You can get some pretty good gaming laptops for under $500 that can run a number of games well, the issue is that newer games like Battlefield 3 have pretty high spec requirements, so while it might be able to run the game, it won't run that well and soon the spec will be insufficient for future releases. The
Lenovo G505s 59406417 a pretty good laptop for under $500 and it will run both Battlefield 3 and Skyrim, but it's not the most optimum as it just meets the spec requirements. I recommend you spend an extra $150 ish and get a
Acer Aspire V5-552PG-X809, It'll run both games pretty smooth and it quite a beast.
Acer Aspire
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AMD A10-5757M 2.5GHz (4MB cache)
8 GB DDR3 RAM
1 TB 5400 rpm Hard Drive
15.6-Inch Screen, AMD Radeon? HD 8750M Graphics
Windows 8, 4.5-hour battery life
Lenovo G505s 59406417
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AMD A10-5750M 2.5 GHz Processor
6 GB DDR3 RAM
AMD Radeon HD 8650G graphics
1 TB 5400 rpm Hard Drive
15.6-Inch Screen
Windows 8.1; 5-Hou