Milton Parker (Vincent Price), an eccentric game inventor, playwright and poet, packs his bags for his leave to Venice, Italy and writes invitations to everybody he knows. At his anniversary, Parker's greedy and estranged relatives and all of his friends show up at the harbour.
The twenty teams consist of:
- Parker's son-in law Henry Motley (Tony Randall), Parker's daughter and Henry's wife, Dorothy (Imogene Coca) and their 4 ill-behaved children.
- Parker's godson, Melvin Saletta (Gene Wilder)
- Melville Crump (Sid Caesar) and his wife, Monica (Edie Adams)