The show opens in Merano, Italy where the World Chess Championships are being held. Frederick Trumper, the American champion arrives with Florence Vassy, his chess second and also his lover. At the press conference he is seen to be arrogant and temperamental, and in complete contrast to the quiet, reflective, yet determined challenger, Anatoly Sergievsky.
Preparations for the match commence and the politics surrounding the game become more apparent. During the first game, Freddie sensationally walks out. Florence and Molokov, the Head of the Russian delegation, arrange a secret meeting between the two champions, but when she tells Freddie of the meeting he accuses her of being fooled by the Russians. He reminds her that it was the Russians that had imprisoned her father in the 1956 uprising in Budapest.
Florence meets Anatoly and they fall in love. Freddie arrives to tell them he has negotiated higher fees and therefore the match can recommence. They continue, and Freddie, aware that he is losing both the match and Florence accuses her of engineering his defeat. She walks out and Freddie quits the Championships. Anatoly is declared the new world champion and sensationally defects to the west, joining Florence.
A year later, Anatoly defends his title in Bangkok with Freddie now reporting for American television. The Russians, determined to succeed for world chess supremacy plan to expose Anatoly to emotional pressure to facilitate a victory for their man, Viigand.
First they bring Anatoly's wife to Bangkok from Russia, then they offer Walter the return of various Americans, held by the Soviets, as well as Florence's father. In return, Walter is to arrange for Florence to persuade Anatoly to lose the Championship. Walter also arranges for an extremely hostile TV interview by Freddie. However, Anatoly refuses to give in.
Ultimately, Freddie's regard for chess rises above politics and love, and he tells Anatoly the strategy, which will secure victory. Anatoly explains to Florence that he had to win to be free, and she realises that he must go back to Russia.
As Florence watches Anatoly leave, she learns that her father is probably not even alive - the promise of his freedom was just a ploy to secure her co-operation.