The Four-Card Problem

The “four-card problem” is a logic puzzle that tests how well a player grasps an “if-then” relationship in a certain context. Suppose I proposed a theory about the four cards above: “If a card has an odd number on one side, it will have Alice on the other side.” Which cards should you turn over to test the theory?

This type of puzzle was invented by the psychologist Peter Wason in the 1960s. It’s sometimes called a Wason selection task. Wason’s task proved more difficult that you’d think. 75% of the people he tested got it wrong or only partly right.

Four Cards, Two Answers

If you chose “1” when looking at the cards above, you’re partly right. Many people choose “1” alone, while others choose both “1” and “Alice.” But the correct answer is “1” and the “White Rabbit.” The “White Rabbit” needs to be checked because if the other side is “1,” the card disproves our whole theory. But the “Alice” card doesn’t need to be checked at all. Our theory doesn’t prevent even-numbered cards from having Alice on the back. So if we flip over the Alice card and see “2,” we’ve disproved nothing.

Our Deeper Biases

People often choose “Alice” in the task above. Why? It’s probably due to a deep psychological tendency known as confirmation bias. When testing theories, we often look for confirmation rather than disproof. By flipping over “Alice,” we seek to confirm that an odd number is there, even though our theory allows odd numbers too. By flipping over the “White Rabbit,” however, we seek disproof. We learn far more from an even number there than we do from the back of “Alice.”

The “4” card, of course, is irrelevant either way. Our theory doesn’t say that even-numbered cards will have the White Rabbit. It also doesn’t say that they won’t have Alice. So there’s no need to flip an even number over.

Logic in Wonderland

I often use themes from Alice in Wonderland when teaching logic. For young adults who enjoy this type of problem, I run a pair of logic classes that include puzzles like the one above. To see what’s available, check out my current course schedule.