
No. Despite the fact that developers are only required to support 720p the video encoder chip built into the Xbox360 has the ability to up-scale and down-scale games to any of the resolutions supported by the Xbox360. This means that even if a game was only developed in 720p you will have the ability to play it in 480i, 480p, or 1080i as well as 720p.
Scaling lagg can come from any type of TV not just crts. The only way to ensure you don't encounter it is to try before you buy. Haul your Xbox to Best buy plug it in and try it.
If your display is native 1080i and doesn't require scaling for that resolution then you'll probably be fine, but often times sets aren't actually native to any HD resolution so they need to scale no matter what you feed it.
Pick a game where audio/video syncing is important , something like DDR would work well to test.