Intel has only made a "video card" one time, about 1998, and it was a disaster. They only make integrated solutions, not "CARDS" at all. If you have such a poor selection where you shop, you need a better shopping venue. There are plenty of AMD and nVIDIA mobile cards out there in reasonably priced laptops. If you are shopping for lowball $500-600 price points, that's your fault. Game machines require more cooling, better input devices, and real graphics. Those things don't come free, like Intel's tinker toy version of video does.
