I tend to prefer working on my own on class projects, so at first I thought that the scientific community game would offer little towards improving the quality of my homeworks. This proved not to be the case. SCG requires one to state predictions and claims in a mathematical way, a skill that (to my knowledge) isn't taught very thoroughly in many CS programs. Furthermore, by forcing one to think in the manner of two adversaries defending and attacking claims, SCG encourages one to think about the problem at hand in a vastly different manner than if one were simply sitting down to write an answer as one would for a typical homework assignment.
I found that playing the role of both Alice and Bob in the SCG helped me to think more deeply about the homework problems by taking an initial intuition about the problem and increasingly improving it. Indeed, with correct play from both Alice and Bob, the game is guaranteed to yield the strongest correct claim. By illustrating these sorts of mathematical ideas, the SCG goes beyond the material in the homework to broader mathematical ideas.