It was D— with the letter in the boudoir; and then it's Dupin with the letter in the apartment. See? "The Purloined Letter" is just like a game of Clue, only without the murder.
Okay, so it was published almost exactly 100 years before Clue, but you see the point. There are allusions to games all over the story, as well as at least two descriptions of specific games. The first is the game of "even and odd" (109). As Dupin says, one player holds marbles in his/her hand. The other player guesses whether there are an odd or even number of marbles in their opponent's hand. Winning the game depends on (1) guessing correctly, and (2) getting your partner to incorrectly guess what you're going to guess.
Dupin apparently once knew an eight year old schoolboy who was a master of even and odd. When Dupin asked him the secret of his success, he said that when he wanted "to find out how wise, or how stupid, or how good, or how wicked is anyone, or what are his thoughts at the moment," he mimicked the person's facial expression "as accurately as possible" and then waited to see what feeling he got in his "mind or heart" (96).
Wow, that's a mouthful from an eight-year-old. As Dupin long-windedly explains, to guess correctly, the boy has to compare his intelligence with his opponent's. He does that by imitating his opponent's face—which might be a great way to develop some empathy, but here is just out of love of the game.
The second game isn't named. Dupin says "There is a game of puzzles […] which is played upon a map" (109). Dupin's description is confusing and long-winded, but the game is pretty simple. One player picks a name from the map—the name of a city, or a river, or what have you. Dupin says that unskilled players will choose names that are shown on the map in very small print, figuring that those will be hardest to find. More experienced players will choose large-print names, because people are more likely to miss things that are "excessively obvious" (109). This, he claims, is why G— couldn't find the letter—because its hiding place was too obvious.
The point is, these games are symbols both of Dupin's methods of detection, and also of a particular attitude toward the world—one that both Dupin and D— seem to hold. In their view, life is a game, but not one of those self-esteem building ones where everyone wins. Nope. This is a deadly serious game of wits.