When we first meet Herbert and his father, they are playing chess. Mr. White makes a reckless move. Herbert and Mrs. White instantly catch the mistake, and Herbert wins the game.
Chess is a game of strategy that depends on a person's ability to anticipate a series of moves ahead of time. The chess game here might be symbolic of Herbert's carefulness and Mr. White's recklessness. Mr. White's recklessness in buying and wishing on the cursed monkey's paw causes plenty of trouble for his family, but unfortunately, Herbert's carefulness doesn't save him. Mr. White seems to have learned his lesson, though. By the end of the story, he's unwilling to take the risk of meeting up with his undead son.