"The Day of Sagittarius" is a short story from the light novel The Rashness of Haruhi Suzumiya, written by Nagaru Tanigawa and illustrated by Noizi Ito. It takes place in November of Kyon and Haruhi's first year of high school.
In this story, the Computer Research Society President challenges the SOS Brigade to a game of The Day of Sagittarius III (a future sci-fi space fleet armada war strategy game they created themselves), in an attempt to win back the computer Haruhi extorted from them in The Melancholy of Haruhi Suzumiya. In return, the Computer Research Society wager four laptops.
The Computer Research Society starts winning immediately, seeming to come out of nowhere and attack before retreating just as quickly. It turns out that the Computer Research Society is cheating, having disabled the fog of war only for themselves while the Brigade members still have limited line of sight. Suspecting she is having fun, Kyon gives Yuki permission to hack the program while it is running and using none of her alien powers, turning the Computer Research Society's fog of war back on. Apparently if you freeze-frame while things are flashing on her screen, you'll see that she's using valid Windows memory-accessing C functions. Using Yuki's amazing micro-management of scout ships to see through the fog of war, the SOS Brigade promptly goes on an all-out offensive and wins the game.
Kyon allows Yuki to become a part-time member of the Computer Research Society, seeing as this and reading are the only things she seems to show interest in. Haruhi decides that since her brigade bested the Computer Research Society, they must now pledge fealty to her.
The gameplay is shown as if it were actually taking place, with each character sitting in the captain's chair of the flagship of their respective fleets. The crews and appearances of these ships are all references to real-world science fiction shows and movies. In the "real world" of the show, the fleets are simply represented as coloured triangles moving around a grid.
There is a Flash version of the game available online here, although it currently features no AI and does not seem to be under development any longer.