There's that thing called the spill not that I once saw on a youtube science video. Also, I think there are, out there, glasses that are studied not to tip over once they're on a hard surface.
A centrifuge wouldn't really upset a game. In fact, there's a drink holder which works on the same principle, and makes it literally impossible to spill your drink as long as you're not bumping it into stuff.
Here's a link to it on Amazon so you can see it better.
My husband uses one of these so he can carry the morning coffee without worrying.
This thing looks like it works for that, https://www.amazon.com/SPILLNOT-449-The-Incredible-Spill/dp/B005E0X23S