Cheap gaming laptops don't exist.
The only laptops that would suffice for gaming are either created for just that (e.g. Alienware i.e. expensive) or those with high-end dedicated graphics cards, usually for digital media development (also expensive).
You're best option to meet in the middle is something like a refurbished HP Elitebook Workstation. They have the high(er) end graphics cards, but you're still going to be shelling out some dough for those too.
I personally have an older Probook that has a dedicated Radeon HD 4350 that I can play games on the lowest quality, but in my experience, you'll pay a kings ransom for a good gaming laptop.
If anyone else knows a better solution, please chime in.