Well, point-a-lap tactics tend to be quite different from points race tactics. The longer the points race (Nine laps? Good grief.) the more true that becomes.
As you've seen, point-a-lap races are often won by whomever gets three or four points. Often you will find a sprinter who takes off from the gun. This works occasionally, if the field spends too long looking at each other. Mostly, though, the field will take off pretty quickly and bring the sprinter back after a couple of laps. It's usually a good idea, then, to take a spot about 5-6 riders back early on and let the pack do the work for the first half of the race. Once the tempo is set and the breathing has gotten a bit ragged, it's either time to contest a few sprints or start a break, depending upon your skills and fitness. In trying to win sprints, it is a very good idea to really go for it, as a common mistake is to half-ass it in concern for the fact that the next sprint is only 20 seconds away. The mistake is that it takes nearly as much effort to finish second or third in a sprint as it does to win it -- and second doesn't count for **** in a point-a-lap. Make your move and stick with it unless it's clear that you're beaten. As a bonus, a 100% sprint in the middle of a point-a-lap often ends up bringing you and one or two competitors off the front. Getting organized and maintaining that gap can make all the difference -- especially if the race is part of an omnium. Guaranteeing a top three finish for yourself is very intelligent, when riding a lottery like a point-a-lap. It's one of those races that isn't likely to win the omnium for you, but can very easily lose it.