In an attempt to win back the computer Haruhi blackmailed from them in episode 2, the Computer Research Society challenges the SOS Brigade to a battle via the game they programmed, Day of Sagittarius III. If the SOS Brigade wins, they get to keep the laptops they will borrow to play the game on. If the Computer Research Society wins, they get the computer back, and Haruhi also flippantly includes Yuki as a possible prize.
The group starts practicing the game and some members pick it up faster than others. The agreed-upon day arrives and they start playing, but they begin losing quickly. Yuki reveals that the Computer Research Society is cheating, and Kyon tells her that she can reprogram the game to even the playing field (but no cheating and giving the SOS Brigade additional advantages).
The SOS Brigade wins the battle, but Kyon notices that Yuki seemed to enjoy the game, and tells her that if she wants to, she can work with the Computer Research Society sometimes.