The Cup Game is a staple of church summer camps, youth conferences, and retreats. There are several variants, and this variant comes from Ferry Beach. I know it’s stupid and pointless; that’s what makes it fun.
(You can find online videos which purport to show you how to play the Cup Game, but these videos are all shot facing someone who is playing it. It is much easier to learn if you can look at it from your own perspective, so that the right hand of the person you’re watching is on the same side as your own right hand; my video shows you how to play from your own perspective.)
Here’s a printable cheat sheet that may also help you learn: