Rex Allerton, a British film star in Hollywood, is haunted and hunted in real life and dreams by his importunate fans. In an effort to escape them he retreats to the Italian lakeside town of Tremaggio. There he is persuaded by the International Syndicate of Computation - a peculiar organization which interests itself in the world's gambling, from Wall Street to Newmarket - to put into effect a joking suggestion that he should offer himself as first prize in a lottery.