The monkey's paw itself is arguably the most important symbol in the story. It stands as a representation of ignorance, greed, and man's endless capacity for folly. Even though Sergeant-Major Morris goes out of his way to warn the Whites of the dangers of this magic talisman they subsequently ignore his wise words and treat the whole matter like it's some kind of joke. After retrieving the paw from the fire after Morris had thrown it there—and that should have been a clue that it was a dangerous item not to be messed around with—the Whites proceed to treat the monkey's paw as little more than a glorified toy, with truly devastating consequences.
The game of chess is also symbolic, representing as it does the danger of taking too many risks. As the story opens, Mr. White and his son Herbert are playing a game of chess by the fire. As a chess player Mr. White is renowned for making excessively risky moves. And on this particular occasion it lands him in trouble, placing his king in jeopardy. Mr. White's recklessness at the chess board foreshadows his recklessness in ignoring Sergeant-Major Morris' dire warnings and making a wish on the monkey's paw.