This thread jogged my memory of another thread (I think on this forum, too?), where someone made the suggestion that to avoid red lights, all you had to do was plan your route so that you alternate directions (e.g. North one block, East one block, North one block, East one block, etc), always taking the direction (e.g. North or East) that was green at the moment you arrived at the intersection.
It kind of bugged me at the time, but it took some thinking to figure out why. The odds (let's say for five intersections or so) of getting to your destination (presuming it's at exactly 45 degrees to your starting point) without being stopped by a red light are against you.
There would have to be an exact combination of green-light intersections in your favour for this to work. For instance, if you have to go five blocks right and five blocks up, the lights in your favour at each intersection would have to come in the order of right, up, right, up, etc. Or, the lights could come in your favour of exactly five right and five up, or some exact combination in between that and the alternating pattern.
What's more likely to happen is that, for instance, you might get five right in a row. Now you've either got to get exactly five up in a row, or back track, or go out of your way.
Kudos to anyone who can come up with a forumula calculating green light odds given any number of intersections, angle to your destination, and the number of blocks between starting point and destination.