This one's called Real Pool (have a look at the screenshot on the right). It's a pretty simple game but then that's one of the things I like about these types of flash games, you can jump onto the site, play for a little while and then leave again without any hassle of logging in, joining a network or anything else like that.
Real Pool is a flash game where you actually play against a computer and they track the shots your taking. While I was playing the computer made a foul pool shot on the second shot and the game comes up with the screen you can see here. It offers feeback on what's happened in the game e.g. it let me know that the computer had made a foul shot and that I had a free shot coming up. That's a pretty good little peice of functionality for a flash game.
The game itself is a little slow. Generally when I'm playing a flash pool game I prefer to have something that is quick and snappy and takes only a few seconds for each shot. In this game, it took a bit longer than most others I've played lately. Including our own game! 🙂