I would assume that the right strategy here varies depending on how many other people are going to enter the competition.
Actually, a "guess how many people will enter this competition" competition would be fun.
What would be interesting now is to repeat the competition after publishing these results; in fact, make sure these results are given on the entry page for the new competition. What would happen this time? Well, a bunch of people would start picking numbers around 109 this time. Except everybody expects everybody to do that, so maybe they'll start picking lower. Meanwhile smartasses will still be picking "2", and smartasses who think they can outsmart those smartasses will be picking "3".
Actually, a "guess how many people will enter this competition" competition would be fun.
What would be interesting now is to repeat the competition after publishing these results; in fact, make sure these results are given on the entry page for the new competition. What would happen this time? Well, a bunch of people would start picking numbers around 109 this time. Except everybody expects everybody to do that, so maybe they'll start picking lower. Meanwhile smartasses will still be picking "2", and smartasses who think they can outsmart those smartasses will be picking "3".