Plot

During 1962's Cuban missile crisis, a troubled math genius finds himself drafted to play in a U.S.-Soviet chess match -- and a deadly game of espionage.

Playing a major chess match in Warsaw against the Russian champion, brilliant but forgotten former US champion, and alcoholic, Josh Mansky is sucked into the world of espionage and conflict between the world's superpowers. As the military crisis escalates the chess match takes on unimaginable importance. The Americans are in danger of losing both games - the chess game and the one for world domination.—ron_whisky

Joshua Mansky (Bill Pullman) is a brilliant middle-aged mathematician, former champion chess player, and an alcoholic, who has reverted to hustling card games at the local bar. He is pulled into the world of espionage and conflict between the world's superpowers when, at the height of the Cold War, he is kidnapped by American secret services and forced to compete in a chess tournament against Soviet champion Alexander Gavrylov (Evgeniy Sidikhin) in the Polish capital Warsaw. Per tournament rules, Mansky is the only eligible substitute for the prior American contender, who is found dead by Soviet poisoning.

Donald Novak (Corey Johnson) is the head of Intelligence Ops in Poland. He reckons that since the US chess master was poisoned the Russians know about the US mission and that there is a mole in Washington who has relayed this info to them. His team are Agents White (James Bloor) and Agent Stone (Lotte Verbeek). The team wants to contact a man named John Gift and they need an excuse to be in Poland, which Mansky provides.

Manksy's American handlers reveal that his chess match is in fact a game within a game, set within the race between US and Soviet intelligence services to find and eliminate high level spies for the other side within their ranks at the tournament. This espionage is itself set within the larger context of the tactical naval and strategic nuclear maneuverings of a rapidly devolving Cuban Missile Crisis, with humanity itself palpably careening toward an imminent thermonuclear fate. Among the tournament attendees is a Soviet officer searching in vain for an opportunity to provide critical information to the Americans regarding Soviet capabilities and intentions in Cuba.

Palace of Culture and Science is headed by Director (Robert Wieckiewicz) and is going to be Mansky and his entourage's home for the next few days as he battles Gavrylov. The Director reports to General Krutov (Aleksey Serebryakov) (Russian Counterintelligence). Meanwhile back in the US as 20 Soviet ships with nuclear cargo move towards Cuba, the US Navy deploys an embargo over Cuba and mobilizes its armed forces on the East coast. A nuclear war is imminent.

Mansky's eccentric behavior and alcoholism is revealed to be partly due to his sheer brilliance, with alcohol slowing his brain function enough to operate more normally, as well as a crisis of conscience related to his prior assistance to Robert Oppenheimer and the Manhattan Project, which birthed the profoundly destructive power of nuclear weapons into human hands.

Variously drunk and sober, confident and paranoid, Mansky dramatically wins some chess match, yet loses others for naught (In one game the Soviets deployed a hypnotist to distract Mansky, which worked, and he lost). He distrusts his US handlers, yet befriends a Polish Communist (the Palace Director), who shares his personal experience of Soviet occupation of Poland and the Warsaw Pact as merely a continuation of the Nazi occupation of Poland. Mansky steals vodka whenever possible, sneaks in and out through the Warsaw sewers, and witnesses multiple sudden violent deaths of American (Agent White is killed in his arms while telling him that John Gift may approach him during the game with vital information) and Soviet tournament attendees, while trying to reconcile his human conscience with the demands of the concentric games in which he is bound.

Agent Stone & Novak tell Mansky that the Us don't know whether Soviets already have nukes in Cuba, while they stop the approaching convoy of Soviet ships and that's what John Gift is supposed to confirm to them. If Soviets already have nukes, the convoy won't stop and its nuclear war. If they don't have nukes, US will call Soviet bluff and the Soviets will have to back off.

John Gift contacts Mansky during the game when he is in the loo and hands him a microfilm, but soon afterwards John Gift and Agent Stone are mercilessly murdered by Soviet operative. Mansky draws the game and then uses the sewers to reach Novak at the US embassy. He reveals that the Soviet who killed Stone and John was himself John Gift and that Stone was the mole who was relaying US secrets to the Soviets. The new John Gift also hands over a microfilm to Mansky, who hands them both over to Novak (he escapes using the ID papers of the Director of the Palace, who has now become his close friend & voluntarily gives his papers to Mansky knowing fully that if Mansky is caught, the Director will be killed by Krutov).

Now Novak develops both films. The first one shows Soviets already have nukes in Cuba, the second one shows nukes are still on their way. Novak asks Mansky if the second person was the real John Gift or the first one. Mansky deploys the prisoner's dilemma algorithm to solve the riddle and concludes that the second man was the real John Gift. Now Mansky puts his own life on the line by re-entering the Palace and helping rescue the real John Gift from Krutov. To do this, Mansky has to forfeit the last chess game against Gavrylov and is later labeled a traitor by his own countrymen.

In the end, knights are sacrificed for bishops on the strategic global chessboard, yet Mansky's efforts help ensure the most crucial tournament victory: the survival of the human race through 1961. Shortly afterward, secret talks commence between the US and USSR, which ultimately result in mutual escalation reduction steps, nuclear arms control agreements such as the INF, and later US assistance with nuclear disarmament in the former Soviet states after the fall of the Berlin Wall.

However, the epilogue notes: "In February 2019, the United States suspended compliance with the INF treaty. The same day, Vladimir Putin announced that Russia also suspended the INF treaty and will develop new intermediate-range missiles."