I can't find a cheap gaming laptop

Whether or not you get 50 FPS will depend in part on the game. Some games are much more demanding than others, leading to the awful catch-phrase "But can it play Crysis?"

What games do you have in mind? If they are hardware-hungry games, there may not be a cheap solution.
 
Need a budget to work with... and it depends on the specific game...

If you want 50 FPS in LoL then that is pretty easy to achieve with a somewhat low budget. If you want 50 FPS in The Witcher 3, then you better have a lot of money for the laptop... especially if you want to avoid using low graphics quality.