The Enterprise is ordered by Starfleet Command to take part in a combat practice simulation in preparation for the Borg threat. A Zakdorn strategist named Sirma Kolrami (Roy Brocksmith) is sent to serve as observer and mediator of the simulation. Before the simulation, Commander Riker challenges Kolrami to a game of Strategema. Riker is beaten easily by the master of the strategic game, but considers it an honor to play him. Doctor Pulaski, thinking Data could easily beat the arrogant Kolrami, pushes Data to challenge him. Data, however, is also beaten easily. He soon becomes convinced he is malfunctioning and removes himself from duty.
The simulation consists of a battle between the Enterprise and an 80-year-old Federation ship called the Hathaway, which is in orbit around a nearby planet in the Braslota system. The crew of the Enterprise is split: Captain Picard and Data command the Enterprise, while Commander Riker, Chief Engineer Lt. La Forge, Lt. Worf and Acting Ensign Wesley Crusher go aboard the Hathaway. Each ship will try its best to disable the other in simulated attacks.
The Hathaway is technologically inferior and devoid of antimatter, making warp drive impossible. However, Wesley, who left an experiment that contains antimatter on the Enterprise, pretends to have forgotten about it and must return to dispose of it. He pretends to beam it off the ship and leave it particlized, but actually beams the experiment over to the Hathaway to use for the warp drive. It will allow them warp 1 for two seconds.
Pulaski and Troi attempt to persuade Data that he is not malfunctioning and that sometimes you can make all the right decisions and still lose. It takes Picard himself to convince Data that he is a fine officer and restores his confidence. As the battle begins, Riker allows Worf to use a trick he designed to fool the Enterprise sensors. The Hathaway disrupts the Enterprise's sensors, causing them to see a fake image of a Romulan warship that is supposedly attacking them. While the Enterprise turns to face the fake Romulan ship, the Hathaway scores direct hits on them.
However, the simulation is abruptly cut short by an attack from an actual enemy: the Ferengi warship Kreechta under the command of DaiMon Bractor (Armin Shimerman). Believing the Kreechta's approach to be another of Worf's sensor tricks, Picard initially ignores it. However, the resulting Ferengi attack on the Enterprise locks the Federation ship's weapons into the harmless war-games mode, leaving it defenseless.
The Ferengi had seen two Federation ships fighting each other, noticed that the fight was hopelessly mismatched as one ship was far superior to the other. They deduce that the smaller, older ship must contain something very valuable and they want to have this valuable thing for themselves. The Ferengi threaten to destroy the Enterprise if it is not turned over to them.
Picard and Riker, using Wesley's "cheat" and Worf's sensor trick, attempt to trick the Ferengi into disengaging. The Enterprise fires photon torpedoes at the Hathaway, to "destroy" it, but an instant before they hit, the Hathaway goes to warp speed. The Ferengi think the Hathaway is destroyed. They then prepare to destroy the Enterprise, but Worf uses his sensor trick and causes the Kreechta to see a fake Federation starship approaching. Thinking they're outnumbered, the Ferengi escape.
With the simulation over, Data challenges Kolrami to a Strategema rematch. However, this time Data alters his strategy by playing to a draw instead of playing to win. Data is then able to play continuously, frustrating Kolrami, who quits the game in disgust.