The amount of RAM you have does not affect how well 90% of all games run, since 90% of all games use 2GB max (usually much less).
What matters more is what CPU and graphics card you have.
Also, what kind of games would you like to play? FPS? RTS? Platformers? Puzzle games? Point and click adventures? Side scrollers? RPG? Tactics? Dungeon crawlers? Survival? Multiplayer? Online? Etc... There are millions and millions of games out there to choose from.