DS9 Season 6 Episode 9 Statistical Probabilities

Plot

Dr. Bashir has volunteered to help treat four genetically augmented individuals who, due to unintended neurological side effects of their augmentation, are unable to function in society: hyperactive, paranoid Jack; hypersexual Lauren; childlike Patrick; and silent, catatonic Sarina. Bashir realizes that their primary problem is boredom: as Jack points out, they are forbidden from pursuing any profession where they could put their enhanced brain power to work.
Meanwhile, Damar, the new leader of Cardassia, proposes peace talks with the Federation. Watching his speech, the augments make several accurate guesses about Damar and how he came to power. Bashir convinces Captain Sisko to allow the augments to review the peace negotiations to see if they can determine the Dominion's agenda.
Based on subtle clues in Damar and Weyoun's speech and behavior, the augments deduce that the Dominion wants to draw the border to secure a planet that has the raw materials needed to make ketracel white, the drug used to control the Dominion's Jem'Hadar soldiers. Knowing this gives the Federation negotiators a huge advantage in the talks.
Starfleet provides the augments with further intelligence in order to develop a statistical model to predict the future. The augments soon come to the conclusion that the Federation is doomed to lose the war and suffer casualties in the hundreds of billions. As a result, they recommend surrender, which will save those lives and still leave the Federation in a position to rise up against the Dominion in the future. Bashir is convinced the augments are right and argues the case before Sisko. However, Sisko and Starfleet reject the suggestion out of hand.
The augments decide to leak Starfleet's strategic plans to the Dominion, hoping to shorten the war and minimize the casualties. When Bashir objects to this treasonous plan, Jack, Lauren, and Patrick overpower him. Bound hand and foot, and left alone with Sarina, Bashir convinces her that her fellow augments' actions will result in their imprisonment and separation. Sarina frees Bashir in the nick of time, and Bashir intercepts the augments on their way to the meeting with the Dominion negotiators.
Bashir realizes that the augments believed they couldn't possibly be wrong because of their superior intellect; but despite the presumed infallibility of their statistical model, the actions of one person (Sarina) completely altered history. The augments return to their institution, promising to continue work on a plan for defeating the Dominion.