It’s no good to ask someone to hang out if you tell yourself they won’t want to. Get in the mindset that you are fun to hang out with and that the person you ask will say yes. If you are confident in yourself and make a direct ask, the person will be more open than if you seem timid when you ask free games.
Don’t say, “You’re probably busy most of the time and have a lot of other friends already, but we could hang out sometime if you want to it. It’s okay if you would rather not.”
For an example, think about a co-worker you’d like to hang out with. Catch them in the break room and say, “We should find something cool to do outside of this place sometime.” It’s simple, shows your interest, and leaves things open to developing.
If you’re in a weekly club with someone, say, “You know, we meet up here every week. Let’s grab some food after the meeting sometime.” Again, it’s direct and shows that you are assuming they would be interested.