Consider Civil War the shorter (and faster) version to beer pong: Called "the world’s angriest historical drinking game" by Williams College students, this will get you hurling ping pongs at each other very fast.
Fill up your Solo cups halfway, and set them up in six diamond shapes (four cups each), three diamonds total at each end of the table.
One team starts with two ping pong balls, the other starts with one. Begin by throwing the balls at the same time, and continue to throw until one of the balls makes it into the opposing team’s cups.
If the ball is sunk in one of your cups, you must drink the contents of the Solo cup before you’re allowed to throw again. Once all of your cups have been sunk, you’re out.
The last person with cups remaining is the winner.