Well, as I'm sure you've all guesed by now, I didn't run out. That rack took place in a tournament and the score was 7 - 7 on the way to nine. I felt it cost me a match. Pretty disheartening at the time. Thanks to all for your analysis and advice.
There are many, many diamond systems. In general, they work by looking at where the balls are, looking at the diamonds (or spots) are on the pool or carom billiard table, doing some calculation according to numbers that are preassigned to each according to the particular system, and then making your cue ball or the object ball go towards the calculated diamond or spot. The "Plus System" is designed for playing the cue ball to end-rail/side-rail for the first two cushions, with the end rail being approached as something like a 45-degree angle. It is an absolutely standard system (even though it doesn't always work well), and it has been around for 50 or 100 years.
See Robert Byrne's books (Standard, Advanced, Wonderful World) for clear explanations of many systems.. Walt Harris's "Billiard Atlas" series has far more diamond systems than anyone could hope to master. Eddie Robin has a good explanation of systems in his first one pocket book.
I don't think there is any complete, clear on-line discussion of all the many diamond systems, but Jim Loy's site at http://www.jimloy.com/billiard/billiard.htm is pretty good and he covers both the corner-five (which many people who don't know there is more than one system call "The Diamond System") and the Plus-two system which I mentioned in my post.