Hmm...you might be able to build a good DESKTOP in that price range...depending on the prices of GPUs right now.
For a laptop though? Ehhh, maybe you could run some low end games. League is not very intensive and can run on most potatoes. I would recommend something around the $800 range though. Take a look at this:
https://www.newegg.com/Product/Product.aspx?Item=N82E16834154733
And you get a $100 rebate. SCHWEEEEET!
[{quoted}](name=l Ryden l,realm=NA,application-id=yrc23zHg,discussion-id=7PejjMAh,comment-id=000c00000000,timestamp=2018-05-03T03:04:21.256+0000)
OP is asking for a laptop. As far as his concern goes, with a budget that tight he's probably not looking into upgrading anytime soon. By the time you're wanting to upgrade your parts might as well all be upgraded to the point where you can build a new computer all over again.
I'm assuming OP isn't living a dank hotel so cleaning heatsinks really isn't an issue. Again, OP is asking for a laptop so get the "build a custom PC" argument out of here. Everyone knows you can save money in terms of price vs performance when it comes to building your own computer but OP is in the market for a laptop.
Who knows, maybe this guy wants a laptop since he also needs to take notes in class? Good luck lugging around a desktop to class and setting it up for your lab experiment.
Surface Pro 4. Amazing tool for note taking and stuff. Definitely would recommend. Won't do shit for games though.