Game Theory and Poe
Julie Rehmeyer of Science News writes in, “The Tell-Tale Anecdote: An Edgar Allan Poe story reveals a flaw in game theory” about a paper Kfir Elias and Ariel Rubenstein called, “Edgar Allan Poe’s Riddle:
Do Guessers Outperform Misleaders in a Repeated Matching Pennies Game?
The paper discusses a game that Poe describes in The Purloined Letter. In it, the Misleader selects a number of marbles, coins, or whatever (grab them in your hand), and the Guesser guesses if the number is even or odd. Poe opines that it’s a game of skill rather than luck. (Read the article for more detail, or even better, the primary source.)
If you look at it from a simple game-theoretic viewpoint, the Guesser and the Misleader have equal odds. They might as well be flipping coins. However, there is a sense in which it’s a game of skill.
Our intrepid mathematicians showed that in their construction of the game, the guesser has a slight advantage — 3% — which is enough to get Las Vegas interested. They also examined modifications of the game and after several modifications brought it back in line with the predictions of game theory.
This brings up a number of interesting things to think about, including that Poe was on to something ahead of his time, as usual. Funny how that wisdom was hiding in plain sight. I wonder if he planned it.
Interestingly, the story by Poe also illustrates a topic about which you wrote a little over a year ago. That is the apparent effectiveness in most cases of hiding in plain sight.
There’s nothing new here. The winning strategy is being random, and humans suck at that. It’s been the same for e.g. rock-paper-scissors, there’s nothing new for game theory here as far as I understand.