J.J. Ford wants very much, just once, to beat Mr. Sam Westing "at his own game".
J.J. Ford is the only character who personally knew Sam Westing, and she has reason to believe that he was an evil man. J.J. thinks that with his intricate inheritance game, Westing is trying to manipulate the heirs in a way so that someone would get hurt. In her mind, the likely candidate for harm is his wife, who left him after their daughter's suicide. J.J. participates in the game because she wants to foil the maker's perceived intentions, and prevent damage from being done to anyone. Unlike the others, she is playing not for the money, but for the satisfaction of for once "outsmarting the master at his own game".
jj ford is not the killer turtle is