Sheila Green (Yvonne Romain) is killed in a hit-and-run car accident while walking home from a party one night. A year later, her multi-millionaire husband, Clinton (James Coburn), invites a group of friends (James Mason, Raquel Welch, Dyan Cannon, Richard Benjamin, Joan Hackett, and Ian McShane) to spend a week with him on his yacht. Clinton loves to play elaborate games and he assigns everyone a secret - one is an alcoholic, another an informer and so on - that they are not to share with anyone. Every day for the next six days, they will call into a port where they will be given clues to discover one person's secret. The game takes a deadly twist when a murder tales place and it all has to do with the game they have been playing and the secrets that Clinton assigned at the outset.