Best gaming laptop for 800 dollars

I would recommend the Lenovo Y or U series*, but both seem to be just at or over your limit. If you can spend $830 then you can get a y410p with a 1600x900 screen, there is a model for $800 but that has a 1366x768 screen which is sub-par at that price. You said you don't care, but honestly it's kind of a rip-off to put such a basic screen in it for that price. The rest of the hardware will do what you want though and maybe then some. The other options are a u430/u530 or a z510. Both the U series I recommend are not really available yet though, only the u530 is but that doesn't have the proper information it seems so they are probably still getting it ready. Still, they both offer a 740m and an i5 or i7 so that is good enough for gaming. The z510 has the same but isnt' an ultrabook like the U series are, and its battery life is 4 hours less as well as it weights more and is thicker but not too much. Also the z510 has no model for sale for a 740m for whatever reason, that might not be completely ready for release.

Either way you want a 740m or better as well as a 4th generation i5 or i7. (model numbers star with a 4, for example th ei7 4700MQ is a common 4th gen model) I would recommend looking at Lenovo as they are cheap yet they have great hardware options. You may have to wait a week or 2 for the newest stuff to come out, but it will be worth the wait.