The story takes place in a future where the world is covered by a new ice age. When the film begins, Altman's camera tracks along a blank, frozen tundra which is seemingly deserted- that is, until two blurry figures in the distance can be just barely made out. They are the seal hunter Essex (Paul Newman); and his pregnant young wife, Vivia (Brigitte Fossey), the daughter of one of Essex's late hunting partners. Having returned from the South, they are venturing further up North where Essex hopes to reunite with his brother, Francha (Thomas Hill).
Essex and Vivia eventually meet up with Francha at his apartment, but the reunion is short-lived. While Essex is in the neighborhood buying firewood, a gambler by the name of Redstone (Craig Richard Nelson) sneaks into Francha's apartment and bombs it with a vial of alcohol, killing Francha, Vivia and the apartment's other inhabitants in the process. Essex, who sees Redstone fleeing from the scene of the explosion, chases him to the sector's "Information Room"; it is here that Essex then witnesses the subsequent murder of Redstone by a Latin-speaking gambler named St. Christopher (Vittorio Gassman). When St. Christopher leaves the scene, Essex finds a piece of paper in Redstone's coat pocket. On the paper is a list of names: Francha, Redstone, Goldstar, Deuca, St. Christopher, and Ambrosia.
Puzzled by the mystery of this tragic chain of events, Essex discovers that Redstone had previously checked into the Hotel Electra, a gambling resort in another sector. Taking matters into his own hands, Essex visits the Hotel Electra and assumes Redstone's identity. Immediately after checking in, Essex is given an unexpected welcome by Grigor (Fernando Rey), who is the dealer in the casino downstairs. Insisting that he means no harm, Grigor invites Essex (who is going by the name of "Redstone") to the casino where gamblers are now heavily involved in a "Quintet" tournament. It is here that Essex first makes acquaintance with Ambrosia (Bibi Andersson), who always plays the "sixth man" in the game.
Essex is unaware that those who are taking part in the current Quintet tournament have been pitted against each other in a survival of the fittest. Those who are "killed" when playing the board game are to literally be slain in real life. Because Grigor and St. Christopher are aware that Essex is not the real Redstone, they ignore him and instead focus on the other victims in the tournament. First the clumsy Goldstar (David Langton) is killed, and then Deuca (Nina Van Pallandt), until the only two official players left in the game are St. Christopher and Ambrosia. Ambrosia, however, insists that because Essex has dared to assume Redstone's identity, he should be counted as a player in the game. Grigor agrees, and informs St. Christopher that he will not be allowed to face off against Ambrosia until he eliminates Essex first.
Essex and St. Christopher have a showdown out in the tundra where St. Christopher eventually meets his own demise- not by Essex, but by a falling avalanche. Essex then returns to Francha's apartment, wondering if Francha possessed the same list that Redstone had. Ambrosia follows Essex to the apartment in a presumably well-meaning manner, but then Essex slits her throat just before she is about to stab him with a hidden knife. Returning to the Hotel Electra to cremate Ambrosia's body, Essex confronts Grigor to demand what "prize" he has won, since he has come out on top as the winner of Quintet. Grigor reveals that there is no prize at all- except for the fact that Essex has survived the game all in one piece. Although Grigor insists that Essex must stay and participate in the tournaments to come, a disgusted Essex condemns the entire practice of Quintet and leaves the Hotel Electra for good. The film ends with another lengthy camera shot, this one showing Essex walking further out into the barren Northern distance until he can be seen no more.