Lately, I've noticed that we've been focusing too much on the rule of threes in our improv. People are focusing more on doing things three times than on doing the things that make great improv. I think that our focus should be on game of the scene. In improv, the rule of threes is just a tool for to gain more laughs on the parts of scenes that aren't what the scene is truly about. I feel that the rule of threes is binding other parts of improv.
For those who might not know, the rule of threes is a universal rule in comedy. Things are funnier when they happen in threes. If someone make a notable gesture in a scene, typically the 2nd time they will get a small laugh, and the 3rd time they will get a larger laugh. The laughs drop of sharply after that. The rule of threes can be applied to most things, and its effects are very apparent, which is where I think the confusion comes from. Although the rule of threes is an excellent tool for getting laughs, it is not the pinnacle of improv humor. I believe that honor lies with game of the scene and reincorporation(for longform).
Game of the scene is, in essence, what a scene is really about. If someone plays a character who has two refrigerators, the scene is about the kind of guy that would have two fridges. In order to further the game, you shouldn't play 'a day in the life of a guy with two fridges;' you should play 'what else is true about a guy with two fridges?" Maybe he has two of everything, two dogs, two coffee makers, two beds, and two wives. Maybe his wife works for an appliance company, and he has another six toasters, eight ovens, and fourteen vacuums. The point here is establish a pattern off of something unusual in a scene. Once you find the pattern (found by asking yourself the question: "If this is true, what else is true."), then you can build the game on top of that.
The whole point of this long-ass trek into improv territory is to give a warning. Know the rule of threes but don't be bounded to it. When you have a game of the scene going, it is not correct to cut it after three instances of the pattern are shown. The pattern continues to be funny by taking it in unexpected directions and by heightening it. The rule of threes should be seen as a tool, not a law.